Solving coin problems: Difference between revisions
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=={{header|Go}}==
This relatively simple program can only solve problems with 2 types of coins (or other objects) or 3 types of coins (but not other objects) without the need for an equation solver. However, it is able to solve all 28 problems of these types which were originally listed in the Perl entry before it was restricted to the subset of those problems (24) involving coins and bills.
<
import (
"fmt"
"math"
"regexp"
"sort"
Line 143 ⟶ 144:
// Checks if the problem involves 3 coins and
// also returns their names and the
func hasThreeCoins(q string) ([]string, []string, bool) {
q = strings.ReplaceAll(q, ".", "")
q = strings.ReplaceAll(q, ",", "")
Line 155 ⟶ 156:
}
if len(coinMap) != 3 {
return nil,
}
maxNum
var maxNames []string
var names []string
for k, v := range coinMap {
names = append(names, k)
if v > maxNum {
maxNum
maxNames = maxNames[:0]
maxNames = append(maxNames, k)
} else if v == maxNum {
maxNames = append(maxNames, k)
}
}
return names,
}
// Processes a problem which involves 3 coins.
func threeCoins(p, q string, names, maxNames []
var relations []relation
am := rx4.FindAllStringSubmatch(q, -1)
Line 205 ⟶ 211:
printAnswers(p, kinds)
} else {
res := getValues(q)
if
}
}
}
var v1, v2, v3 string
var n1, n2, n3 int
if le == 2 {
coins[relations[1].variable1]*relations[1].constant1 + coins[maxName]
tv -= coins[relations[0].variable1]*relations[0].constant2 +
coins[relations[1].variable1]*relations[1].constant2
v1, v2, v3 = maxName, relations[0].variable1, relations[1].variable1
n1 = int(tv/tmc + 0.5)
n2 = int(relations[0].constant1*float64(n1) + relations[0].constant2 + 0.5)
n3 = int(relations[1].constant1*float64(n1) + relations[1].constant2 + 0.5)
} else {
res2 := getNumbers(q)
tn := float64(res2[len(res2)-1])
v1, v2 = relations[0].variable1, relations[0].variable2
for _, name := range names {
if name != v1 && name != v2 {
v3 = name
break
}
}
mult1, mult2, mult3 := coins[v1], coins[v2], coins[v3]
n2 = int(((tn-relations[0].constant2)*mult3-tv+relations[0].constant2*mult1)/
((relations[0].constant1+1)*mult3-relations[0].constant1*mult1-mult2) + 0.5)
n1 = int(float64(n2)*relations[0].constant1 + relations[0].constant2 + 0.5)
n3 = int(tn) - n1 - n2
}
calcValue := float64(n1)*coins[v1] + float64(n2)*coins[v2] + float64(n3)*coins[v3]
if math.Abs(totalValue-calcValue) <= 1e-14 {
kinds := []kind{kind{v1, 0, n1}, kind{v2, 0, n2}, kind{v3, 0, n3}}
printAnswers(p, kinds)
return
}
}
errorMsg(p)
}
return
Line 320 ⟶ 334:
q = strings.ReplaceAll(q, " bill", "")
// check if there are 3 coins involved
if names,
threeCoins(p, q, names,
continue
}
Line 414 ⟶ 428:
printAnswers(p, kinds)
}
}</
{{out}}
Line 501 ⟶ 515:
A person has 12 coins consisting of dimes and pennies. If the total amount of money is $0.30, how many of each coin are there?
ANSWER: 2 dimes, 10 pennies
</pre>
=={{header|Julia}}==
Uses the JuMP optimization library as a solver. The examples are from the Go code, and a few regex are from the Perl code.
<syntaxhighlight lang="julia">using JuMP, GLPK
const nums = Dict(
"zero" => 0, "one" => 1, "two" => 2, "three" => 3,
"four" => 4, "five" => 5, "six" => 6, "seven" => 7,
"eight" => 8, "nine" => 9, "ten" => 10, "eleven" => 11,
"twelve" => 12, "thirteen" => 13, "fourteen" => 14, "fifteen" => 15,
"sixteen" => 16, "seventeen" => 17, "eighteen" => 18, "nineteen" => 19,
"twenty" => 20,
)
function coinproblemsolver(text, maxitems=4, verbose=false)
coin_problem = Model(GLPK.Optimizer)
for line in strip.(split(text, r"\n\n"))
# save original version
oldline = deepcopy(line)
# ignore short or commented lines
length(line) < 5 && continue
line[1] == '#' && continue
# create the data structures and registration function
monies = Dict(
"dollar_coin" => 100, "half_dollar" => 50, "quarter" => 25, "dime" => 10,
"nickel" => 5, "penny" => 1,
)
foreach(d -> (monies["_" * "$d" * "_bill"] = 100 * d), [1, 2, 5, 10, 20, 50, 100, 500, 1000])
itemnames = String[]
itemvalues = Int[]
function register_variables(vars)
indices = Int[]
for cap in vars
idx = findfirst(x -> cap == x, itemnames)
if !(idx isa Nothing)
push!(indices, idx)
else
push!(itemnames, cap)
push!(indices, length(itemnames))
push!(itemvalues, get(monies, cap, 0))
end
end
return indices
end
# set up the optimizer / problem solver
@variables(coin_problem, begin x[1:maxitems] >= 0 end)
# Simplify sentence and standardize quantities
# convert hyphens to spaces, lowercase, newlines to spaces
line = replace(replace(lowercase(line), "-" => " "), "\n" => " ")
# fractions/multipliers to parsable forms
line = replace(line, r"half.dollars?" => "half_dollar")
line = replace(line, r"\bone\s+half\b" => "0.5")
line = replace(line, r"\btwice\b" => "two times")
# convert spelled out number to integer text per nums dictionary
for p in nums
line = replace(line, Regex("\\b" * p[1] * "\\b") => string(p[2]))
end
# remove plurals of coinage
line = replace(line, r"(quarter|dime|nickel|dollar|coin|bill)s" => s"\1")
line = replace(line, "pennies" => "penny")
# change numerals to quantites and monies
line = replace(line, r"dollar coin|all dollar" => "dollar_coin")
line = replace(line, r"\$(\d+) bill" => s"_\1_bill")
line = replace(line, r"(\d+) dollar bill" => s"_\1_bill")
line = replace(line, r"((?:\d+\s+)+\d+)" => (s) -> mapreduce(x -> parse(Int, x), +, split(s))) # 20 6 -> 26
# remove most unparsed words
line = replace(line, r"\b(the|a|to|of|i|is|that|it|on|you|this|for|but|with|are|have|be|at|or|was|so|if|out|not|he|she|they|has|do|did|does)\b" => "")
# simplify spacing
line = replace(line, r"\s+" => " ")
# Add variables and constraints to the problem
for m in eachmatch(r"([\d\.]+) (?:times )?as many (\w+) as (\w+)", line)
indices = register_variables([m[2], m[3]])
@constraints(coin_problem, begin x[indices[1]] == x[indices[2]] * parse(Float64, m[1]) end)
end
for m in eachmatch(r"(\d+) more (\w+) than (\w+)", line)
indices = register_variables([m[2], m[3]])
@constraints(coin_problem, begin x[indices[1]] == x[indices[2]] + parse(Int, m[1]) end)
end
for m in eachmatch(r"(\d+) less (\w+) than (\w+)", line)
indices = register_variables([m[2], m[3]])
@constraints(coin_problem, begin x[indices[1]] == x[indices[2]] - parse(Int, m[1]) end)
end
if (m = match(r"same number (\w+), (\w+),? and (\w+)", line)) != nothing
indices = register_variables(m.captures)
@constraints(coin_problem, begin
x[indices[1]] == x[indices[2]]
x[indices[2]] == x[indices[3]]
end)
end
if (m = match(r"(\d+) (?:\w+ )?(\w+),? consist\D+\$([\d\.]+)\D+\$([\d\.]+)", line)) != nothing
n1, n2 = Int(round(100 * parse(Float64, m[3]))), Int(round(100 * parse(Float64, m[4])))
s1, s2 = m[2] * "_costing_" * string(n1), m[2] * "_costing_" * string(n2)
monies[s1], monies[s2] = n1, n2
indices = register_variables([s1, s2])
@constraints(coin_problem, begin sum(x) == parse(Int, m[1]) end)
end
if (m = match(r"(\d+) (?:\w+ )?(\w+),? consist\D+([\d\.]+)¢\D+([\d\.]+)¢", line)) != nothing
n1, n2 = parse(Int, m[3]), parse(Int, m[4])
s1, s2 = m[2] * "_costing_" * string(n1), m[2] * "_costing_" * string(n2)
monies[s1], monies[s2] = n1, n2
indices = register_variables([s1, s2])
@constraints(coin_problem, begin sum(x) == parse(Int, m[1]) end)
end
if (m = match(r"(\d+) (?:coin|bill),? consist(?:s|ing) (\w+) and (\w+)", line)) != nothing
indices = register_variables([m[2], m[3]])
@constraints(coin_problem, begin sum(x) == parse(Int, m[1]) end)
end
if (m = match(r"(\d+) (?:coin)[^\d\.,]+pocket (\w+) and (\w+)", line)) != nothing
indices = register_variables([m[2], m[3]])
@constraints(coin_problem, begin sum(x) == parse(Int, m[1]) end)
end
if (m = match(r"(\d+) (?:coin|bill),? consist(?:s|ing) (\w+), (\w+), and (\w+)", line)) != nothing
indices = register_variables([m[2], m[3], m[4]])
@constraints(coin_problem, begin sum(x) == parse(Int, m[1]) end)
end
if (m = match(r"\$([\d\.]+) ream\D+\$([\d\.]+)\D+(\d+) reams", line)) != nothing
n1, n2 = Int(round(100 * parse(Float64, m[1]))), Int(round(100 * parse(Float64, m[2])))
s1, s2 = "ream_costing_" * string(n1), "ream_costing_" * string(n2)
monies[s1], monies[s2] = n1, n2
indices = register_variables([s1, s2])
@constraints(coin_problem, begin sum(x) == parse(Int, m[3]) end)
end
if (m = match(r"(?:in my wallet,?|only accepts) (\w+), (\w+),? and (\w+)", line)) != nothing
indices = register_variables([m.captures[1], m.captures[2], m.captures[3]])
end
if (m = match(r"(\d+) coin in (\w+) and (\w+) only", line)) != nothing
indices = register_variables([m.captures[2], m.captures[3]])
@constraints(coin_problem, begin sum(x) == parse(Int, m[1]) end)
end
if (m = match(r"(\d+) coin (?:total|in all)", line)) != nothing
@constraints(coin_problem, begin sum(x) == parse(Int, m[1]) end)
end
if (m = match(r"(?:had only|in) (\w+) and (\w+)[,\.\?]", line)) != nothing
indices = register_variables([m.captures[1], m.captures[2]])
end
if (m = match(r"(?:sold total|all together,? there) (\d+)", line)) != nothing
@constraints(coin_problem, begin sum(x) == parse(Int, m[1]) end)
end
for m in eachmatch(r"cost \$([\d\.]+) each", line)
s = "item_costing_" * m.captures[1]
monies[s] = Int(round(100 * parse(Float64, m.captures[1])))
register_variables([s])
end
# find a total
m = match(r"add up \$?([\d\.]+)", line)
if m isa Nothing
m = match(r"(?:cost stamps|total cost|paid|value|valuing|store made)[^\$]+\$([\d\.]+)", line)
end
if m isa Nothing
m = match(r"(?:total|value of|store made|given)[^\$]+\$([\d\.]+)", line)
end
if m isa Nothing
m = match(r"\$([\d\.]+) (?:coin )?in", line)
end
if !(m isa Nothing)
m1 = m.captures[1][end] == '.' ? m.captures[1][1:end-1] : m.captures[1]
@constraints(coin_problem, begin
sum([itemvalues[i] * x[i] for i in 1:length(itemnames)]) == Int(round(100 * parse(Float64, m1)))
end)
else
m = match(r"total (?:amount coin )([\d\.]+)¢", line)
if !(m isa Nothing)
@constraints(coin_problem, begin
sum([itemvalues[i] * x[i] for i in 1:length(itemnames)]) == parse(Int, m[1])
end)
else
error("Missing or unparsed total funds constraint")
end
end
# set unused x components to 0
for i in length(itemnames)+1:maxitems
@constraints(coin_problem, begin x[i] == 0 end)
end
# solve
optimize!(coin_problem)
verbose && println(line)
verbose && println(coin_problem)
print(oldline, "\nAnswer: ")
for i in eachindex(itemnames)
print(rpad(itemnames[i] * "(s)", 10), ": ", rpad(Int(round(JuMP.value(x[i]))), 10))
end
println("\n")
JuMP.empty!(coin_problem)
end
end
const DATA = raw"""
If a person has three times as many quarters as dimes and the total amount of money is $5.95,
find the number of quarters and dimes.
A pile of 18 coins consists of pennies and nickels. If the total amount of the coins is 38¢,
find the number of pennies and nickels.
A small child has 6 more quarters than nickels. If the total amount of coins is $3.00,
find the number of nickels and quarters the child has.
A child's bank contains 32 coins consisting of nickels and quarters. If the total amount of
money is $3.80, find the number of nickels and quarters in the bank.
A person has twice as many dimes as she has pennies and three more nickels than pennies. If
the total amount of the coins is $1.97, find the numbers of each type of coin the person has.
In a bank, there are three times as many quarters as half dollars and 6 more dimes than
half dollars. If the total amount of the money in the bank is $4.65, find the number of
each type of coin in the bank.
A person bought 12 stamps consisting of 37¢ stamps and 23¢ stamps. If the cost of the stamps
is $3.74, find the number of each type of the stamps purchased.
A dairy store sold a total of 80 ice cream sandwiches and ice cream bars. If the sandwiches
cost $0.69 each and the bars cost $0.75 each and the store made $58.08, find the number
of each sold.
An office supply store sells college-ruled notebook paper for $1.59 a ream and wide-ruled
notebook paper for $2.29 a ream. If a student purchased 9 reams of notebook paper and
paid $15.71, how many reams of each type of paper did the student purchase?
A clerk is given $75 in bills to put in a cash drawer at the start of a workday. There are
twice as many $1 bills as $5 bills and one less $10 bill than $5 bills. How many of each
type of bill are there?
A person has 8 coins consisting of quarters and dimes. If the total amount of this change
is $1.25, how many of each kind of coin are there?
A person has 3 times as many dimes as he has nickels and 5 more pennies than nickels. If the
total amount of these coins is $1.13, how many of each kind of coin does he have?
A person bought ten greeting cards consisting of birthday cards costing $1.50 each and
anniversary cards costing $2.00 each. If the total cost of the cards was $17.00, find the
number of each kind of card the person bought.
A person has 9 more dimes than nickels. If the total amount of money is $1.20, find the
number of dimes the person has.
A person has 20 bills consisting of $1 bills and $2 bills. If the total amount of money
the person has is $35, find the number of $2 bills the person has.
A bank contains 8 more pennies than nickels and 3 more dimes than nickels. If the total
amount of money in the bank is $3.10, find the number of dimes in the bank.
Your uncle walks in, jingling the coins in his pocket. He grins at you and tells you that you
can have all the coins if you can figure out how many of each kind of coin he is carrying.
You're not too interested until he tells you that he's been collecting those gold-tone
one-dollar coins. The twenty-six coins in his pocket are all dollars and quarters, and they
add up to seventeen dollars in value. How many of each coin does he have?
A collection of 33 coins, consisting of nickels, dimes, and quarters, has a value of $3.30.
If there are three times as many nickels as quarters, and one-half as many dimes as nickels,
how many coins of each kind are there?
A wallet contains the same number of pennies, nickels, and dimes. The coins total $1.44. How
many of each type of coin does the wallet contain?
Suppose Ken has 25 coins in nickels and dimes only and has a total of $1.65. How many of
each coin does he have?
Terry has 2 more quarters than dimes and has a total of $6.80. The number of quarters and dimes
is 38. How many quarters and dimes does Terry have?
In my wallet, I have one-dollar bills, five-dollar bills, and ten-dollar bills. The total
amount in my wallet is $43. I have four times as many one-dollar bills as ten-dollar bills.
All together, there are 13 bills in my wallet. How many of each bill do I have?
Marsha has three times as many one-dollar bills as she does five dollar bills. She has a
total of $32. How many of each bill does she have?
A vending machine has $41.25 in it. There are 255 coins total and the machine only accepts
nickels, dimes and quarters. There are twice as many dimes as nickels. How many of each coin
are in the machine?
Michael had 27 coins in all, valuing $4.50. If he had only quarters and dimes, how many coins
of each kind did he have?
Lucille had $13.25 in nickels and quarters. If she had 165 coins in all, how many of each
type of coin did she have?
Ben has $45.25 in quarters and dimes. If he has 29 less quarters than dimes, how many of each
type of coin does he have?
A person has 12 coins consisting of dimes and pennies. If the total amount of money is $0.30,
how many of each coin are there?
"""
coinproblemsolver(DATA)
</syntaxhighlight>{{out}}
<pre>
If a person has three times as many quarters as dimes and the total amount of money is $5.95,
find the number of quarters and dimes.
Answer: quarter(s): 21 dime(s) : 7
A pile of 18 coins consists of pennies and nickels. If the total amount of the coins is 38¢,
find the number of pennies and nickels.
Answer: penny(s) : 13 nickel(s) : 5
A small child has 6 more quarters than nickels. If the total amount of coins is $3.00,
find the number of nickels and quarters the child has.
Answer: quarter(s): 11 nickel(s) : 5
A child's bank contains 32 coins consisting of nickels and quarters. If the total amount of
money is $3.80, find the number of nickels and quarters in the bank.
Answer: nickel(s) : 21 quarter(s): 11
A person has twice as many dimes as she has pennies and three more nickels than pennies. If
the total amount of the coins is $1.97, find the numbers of each type of coin the person has.
Answer: dime(s) : 14 penny(s) : 7 nickel(s) : 10
In a bank, there are three times as many quarters as half dollars and 6 more dimes than
half dollars. If the total amount of the money in the bank is $4.65, find the number of
each type of coin in the bank.
Answer: quarter(s): 9 half_dollar(s): 3 dime(s) : 9
A person bought 12 stamps consisting of 37¢ stamps and 23¢ stamps. If the cost of the stamps
is $3.74, find the number of each type of the stamps purchased.
Answer: stamps_costing_37(s): 7 stamps_costing_23(s): 5
A dairy store sold a total of 80 ice cream sandwiches and ice cream bars. If the sandwiches
cost $0.69 each and the bars cost $0.75 each and the store made $58.08, find the number
of each sold.
Answer: item_costing_0.69(s): 32 item_costing_0.75(s): 48
An office supply store sells college-ruled notebook paper for $1.59 a ream and wide-ruled
notebook paper for $2.29 a ream. If a student purchased 9 reams of notebook paper and
paid $15.71, how many reams of each type of paper did the student purchase?
Answer: ream_costing_159(s): 7 ream_costing_229(s): 2
A clerk is given $75 in bills to put in a cash drawer at the start of a workday. There are
twice as many $1 bills as $5 bills and one less $10 bill than $5 bills. How many of each
type of bill are there?
Answer: _1_bill(s): 10 _5_bill(s): 5 _10_bill(s): 4
A person has 8 coins consisting of quarters and dimes. If the total amount of this change
is $1.25, how many of each kind of coin are there?
Answer: quarter(s): 3 dime(s) : 5
A person has 3 times as many dimes as he has nickels and 5 more pennies than nickels. If the
total amount of these coins is $1.13, how many of each kind of coin does he have?
Answer: dime(s) : 9 nickel(s) : 3 penny(s) : 8
A person bought ten greeting cards consisting of birthday cards costing $1.50 each and
anniversary cards costing $2.00 each. If the total cost of the cards was $17.00, find the
number of each kind of card the person bought.
Answer: cards_costing_150(s): 6 cards_costing_200(s): 4
A person has 9 more dimes than nickels. If the total amount of money is $1.20, find the
number of dimes the person has.
Answer: dime(s) : 11 nickel(s) : 2
A person has 20 bills consisting of $1 bills and $2 bills. If the total amount of money
the person has is $35, find the number of $2 bills the person has.
Answer: _1_bill(s): 5 _2_bill(s): 15
A bank contains 8 more pennies than nickels and 3 more dimes than nickels. If the total
amount of money in the bank is $3.10, find the number of dimes in the bank.
Answer: penny(s) : 25 nickel(s) : 17 dime(s) : 20
Your uncle walks in, jingling the coins in his pocket. He grins at you and tells you that you
can have all the coins if you can figure out how many of each kind of coin he is carrying.
You're not too interested until he tells you that he's been collecting those gold-tone
one-dollar coins. The twenty-six coins in his pocket are all dollars and quarters, and they
add up to seventeen dollars in value. How many of each coin does he have?
Answer: dollar_coin(s): 14 quarter(s): 12
A collection of 33 coins, consisting of nickels, dimes, and quarters, has a value of $3.30.
If there are three times as many nickels as quarters, and one-half as many dimes as nickels,
how many coins of each kind are there?
Answer: nickel(s) : 18 quarter(s): 6 dime(s) : 9
A wallet contains the same number of pennies, nickels, and dimes. The coins total $1.44. How
many of each type of coin does the wallet contain?
Answer: penny(s) : 9 nickel(s) : 9 dime(s) : 9
Suppose Ken has 25 coins in nickels and dimes only and has a total of $1.65. How many of
each coin does he have?
Answer: nickel(s) : 17 dime(s) : 8
Terry has 2 more quarters than dimes and has a total of $6.80. The number of quarters and dimes
is 38. How many quarters and dimes does Terry have?
Answer: quarter(s): 20 dime(s) : 18
In my wallet, I have one-dollar bills, five-dollar bills, and ten-dollar bills. The total
amount in my wallet is $43. I have four times as many one-dollar bills as ten-dollar bills.
All together, there are 13 bills in my wallet. How many of each bill do I have?
Answer: _1_bill(s): 8 _10_bill(s): 2 _5_bill(s): 3
Marsha has three times as many one-dollar bills as she does five dollar bills. She has a
total of $32. How many of each bill does she have?
Answer: _1_bill(s): 12 _5_bill(s): 4
A vending machine has $41.25 in it. There are 255 coins total and the machine only accepts
nickels, dimes and quarters. There are twice as many dimes as nickels. How many of each coin
are in the machine?
Answer: dime(s) : 90 nickel(s) : 45 quarter(s): 120
Michael had 27 coins in all, valuing $4.50. If he had only quarters and dimes, how many coins
of each kind did he have?
Answer: quarter(s): 12 dime(s) : 15
Lucille had $13.25 in nickels and quarters. If she had 165 coins in all, how many of each
type of coin did she have?
Answer: nickel(s) : 140 quarter(s): 25
Ben has $45.25 in quarters and dimes. If he has 29 less quarters than dimes, how many of each
type of coin does he have?
Answer: quarter(s): 121 dime(s) : 150
A person has 12 coins consisting of dimes and pennies. If the total amount of money is $0.30,
how many of each coin are there?
Answer: dime(s) : 2 penny(s) : 10
</pre>
=={{header|Perl}}==
Coin-type 'word problems' are analyzed into their constituent algebraic relationships, in a format suitable for processing by MAXIMA, a free computer algebra system. NB: MAXIMA <b>must</b> be locally installed for this task to function.
<
use warnings;
use List::Util qw(sum uniq);
use File::Temp qw(tempfile);
my %nums = (
Line 519 ⟶ 964:
);
my $decimal = qr/(?:[1-9][0-9]*\.?[0-9]*)|(?:0?\.[0-9]+)/;
while (<DATA>) {
chomp;
next if /^\s*$/ or /^\s*#.*$/; # skip blank and comment lines
my($count, $total) = (0, 0);
our @words = our @eqns = our @vars = our @types = ();
sub add_type {
push @vars, "v_$type: $value";
push @types, $type;
}
# Step 1: standardize language
s/-/ /g; # convert hyphens to spaces
$_ = lc($_); # convert to lower case
# tokenize sentence boundaries, punctuation, symbols
s/([\
s/([\.\?\!])$/ $1\n/g;
s/\$(.)/\$ $1/g; # prefix
s/(.)([\;\:\%',¢])/$1 $2/g; # suffix
# fractions/multipliers
s/half.dollars?/half_dollar/g;
s/\b(one )?half\b/0.5/g;
s/\btwice\b/two times/g;
# convert English number-names to numbers
foreach my $key (keys %nums) { s/\b$key\b/$nums{$key}/eg }
# remove plurals
s/
s/
# misc
s/dollar coin/dollar_coin/g;
s/(\d+) dollar\b/\$ $1/g;
s/((?:\d+ )*\d+)/sum(split(' ',$1))/eg;
# remove non-essential words
s/\b(the|a|to|of|i|is|that|it|on|you|this|for|but|with|are|have|be|at|or|was|so|if|out|not|he|she|they|has|do|did|does)\b\s*//g;
# Step 2: assign numeric values to terms
add_type('dollar_coin',100) if /dollar_coin/;
add_type('half_dollar',50) if /half_dollar/;
add_type('quarter',25) if /quarter/;
add_type('dime',10) if /dime/;
add_type('nickel',5) if /nickel/;
add_type('penny',1) if /penny/;
add_type($1, 100 * $1) while /\$ (\d+) bill/g;
# Step 3: determine algebraic relationships
while (/(
while (/($decimal) (?:times )?as many (\w+) as (\w+)/g) { push @eqns, "n_$2 = n_$3
while (/(\d+) more (\w+) than (\w+)/g) { push @eqns, "n_$2 = n_$3 + $1" }
while (/(\d+) less (\w+) than (\w+)/g) { push @eqns, "n_$2 = n_$3 - $1" }
while (/(\d+) less \$ (\d+) bill than \$ (\d+) bill/g) { push @eqns, "n_$2 = n_$3 - $1" }
if (/same number (\w+) , (\w+) (?:, )?and (\w+)/) {
push @eqns, "n_$1 = n_$2";
push @eqns, "n_$2 = n_$3";
}
if (/(\d+) (?:\w+ )*
$count = $1; push @vars, "count: $count"
}
if (/total (?:\w+ )*\$ ($decimal)/ or /valu(?:e|ing) \$ ($
$total = 100 * $1;
push @vars, "total: $total";
}
if (/total (?:\w+ )*
$total = $1;
push @vars, "total: $total";
}
# Step 4: tally final total value, coin count
# sum total, dot product of values and quantities
my $dot_product = join(' + ', map {"n_$_ * v_$_"} uniq @types);
# count of all coins, sum of counts of each coin type
# Step 5: prepare batch file for external processing, run 'MAXIMA', output results
printf "problem: %s\n", s/\n/ /gr; # condensed problem statement
my $maxima_vars = join("\$\n", uniq @vars);
my $
my $maxima_find = '['. join(', ', map {"n_$_"} @types) . ']';
if (@eqns and @vars) {
my ($fh, $maxima_script) = tempfile(UNLINK => 1);
open $fh, '>', $maxima_script or die "Couldn't open temporary file: $!\n";
print $fh <<~"END";
$maxima_vars\$
solve($maxima_eqns, $maxima_find);
END
close $fh;
open my $maxima_output, "/opt/local/bin/maxima -q -b $maxima_script |" or die "Couldn't open maxima: $!\n";
while (<$maxima_output>) {
print "solution: $1\n" if /\(\%o\d+\)\s+\[\[([^\]]+)\]\]/; # only display solution
}
close $maxima_output;
} else {
print "Couldn't deduce enough information to formulate equations.\n"
}
print
}
Line 711 ⟶ 1,093:
A small child has 6 more quarters than nickels. If the total amount of coins is $3.00, find the number of nickels and quarters the child has.
A
A person has twice as many dimes as she has pennies and three more nickels than pennies. If the total amount of the coins is $1.97, find the numbers of each type of coin the person has.
Line 751 ⟶ 1,133:
Ben has $45.25 in quarters and dimes. If he has 29 less quarters than dimes, how many of each type of coin does he have?
A person has 12 coins consisting of dimes and pennies. If the total amount of money is $0.30, how many of each coin are there?</
{{out}}
<pre>problem: person 3 times as many quarter as dime and total amount money $ 5.95 , find number quarter and dime .
Line 762 ⟶ 1,144:
solution: n_quarter = 11, n_nickel = 5
problem:
solution: n_quarter = 11, n_nickel = 21
Line 832 ⟶ 1,214:
though all examples below are for 2 and 3 only. A couple (14 and 17) also sail perilously close to getting a divide by zero.
This task was quite a bit of fun, once I got stuck in.
<!--<syntaxhighlight lang="phix">(phixonline)-->
<span style="color: #000080;font-style:italic;">-- demo\rosetta\Solving_coin_problems.exw</span>
<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span>
<span style="color: #008080;">constant</span> <span style="color: #000000;">source</span> <span style="color: #0000FF;">=</span> <span style="color: #008000;">"""
--==
A
--==
A small child
--==
A
--==
--==
--==
A
--==
A person has
--==
A person has
--==
A person has
--==
A
--==
A bank contains 8 more pennies than nickels and 3 more dimes than nickels. If the total amount of money in the bank is $3.10, find the number of dimes in the bank.
--==
Your uncle walks in, jingling the coins in his pocket. He grins at you and tells you that you can have all the coins if you can figure out how many of each kind of coin he is carrying. You're not too interested until he tells you that he's been collecting those gold-tone one-dollar coins. The twenty-six coins in his pocket are all dollars and quarters, and they add up to seventeen dollars in value. How many of each coin does he have?
--==
A collection of 33 coins, consisting of nickels, dimes, and quarters, has a value of $3.30. If there are three times as many nickels as quarters, and one-half as many dimes as nickels, how many coins of each kind are there?
--==
--==
--==
Terry has 2 more quarters than dimes and has a total of $6.80. The number of quarters and dimes is 38. How many quarters and dimes does Terry have?
--==
--==
--==
--==
--==
--==
--==
A person has 12 coins consisting of dimes and pennies. If the total amount of money is $0.30, how many of each coin are there?
--==>expected:dimes = 2, pennies = 10"""</span><span style="color: #0000FF;">,</span>
<span style="color: #0000FF;">{</span><span style="color: #000000;">texts</span><span style="color: #0000FF;">,</span><span style="color: #000000;">replacements</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">columnize</span><span style="color: #0000FF;">({{</span><span style="color: #008000;">"."</span><span style="color: #0000FF;">,</span><span style="color: #008000;">" ."</span><span style="color: #0000FF;">},</span>
<span style="color: #0000FF;">{</span><span style="color: #008000;">","</span><span style="color: #0000FF;">,</span><span style="color: #008000;">" ,"</span><span style="color: #0000FF;">},</span>
<span style="color: #0000FF;">{</span><span style="color: #008000;">"had"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"has"</span><span style="color: #0000FF;">},</span>
<span style="color: #0000FF;">{</span><span style="color: #008000;">"contain?"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"have?"</span><span style="color: #0000FF;">},</span>
<span style="color: #0000FF;">{</span><span style="
<span style="color: #0000FF;">{</span><span style="color: #008000;">"in the bank ."</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"have?"</span><span style="color: #0000FF;">},</span>
<span style="color: #0000FF;">{</span><span style="color: #008000;">"in the machine ."</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"have?"</span><span style="color: #0000FF;">},</span>
<span style="color: #0000FF;">{</span><span style="color: #008000;">"as many"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"asmany"</span><span style="color: #0000FF;">},</span>
<span style="color: #0000FF;">{</span><span style="color:
<span style="color: #0000FF;">{</span><span style="color:
<span style="color: #0000FF;">{</span><span style="color: #008000;">" only and has a total"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">" . total"</span><span style="color: #0000FF;">},</span>
<span style="color: #0000FF;">{</span><span style="
<span style="color: #0000FF;">{</span><span style="color: #008000;">"All together ,"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"total"</span><span style="color: #0000FF;">},</span>
<span style="color: #0000FF;">{</span><span style="color: #008000;">"A vending machine has"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"total"</span><span style="color: #0000FF;">},</span>
<span style="color: #0000FF;">{</span><span style="color: #008000;">"valuing"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"total"</span><span style="color: #0000FF;">},</span>
<span style="color: #0000FF;">{</span><span style="color: #008000;">"coins in all ,"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"coins ."</span><span style="color: #0000FF;">},</span>
<span style="color: #0000FF;">{</span><span style="color: #008000;">"coins total and"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"coins ."</span><span style="color: #0000FF;">},</span>
<span style="color: #0000FF;">{</span><span style="color: #008000;">"find"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"many"</span><span style="color: #0000FF;">},</span>
<span style="color: #0000FF;">{</span><span style="color: #008000;">"consists"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"consisting"</span><span style="color: #0000FF;">},</span>
<span style="color: #0000FF;">{</span><span style="color: #008000;">"twenty-six"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"26"</span><span style="color: #0000FF;">},</span>
<span style="color: #0000FF;">{</span><span style="color: #008000;">"seventeen dollars in value"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"$17.00"</span><span style="color: #0000FF;">},</span>
<span style="color: #0000FF;">{</span><span style="color: #008000;">" one "</span><span style="color: #0000FF;">,</span><span style="color: #008000;">" 1 "</span><span style="color: #0000FF;">},</span>
<span style="color: #0000FF;">{</span><span style="color: #008000;">"three"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"3"</span><span style="color: #0000FF;">},</span>
<span style="color: #0000FF;">{</span><span style="color: #008000;">"four"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"4"</span><span style="color: #0000FF;">},</span>
<span style="color: #0000FF;">{</span><span style="color: #008000;">"twice"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"2 times"</span><span style="color: #0000FF;">},</span>
<span style="color: #0000FF;">{</span><span style="color: #008000;">"ten"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"10"</span><span style="color: #0000FF;">},</span>
<span style="color: #0000FF;">{</span><span style="color: #008000;">" and the total"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">" . total"</span><span style="color: #0000FF;">},</span>
<span style="color: #0000FF;">{</span><span style="color: #008000;">"half dollars"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"half_dollars"</span><span style="color: #0000FF;">},</span>
<span style="color: #0000FF;">{</span><span style="color: #008000;">"$1 bills"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"one_dollar_bills"</span><span style="color: #0000FF;">},</span>
<span style="color: #0000FF;">{</span><span style="color: #008000;">"$2 bills"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"two_dollar_bills"</span><span style="color: #0000FF;">},</span>
<span style="color: #0000FF;">{</span><span style="color: #008000;">"$5 bills"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"five_dollar_bills"</span><span style="color: #0000FF;">},</span>
<span style="color: #0000FF;">{</span><span style="color: #008000;">"$10 bill"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"ten_dollar_bills"</span><span style="color: #0000FF;">},</span>
<span style="color: #0000FF;">{</span><span style="
<span style="color: #0000FF;">{</span><span style="
<span style="color: #0000FF;">{</span><span style="color: #008000;">"five dollar bills"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"five_dollar_bills"</span><span style="color: #0000FF;">},</span>
<span style="color: #0000FF;">{</span><span style="color: #008000;">"10-dollar bills"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"ten_dollar_bills"</span><span style="color: #0000FF;">},</span>
<span style="color: #0000FF;">{</span><span style="color: #008000;">"10_dollar_bills"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"ten_dollar_bills"</span><span style="color: #0000FF;">}}),</span>
<span style="color: #000000;">noise</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">split</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"the|a|to|of|i|is|that|it|on|you|this|for|but|with|are|have|be|at|or|was|so|if|out|not|he|she|they|has|do|does"</span><span style="color: #0000FF;">&</span>
<span style="color: #008000;">"|in|these|person|small|child|child's|bank|pile|clerk|given|put|there|cash|drawer|start|workday|his|suppose|ken"</span><span style="color: #0000FF;">&</span>
<span style="color: #008000;">"|terry|how|my|marsha|machine|accepts|michael|lucille|ben|number|type|kind|amount|collection|contains|change"</span><span style="color: #0000FF;">&</span>
<span style="color: #008000;">"|wallet|did|numbers|pocket"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"|"</span><span style="color: #0000FF;">),</span>
<span style="color: #000080;font-style:italic;">-- one spectacularly irksome preamble containing absolutely no useful information whatsoever...:</span>
<span style="color: #000000;">uncle</span> <span style="color: #0000FF;">=</span> <span style="color: #008000;">"your uncle walks in , jingling the coins in his pocket . "</span><span style="color: #0000FF;">&</span>
<span style="
<span style="color: #008000;">"if you can figure out how many of each kind of coin he is carrying . "</span><span style="color: #0000FF;">&</span>
<span style="color: #008000;">"you're not too interested until he tells you that he's been collecting "</span><span style="color: #0000FF;">&</span>
<span style="color: #008000;">"those gold-tone one-dollar coins . "</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">vocab</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #008000;">"times"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"asmany"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"quarters"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"as"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"dimes"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"and"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"total"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"money"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"many"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"have?"</span><span style="color: #0000FF;">,</span>
<span style="color: #008000;">"coins"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"consisting"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"pennies"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"nickels"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"more"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"less"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"than"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"each"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"coin"</span><span style="color: #0000FF;">,</span>
<span style="color: #008000;">"half_dollars"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"bills"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"bill"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"all"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"dollars"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"one-half"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"same"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"only"</span><span style="color: #0000FF;">,</span>
<span style="color: #008000;">"one_dollar_bills"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"two_dollar_bills"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"five_dollar_bills"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"ten_dollar_bills"</span><span style="color: #0000FF;">},</span>
<span style="color: #0000FF;">{</span><span style="color: #000000;">assets</span><span style="color: #0000FF;">,</span><span style="color: #000000;">assetv</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">columnize</span><span style="color: #0000FF;">({{</span><span style="color: #008000;">"ten_dollar_bills"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1000</span><span style="color: #0000FF;">},</span>
<span style="color: #0000FF;">{</span><span style="color: #008000;">"five_dollar_bills"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">500</span><span style="color: #0000FF;">},</span>
<span style="color: #0000FF;">{</span><span style="color: #008000;">"two_dollar_bills"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">200</span><span style="color: #0000FF;">},</span>
<span style="color: #0000FF;">{</span><span style="color: #008000;">"one_dollar_bills"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">100</span><span style="color: #0000FF;">},</span>
<span style="color: #0000FF;">{</span><span style="color: #008000;">"dollars"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">100</span><span style="color: #0000FF;">},</span>
<span style="color: #0000FF;">{</span><span style="color: #008000;">"half_dollars"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">50</span><span style="color: #0000FF;">},</span>
<span style="color: #0000FF;">{</span><span style="color: #008000;">"quarters"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">25</span><span style="color: #0000FF;">},</span>
<span style="color: #0000FF;">{</span><span style="color: #008000;">"dimes"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">10</span><span style="color: #0000FF;">},</span>
<span style="color: #0000FF;">{</span><span style="color: #008000;">"nickels"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">5</span><span style="color: #0000FF;">},</span>
<span style="color: #0000FF;">{</span><span style="color: #008000;">"pennies"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">}})</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">count</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">lines</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">split</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">substitute_all</span><span style="color: #0000FF;">(</span><span style="color: #000000;">source</span><span style="color: #0000FF;">,</span><span style="color: #000000;">texts</span><span style="color: #0000FF;">,</span><span style="color: #000000;">replacements</span><span style="color: #0000FF;">),</span><span style="color: #008000;">"\n"</span><span style="color: #0000FF;">),</span>
<span style="color: #000000;">expectations</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{},</span>
<span style="color: #000000;">vused</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #004600;">false</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">vocab</span><span style="color: #0000FF;">))</span>
<span style="color: #008080;">procedure</span> <span style="color: #000000;">cleanup_lines</span><span style="color: #0000FF;">()</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">words</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">lines</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">by</span> <span style="color: #000000;">2</span> <span style="color: #008080;">do</span>
<span style="color: #004080;">string</span> <span style="color: #000000;">li</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">lower</span><span style="color: #0000FF;">(</span><span style="color: #000000;">lines</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">])</span>
<span style="color: #008080;">if</span> <span style="color: #7060A8;">match</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"your uncle"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">li</span><span style="color: #0000FF;">)=</span><span style="color: #000000;">1</span> <span style="color: #008080;">then</span>
<span style="color: #000080;font-style:italic;">-- note: if you tweak texts/replacements then you may
-- need to tweak the uncle constant to match.</span>
<span style="color: #008080;">if</span> <span style="color: #7060A8;">match</span><span style="color: #0000FF;">(</span><span style="color: #000000;">uncle</span><span style="color: #0000FF;">,</span><span style="color: #000000;">li</span><span style="color: #0000FF;">)!=</span><span style="color: #000000;">1</span> <span style="color: #008080;">then</span> <span style="color: #0000FF;">?</span><span style="color: #000000;">9</span><span style="color: #0000FF;">/</span><span style="color: #000000;">0</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #000000;">li</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">li</span><span style="color: #0000FF;">[</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">uncle</span><span style="color: #0000FF;">)+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">..$]</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #000000;">words</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">split</span><span style="color: #0000FF;">(</span><span style="color: #000000;">li</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">noise</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
<span style="color: #000000;">words</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">remove_all</span><span style="color: #0000FF;">(</span><span style="color: #000000;">noise</span><span style="color: #0000FF;">[</span><span style="color: #000000;">n</span><span style="color: #0000FF;">],</span><span style="color: #000000;">words</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">words</span><span style="color: #0000FF;">[$]=</span><span style="color: #008000;">"."</span> <span style="color: #008080;">and</span> <span style="color: #7060A8;">find</span><span style="color: #0000FF;">(</span><span style="color: #000000;">words</span><span style="color: #0000FF;">[$-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">],{</span><span style="color: #008000;">"dimes"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"nickels"</span><span style="color: #0000FF;">})</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">words</span><span style="color: #0000FF;">[$]</span> <span style="color: #0000FF;">=</span> <span style="color: #008000;">"have?"</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">words</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]=</span><span style="color: #008000;">","</span> <span style="color: #008080;">then</span> <span style="color: #000000;">words</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">words</span><span style="color: #0000FF;">[</span><span style="color: #000000;">2</span><span style="color: #0000FF;">..$]</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">w</span><span style="color: #0000FF;">=</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">words</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">to</span> <span style="color: #000000;">2</span> <span style="color: #008080;">by</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">1</span> <span style="color: #008080;">do</span>
<span style="color: #000080;font-style:italic;">-- re-join eg "$3" and ".99" (oops)</span>
<span style="color: #008080;">if</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">words</span><span style="color: #0000FF;">[</span><span style="color: #000000;">w</span><span style="color: #0000FF;">])></span><span style="color: #000000;">1</span> <span style="color: #008080;">and</span> <span style="color: #000000;">words</span><span style="color: #0000FF;">[</span><span style="color: #000000;">w</span><span style="color: #0000FF;">][</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]=</span><span style="color: #008000;">'.'</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">words</span><span style="color: #0000FF;">[</span><span style="color: #000000;">w</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">..</span><span style="color: #000000;">w</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">words</span><span style="color: #0000FF;">[</span><span style="color: #000000;">w</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]&</span><span style="color: #000000;">words</span><span style="color: #0000FF;">[</span><span style="color: #000000;">w</span><span style="color: #0000FF;">]}</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #000000;">words</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">match_replace</span><span style="color: #0000FF;">({</span><span style="color: #008000;">","</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"many"</span><span style="color: #0000FF;">},</span><span style="color: #000000;">words</span><span style="color: #0000FF;">,{</span><span style="color: #008000;">"."</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"many"</span><span style="color: #0000FF;">})</span>
<span style="color: #000000;">words</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">match_replace</span><span style="color: #0000FF;">({</span><span style="color: #008000;">","</span><span style="color: #0000FF;">},</span><span style="color: #000000;">words</span><span style="color: #0000FF;">,{})</span>
<span style="color: #000000;">count</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">1</span>
<span style="color: #000000;">lines</span><span style="color: #0000FF;">[</span><span style="color: #000000;">count</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">words</span>
<span style="color: #000000;">li</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">lines</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]</span>
<span style="color: #008080;">if</span> <span style="color: #7060A8;">match</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"--==>expected:"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">li</span><span style="color: #0000FF;">)!=</span><span style="color: #000000;">1</span> <span style="color: #008080;">then</span> <span style="color: #0000FF;">?</span><span style="color: #000000;">9</span><span style="color: #0000FF;">/</span><span style="color: #000000;">0</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #000000;">li</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">li</span><span style="color: #0000FF;">[</span><span style="color: #000000;">15</span><span style="color: #0000FF;">..$]</span>
<span style="color: #000000;">li</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">substitute</span><span style="color: #0000FF;">(</span><span style="color: #000000;">li</span><span style="color: #0000FF;">,</span><span style="color: #008000;">" ,"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">","</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">expectations</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">append</span><span style="color: #0000FF;">(</span><span style="color: #000000;">expectations</span><span style="color: #0000FF;">,</span><span style="color: #000000;">li</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #000000;">lines</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">lines</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">..</span><span style="color: #000000;">count</span><span style="color: #0000FF;">]</span>
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"%d puzzles:\n"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">count</span><span style="color: #0000FF;">)</span>
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"Step 1: remove noise and otherwise simplify (if nothing else, down to a %d-word vocab):\n\n"</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">vocab</span><span style="color: #0000FF;">))</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">count</span> <span style="color: #008080;">do</span>
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"%d: %s\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">i</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">join</span><span style="color: #0000FF;">(</span><span style="color: #000000;">lines</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">])})</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">procedure</span>
<span style="color: #000000;">cleanup_lines</span><span style="color: #0000FF;">()</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">add_unknowns</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">unknowns</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">words</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">words</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
<span style="color: #004080;">string</span> <span style="color: #000000;">word</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">words</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span>
<span style="color: #008080;">if</span> <span style="color: #008080;">not</span> <span style="color: #7060A8;">find</span><span style="color: #0000FF;">(</span><span style="color: #000000;">word</span><span style="color: #0000FF;">,</span><span style="color: #000000;">unknowns</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">and</span> <span style="color: #008080;">not</span> <span style="color: #7060A8;">find</span><span style="color: #0000FF;">(</span><span style="color: #000000;">word</span><span style="color: #0000FF;">,{</span><span style="color: #008000;">"as"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"consisting"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"all"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"and"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"than"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"only"</span><span style="color: #0000FF;">})</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">unknowns</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">append</span><span style="color: #0000FF;">(</span><span style="color: #000000;">unknowns</span><span style="color: #0000FF;">,</span><span style="color: #000000;">word</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">return</span> <span style="color: #000000;">unknowns</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">parse_sentence</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">words</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">unknowns</span><span style="color: #0000FF;">)</span>
<span style="color: #000080;font-style:italic;">-- Converts eg {"$1.00","quarters","and","nickels"} to {100,25,5}.
-- An "equation" of {100,25,5} means "100==25*unknown[1]+5*unknown[2]".
-- Obviously this is suitably scruffy, but the 31-word vocab certainly helps!
-- It is worth noting that by this stage most sentences begin or end in a number.
-- Since we may not have the full set of unknowns, each equation ends with a code:
-- 0: pad with 0, 1: pad with 1, 'a': pad with the unknown asset values</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">sentences</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{},</span>
<span style="color: #000000;">sentence</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">rest</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{},</span>
<span style="color: #000000;">isnumber</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">words</span><span style="color: #0000FF;">))</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">k</span>
<span style="color: #004080;">bool</span> <span style="color: #000000;">set_asset_sum</span> <span style="color: #0000FF;">=</span> <span style="color: #004600;">false</span>
<span style="color: #000000;">unknowns</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">deep_copy</span><span style="color: #0000FF;">(</span><span style="color: #000000;">unknowns</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">w</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">words</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
<span style="color: #004080;">string</span> <span style="color: #000000;">ww</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">words</span><span style="color: #0000FF;">[</span><span style="color: #000000;">w</span><span style="color: #0000FF;">]</span>
<span style="color: #000000;">k</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">find</span><span style="color: #0000FF;">(</span><span style="color: #000000;">ww</span><span style="color: #0000FF;">,</span><span style="color: #000000;">vocab</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">k</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span> <span style="color: #008080;">then</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">r</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">f</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">3</span> <span style="color: #008080;">do</span>
<span style="color: #000000;">r</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">scanf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">ww</span><span style="color: #0000FF;">,{</span><span style="color: #008000;">"%d"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"%dc"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"$%f"</span><span style="color: #0000FF;">}[</span><span style="color: #000000;">f</span><span style="color: #0000FF;">])</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">r</span><span style="color: #0000FF;">!={}</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">isnumber</span><span style="color: #0000FF;">[</span><span style="color: #000000;">w</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #008080;">iif</span><span style="color: #0000FF;">(</span><span style="color: #000000;">f</span><span style="color: #0000FF;">=</span><span style="color: #000000;">3</span><span style="color: #0000FF;">?</span><span style="color: #7060A8;">round</span><span style="color: #0000FF;">(</span><span style="color: #000000;">r</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">][</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]*</span><span style="color: #000000;">100</span><span style="color: #0000FF;">):</span><span style="color: #000000;">r</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">][</span><span style="color: #000000;">1</span><span style="color: #0000FF;">])</span>
<span style="color: #008080;">exit</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">r</span><span style="color: #0000FF;">={}</span> <span style="color: #008080;">then</span> <span style="color: #0000FF;">?</span><span style="color: #000000;">ww</span> <span style="color: #0000FF;">?</span><span style="color: #000000;">9</span><span style="color: #0000FF;">/</span><span style="color: #000000;">0</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span
<span style="color: #000000;">vused</span><span style="color: #0000FF;">[</span><span style="color: #000000;">k</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #004600;">true</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">isnumber</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]</span> <span style="color: #008080;">then</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">words</span><span style="color: #0000FF;">[</span><span style="color: #000000;">2</span><span style="color: #0000FF;">]=</span><span style="color: #008000;">"times"</span> <span style="color: #008080;">then</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">words</span><span style="color: #0000FF;">[</span><span style="color: #000000;">3</span><span style="color: #0000FF;">]!=</span><span style="color: #008000;">"asmany"</span> <span style="color: #008080;">then</span> <span style="color: #0000FF;">?</span><span style="color: #000000;">9</span><span style="color: #0000FF;">/</span><span style="color: #000000;">0</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #000000;">k</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">find</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"and"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">words</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">k</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">rest</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">words</span><span style="color: #0000FF;">[</span><span style="color: #000000;">k</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">..$]</span>
<span style="color: #000000;">words</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">words</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">..</span><span style="color: #000000;">k</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #000080;font-style:italic;">-- eg {"3","times","asmany","quarters","as","dimes"}</span>
<span style="color: #008080;">if</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">words</span><span style="color: #0000FF;">)!=</span><span style="color: #000000;">6</span> <span style="color: #008080;">or</span> <span style="color: #000000;">words</span><span style="color: #0000FF;">[</span><span style="color: #000000;">5</span><span style="color: #0000FF;">]!=</span><span style="color: #008000;">"as"</span> <span style="color: #008080;">then</span> <span style="color: #0000FF;">?</span><span style="color: #000000;">9</span><span style="color: #0000FF;">/</span><span style="color: #000000;">0</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #000000;">unknowns</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">add_unknowns</span><span style="color: #0000FF;">(</span><span style="color: #000000;">unknowns</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">words</span><span style="color: #0000FF;">[</span><span style="color: #000000;">4</span><span style="color: #0000FF;">..</span><span style="color: #000000;">6</span><span style="color: #0000FF;">])</span>
<span style="color: #000000;">sentence</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">unknowns</span><span style="color: #0000FF;">)+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">k</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">find</span><span style="color: #0000FF;">(</span><span style="color: #000000;">words</span><span style="color: #0000FF;">[</span><span style="color: #000000;">4</span><span style="color: #0000FF;">],</span><span style="color: #000000;">unknowns</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">sentence</span><span style="color: #0000FF;">[</span><span style="color: #000000;">k</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1</span>
<span style="color: #000000;">k</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">find</span><span style="color: #0000FF;">(</span><span style="color: #000000;">words</span><span style="color: #0000FF;">[</span><span style="color: #000000;">6</span><span style="color: #0000FF;">],</span><span style="color: #000000;">unknowns</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">sentence</span><span style="color: #0000FF;">[</span><span style="color: #000000;">k</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">isnumber</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]</span>
<span style="color: #000000;">sentence</span> <span style="color: #0000FF;">&=</span> <span style="color: #000000;">0</span>
<span style="color: #000000;">sentences</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">append</span><span style="color: #0000FF;">(</span><span style="color: #000000;">sentences</span><span style="color: #0000FF;">,</span><span style="color: #000000;">sentence</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">elsif</span> <span style="color: #000000;">words</span><span style="color: #0000FF;">[</span><span style="color: #000000;">2</span><span style="color: #0000FF;">]=</span><span style="color: #008000;">"coins"</span>
<span style="color: #008080;">or</span> <span style="color: #0000FF;">(</span><span style="color: #000000;">words</span><span style="color: #0000FF;">[</span><span style="color: #000000;">2</span><span style="color: #0000FF;">]=</span><span style="color: #008000;">"bills"</span> <span style="color: #008080;">and</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">words</span><span style="color: #0000FF;">)></span><span style="color: #000000;">2</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span>
<span style="color: #000080;font-style:italic;">--/* eg:
{"18","coins","consisting","pennies","and","nickels"}
{"26","coins","all","dollars","and","quarters"}
{"25","coins","nickels","and","dimes"}
{"33","coins","consisting","nickels","dimes","and","quarters"}
{"20","bills","consisting","one_dollar_bills","and","two_dollar_bills"}
<span style="color: #000000;">unknowns</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">add_unknowns</span><span style="color: #0000FF;">(</span><span style="color: #000000;">unknowns</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">words</span><span style="color: #0000FF;">[</span><span style="color: #000000;">3</span><span style="color: #0000FF;">..$])</span>
<span style="color: #000000;">sentence</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">isnumber</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]}&</span><span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">unknowns</span><span style="color: #0000FF;">))</span>
<span style="color: #000000;">sentence</span> <span style="color: #0000FF;">&=</span> <span style="color: #000000;">1</span>
<span style="color: #000000;">sentences</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">append</span><span style="color: #0000FF;">(</span><span style="color: #000000;">sentences</span><span style="color: #0000FF;">,</span><span style="color: #000000;">sentence</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">elsif</span> <span style="color: #7060A8;">find</span><span style="color: #0000FF;">(</span><span style="color: #000000;">words</span><span style="color: #0000FF;">[</span><span style="color: #000000;">2</span><span style="color: #0000FF;">],{</span><span style="color: #008000;">"more"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"less"</span><span style="color: #0000FF;">})</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">k</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">find</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"and"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">words</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">k</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">rest</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">words</span><span style="color: #0000FF;">[</span><span style="color: #000000;">k</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">..$]</span>
<span style="color: #000000;">words</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">words</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">..</span><span style="color: #000000;">k</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #000080;font-style:italic;">--/* eg:
<span style="color: #008080;">if</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">words</span><span style="color: #0000FF;">)!=</span><span style="color: #000000;">5</span> <span style="color: #008080;">or</span> <span style="color: #000000;">words</span><span style="color: #0000FF;">[</span><span style="color: #000000;">4</span><span style="color: #0000FF;">]!=</span><span style="color: #008000;">"than"</span> <span style="color: #008080;">then</span> <span style="color: #0000FF;">?</span><span style="color: #000000;">9</span><span style="color: #0000FF;">/</span><span style="color: #000000;">0</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #000000;">unknowns</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">add_unknowns</span><span style="color: #0000FF;">(</span><span style="color: #000000;">unknowns</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">words</span><span style="color: #0000FF;">[</span><span style="color: #000000;">3</span><span style="color: #0000FF;">..$])</span>
<span style="color: #000000;">sentence</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">isnumber</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]}&</span><span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">unknowns</span><span style="color: #0000FF;">))</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">less</span> <span style="color: #0000FF;">=</span> <span style="color: #008080;">iff</span><span style="color: #0000FF;">(</span><span style="color: #000000;">words</span><span style="color: #0000FF;">[</span><span style="color: #000000;">2</span><span style="color: #0000FF;">]=</span><span style="color: #008000;">"less"</span><span style="color: #0000FF;">?-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">:+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">k</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">find</span><span style="color: #0000FF;">(</span><span style="color: #000000;">words</span><span style="color: #0000FF;">[</span><span style="color: #000000;">3</span><span style="color: #0000FF;">],</span><span style="color: #000000;">unknowns</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">sentence</span><span style="color: #0000FF;">[</span><span style="color: #000000;">k</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">less</span>
<span style="color: #000000;">k</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">find</span><span style="color: #0000FF;">(</span><span style="color: #000000;">words</span><span style="color: #0000FF;">[</span><span style="color: #000000;">5</span><span style="color: #0000FF;">],</span><span style="color: #000000;">unknowns</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">sentence</span><span style="color: #0000FF;">[</span><span style="color: #000000;">k</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">less</span>
<span style="color: #000000;">sentence</span> <span style="color: #0000FF;">&=</span> <span style="color: #000000;">0</span>
<span style="color: #000000;">sentences</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">append</span><span style="color: #0000FF;">(</span><span style="color: #000000;">sentences</span><span style="color: #0000FF;">,</span><span style="color: #000000;">sentence</span><span style="color: #0000FF;">)</span>
<span style="color:
<span style="color: #000080;font-style:italic;">--/* eg:
<span style="color: #008080;">if</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">words</span><span style="color: #0000FF;">)></span><span style="color: #000000;">2</span> <span style="color: #008080;">then</span>
<span style="color: #000080;font-style:italic;">-- log assets:
-- eg {"$13.25","nickels","and","quarters"}</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">words</span><span style="color: #0000FF;">[</span><span style="color: #000000;">3</span><span style="color: #0000FF;">]!=</span><span style="color: #008000;">"and"</span> <span style="color: #008080;">or</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">words</span><span style="color: #0000FF;">)!=</span><span style="color: #000000;">4</span> <span style="color: #008080;">then</span> <span style="color: #0000FF;">?</span><span style="color: #000000;">9</span><span style="color: #0000FF;">/</span><span style="color: #000000;">0</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #000000;">unknowns</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">add_unknowns</span><span style="color: #0000FF;">(</span><span style="color: #000000;">unknowns</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">words</span><span style="color: #0000FF;">[</span><span style="color: #000000;">2</span><span style="color: #0000FF;">..$])</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #000000;">sentence</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">isnumber</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]}</span>
<span style="color: #000000;">set_asset_sum</span> <span style="color: #0000FF;">=</span> <span style="color: #004600;">true</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">elsif</span> <span style="color: #000000;">isnumber</span><span style="color: #0000FF;">[$]</span> <span style="color: #008080;">then</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">words</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]=</span><span style="color: #008000;">"total"</span>
<span style="color: #008080;">or</span> <span style="color: #0000FF;">(</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">words</span><span style="color: #0000FF;">)=</span><span style="color: #000000;">3</span> <span style="color: #008080;">and</span> <span style="color: #000000;">words</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">..</span><span style="color: #000000;">2</span><span style="color: #0000FF;">]={</span><span style="color: #008000;">"coins"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"total"</span><span style="color: #0000FF;">})</span> <span style="color: #008080;">then</span>
<span style="color:
<span style="color: #000000;">sentence</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">isnumber</span><span style="color: #0000FF;">[$]}</span>
<span style="color: #000000;">set_asset_sum</span> <span style="color: #0000FF;">=</span> <span style="color: #004600;">true</span>
<span style="color: #008080;">else</span>
<span style="color: #000080;font-style:italic;">-- eg {"quarters","and","dimes","38"}</span>
<span style="color: #000000;">unknowns</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">add_unknowns</span><span style="color: #0000FF;">(</span><span style="color: #000000;">unknowns</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">words</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">..$-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">])</span>
<span style="color: #000000;">sentence</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">isnumber</span><span style="color: #0000FF;">[$]}&</span><span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">unknowns</span><span style="color: #0000FF;">))</span>
<span style="color: #000000;">sentence</span> <span style="color: #0000FF;">&=</span> <span style="color: #000000;">1</span>
<span style="color: #000000;">sentences</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">append</span><span style="color: #0000FF;">(</span><span style="color: #000000;">sentences</span><span style="color: #0000FF;">,</span><span style="color: #000000;">sentence</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">elsif</span> <span style="color: #000000;">words</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]=</span><span style="color: #008000;">"one-half"</span> <span style="color: #008080;">then</span>
<span style="color: #000080;font-style:italic;">-- eg {"one-half","asmany","dimes","as","nickels"}</span>
<span style="color: #008080;">if</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">words</span><span style="color: #0000FF;">)!=</span><span style="color: #000000;">5</span> <span style="color: #008080;">or</span> <span style="color: #000000;">words</span><span style="color: #0000FF;">[</span><span style="color: #000000;">2</span><span style="color: #0000FF;">]!=</span><span style="color: #008000;">"asmany"</span> <span style="color: #008080;">or</span> <span style="color: #000000;">words</span><span style="color: #0000FF;">[</span><span style="color: #000000;">4</span><span style="color: #0000FF;">]!=</span><span style="color: #008000;">"as"</span> <span style="color: #008080;">then</span> <span style="color: #0000FF;">?</span><span style="color: #000000;">9</span><span style="color: #0000FF;">/</span><span style="color: #000000;">0</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #000000;">unknowns</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">add_unknowns</span><span style="color: #0000FF;">(</span><span style="color: #000000;">unknowns</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">words</span><span style="color: #0000FF;">[</span><span style="color: #000000;">3</span><span style="color: #0000FF;">..$])</span>
<span style="color: #000000;">sentence</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">unknowns</span><span style="color: #0000FF;">)+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">k</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">find</span><span style="color: #0000FF;">(</span><span style="color: #000000;">words</span><span style="color: #0000FF;">[</span><span style="color: #000000;">3</span><span style="color: #0000FF;">],</span><span style="color: #000000;">unknowns</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">sentence</span><span style="color: #0000FF;">[</span><span style="color: #000000;">k</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">2</span>
<span style="color: #000000;">k</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">find</span><span style="color: #0000FF;">(</span><span style="color: #000000;">words</span><span style="color: #0000FF;">[</span><span style="color: #000000;">5</span><span style="color: #0000FF;">],</span><span style="color: #000000;">unknowns</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">sentence</span><span style="color: #0000FF;">[</span><span style="color: #000000;">k</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1</span>
<span style="color: #000000;">sentence</span> <span style="color: #0000FF;">&=</span> <span style="color: #000000;">0</span>
<span style="color: #000000;">sentences</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">append</span><span style="color: #0000FF;">(</span><span style="color: #000000;">sentences</span><span style="color: #0000FF;">,</span><span style="color: #000000;">sentence</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">elsif</span> <span style="color: #000000;">words</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]=</span><span style="color: #008000;">"many"</span> <span style="color: #008080;">then</span>
<span style="color: #000080;font-style:italic;">--/* eg
{"many","quarters","and","dimes","have?"}
{"many","each","coin","have?"}
{"many","each","have?"}
{"many","each","bill","have?"}
{"many","coins","each","have?"}
<span style="color: #008080;">if</span> <span style="color: #000000;">words</span><span style="color: #0000FF;">[$]!=</span><span style="color: #008000;">"have?"</span> <span style="color: #008080;">then</span> <span style="color: #0000FF;">?</span><span style="color: #000000;">9</span><span style="color: #0000FF;">/</span><span style="color: #000000;">0</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #000080;font-style:italic;">-- no rule, as yet, just outputs everything instead.</span>
<span style="color: #008080;">elsif</span> <span style="color: #000000;">words</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]=</span><span style="color: #008000;">"same"</span> <span style="color: #008080;">then</span>
<span style="color: #000080;font-style:italic;">-- eg {"
<span style="color: #000000;">unknowns</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">add_unknowns</span><span style="color: #0000FF;">(</span><span style="color: #000000;">unknowns</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">words</span><span style="color: #0000FF;">[</span><span style="color: #000000;">2</span><span style="color: #0000FF;">..$])</span>
<span style="color: #008080;">if</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">unknowns</span><span style="color: #0000FF;">)!=</span><span style="color: #000000;">3</span> <span style="color: #008080;">then</span> <span style="color: #0000FF;">?</span><span style="color: #000000;">9</span><span style="color: #0000FF;">/</span><span style="color: #000000;">0</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #000000;">sentences</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">append</span><span style="color: #0000FF;">(</span><span style="color: #000000;">sentences</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0</span><span style="color: #0000FF;">})</span> <span style="color: #000080;font-style:italic;">-- (p==n)</span>
<span style="color: #000000;">sentences</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">append</span><span style="color: #0000FF;">(</span><span style="color: #000000;">sentences</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0</span><span style="color: #0000FF;">})</span> <span style="color: #000080;font-style:italic;">-- (n==d)</span>
<span style="color: #008080;">elsif</span> <span style="color: #000000;">words</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]=</span><span style="color: #008000;">"total"</span> <span style="color: #008080;">then</span>
<span style="color: #000080;font-style:italic;">-- eg {"total","13","bills"}</span>
<span style="color: #008080;">if</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">words</span><span style="color: #0000FF;">)!=</span><span style="color: #000000;">3</span> <span style="color: #008080;">or</span> <span style="color: #008080;">not</span> <span style="color: #000000;">isnumber</span><span style="color: #0000FF;">[</span><span style="color: #000000;">2</span><span style="color: #0000FF;">]</span> <span style="color: #008080;">or</span> <span style="color: #000000;">words</span><span style="color: #0000FF;">[</span><span style="color: #000000;">3</span><span style="color: #0000FF;">]!=</span><span style="color: #008000;">"bills"</span> <span style="color: #008080;">then</span> <span style="color: #0000FF;">?</span><span style="color: #000000;">9</span><span style="color: #0000FF;">/</span><span style="color: #000000;">0</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #000000;">sentence</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">isnumber</span><span style="color: #0000FF;">[</span><span style="color: #000000;">2</span><span style="color: #0000FF;">]}&</span><span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">unknowns</span><span style="color: #0000FF;">))</span>
<span style="color: #000000;">sentence</span> <span style="color: #0000FF;">&=</span> <span style="color: #000000;">1</span>
<span style="color: #000000;">sentences</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">append</span><span style="color: #0000FF;">(</span><span style="color: #000000;">sentences</span><span style="color: #0000FF;">,</span><span style="color: #000000;">sentence</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">else</span>
<span style="color: #000080;font-style:italic;">--/* eg:
{"one_dollar_bills","five_dollar_bills","and","ten_dollar_bills"}
{"only","nickels","dimes","and","quarters"}
-- just log
<span style="color: #000000;">unknowns</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">add_unknowns</span><span style="color: #0000FF;">(</span><span style="color: #000000;">unknowns</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">words</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">set_asset_sum</span> <span style="color: #008080;">then</span>
<span style="color: #000080;font-style:italic;">-- common code for eg {"total","$3.74"} and {"$75","bills"}</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">u</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">unknowns</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
<span style="color: #004080;">string</span> <span style="color: #000000;">uu</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">unknowns</span><span style="color: #0000FF;">[</span><span style="color: #000000;">u</span><span style="color: #0000FF;">]</span>
<span style="color: #000000;">k</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">find</span><span style="color: #0000FF;">(</span><span style="color: #000000;">uu</span><span style="color: #0000FF;">,</span><span style="color: #000000;">assets</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">sentence</span> <span style="color: #0000FF;">&=</span> <span style="color: #000000;">assetv</span><span style="color: #0000FF;">[</span><span style="color: #000000;">k</span><span style="color: #0000FF;">]</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #000000;">sentence</span> <span style="color: #0000FF;">&=</span> <span style="color: #008000;">'a'</span>
<span style="color: #000000;">sentences</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">append</span><span style="color: #0000FF;">(</span><span style="color: #000000;">sentences</span><span style="color: #0000FF;">,</span><span style="color: #000000;">sentence</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">if</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">rest</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span>
<span style="color: #000080;font-style:italic;">-- {sequence s2,unknowns} = parse_sentence(rest,unknowns)</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">s2</span>
<span style="color: #0000FF;">{</span><span style="color: #000000;">s2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">unknowns</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">parse_sentence</span><span style="color: #0000FF;">(</span><span style="color: #000000;">rest</span><span style="color: #0000FF;">,</span><span style="color: #000000;">unknowns</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">sentences</span> <span style="color: #0000FF;">&=</span> <span style="color: #000000;">s2</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">return</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">sentences</span><span style="color: #0000FF;">,</span><span style="color: #000000;">unknowns</span><span style="color: #0000FF;">}</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #008080;">procedure</span> <span style="color: #000000;">solveN</span><span style="color: #0000FF;">(</span><span style="color: #004080;">integer</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">sequence</span> <span style="color: #000000;">rules</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">unknowns</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">string</span> <span style="color: #000000;">expected</span><span style="color: #0000FF;">)</span>
<span style="color: #000080;font-style:italic;">--
-- Based on https://mathcs.clarku.edu/~djoyce/ma105/simultaneous.html
-- aka the ancient Chinese Jiuzhang suanshu ~100 B.C. (!!)
--
-- Example (ignoring n, which is solely for output):
-- rules = {{18,1,1},{38,1,5}}, ie 18==p+n, 38==p+5*n
-- unknowns = {"pennies","nickels"}
-- expected = "pennies = 13, nickels = 5"
--
-- In the elimination phase, both p have multipliers of 1, so we can
-- ignore those two sq_mul and just do (38=p+5n)-(18=p+n)==>(20=4n).
-- Obviously therefore n is 5 and substituting backwards p is 13.
--</span>
<span style="color: #004080;">string</span> <span style="color: #000000;">res</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">sentences</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">rules</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">ri</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">rj</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">l</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">rules</span><span style="color: #0000FF;">),</span> <span style="color: #000000;">rii</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">rji</span>
<span style="color: #000000;">rules</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">deep_copy</span><span style="color: #0000FF;">(</span><span style="color: #000000;">rules</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">l</span> <span style="color: #008080;">do</span>
<span style="color: #000080;font-style:italic;">-- successively eliminate (grow lower left triangle of 0s)</span>
<span style="color: #000000;">ri</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">rules</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span>
<span style="color: #008080;">if</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">ri</span><span style="color: #0000FF;">)!=</span><span style="color: #000000;">l</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span> <span style="color: #008080;">then</span> <span style="color: #0000FF;">?</span><span style="color: #000000;">9</span><span style="color: #0000FF;">/</span><span style="color: #000000;">0</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #000000;">rii</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">ri</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">rii</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span> <span style="color: #008080;">then</span> <span style="color: #0000FF;">?</span><span style="color: #000000;">9</span><span style="color: #0000FF;">/</span><span style="color: #000000;">0</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">j</span><span style="color: #0000FF;">=</span><span style="color: #000000;">i</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">l</span> <span style="color: #008080;">do</span>
<span style="color: #000000;">rj</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">rules</span><span style="color: #0000FF;">[</span><span style="color: #000000;">j</span><span style="color: #0000FF;">]</span>
<span style="color: #000000;">rji</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">rj</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">rji</span><span style="color: #0000FF;">!=</span><span style="color: #000000;">0</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">rj</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">sq_sub</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">sq_mul</span><span style="color: #0000FF;">(</span><span style="color: #000000;">rj</span><span style="color: #0000FF;">,</span><span style="color: #000000;">rii</span><span style="color: #0000FF;">),</span><span style="color: #7060A8;">sq_mul</span><span style="color: #0000FF;">(</span><span style="color: #000000;">ri</span><span style="color: #0000FF;">,</span><span style="color: #000000;">rji</span><span style="color: #0000FF;">))</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">rj</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]!=</span><span style="color: #000000;">0</span> <span style="color: #008080;">then</span> <span style="color: #0000FF;">?</span><span style="color: #000000;">9</span><span style="color: #0000FF;">/</span><span style="color: #000000;">0</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span> <span style="color: #000080;font-style:italic;">-- (job done)</span>
<span style="color: #000000;">rules</span><span style="color: #0000FF;">[</span><span style="color: #000000;">j</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">rj</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">l</span> <span style="color: #008080;">to</span> <span style="color: #000000;">1</span> <span style="color: #008080;">by</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">1</span> <span style="color: #008080;">do</span>
<span style="color: #000080;font-style:italic;">-- then substitute each backwards</span>
<span style="color: #000000;">ri</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">rules</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span>
<span style="color: #000000;">rii</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">ri</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]/</span><span style="color: #000000;">ri</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]</span> <span style="color: #000080;font-style:italic;">-- (all else should be 0)</span>
<span style="color: #000000;">rules</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">sprintf</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"%s = %d"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">unknowns</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">],</span><span style="color: #000000;">rii</span><span style="color: #0000FF;">})</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">j</span><span style="color: #0000FF;">=</span><span style="color: #000000;">i</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">1</span> <span style="color: #008080;">by</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">1</span> <span style="color: #008080;">do</span>
<span style="color: #000000;">rj</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">rules</span><span style="color: #0000FF;">[</span><span style="color: #000000;">j</span><span style="color: #0000FF;">]</span>
<span style="color: #000000;">rji</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">rj</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">rji</span><span style="color: #0000FF;">!=</span><span style="color: #000000;">0</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">rules</span><span style="color: #0000FF;">[</span><span style="color: #000000;">j</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span>
<span style="color: #000000;">rj</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">-=</span> <span style="color: #000000;">rji</span><span style="color: #0000FF;">*</span><span style="color: #000000;">rii</span>
<span style="color: #000000;">rj</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span>
<span style="color: #000000;">rules</span><span style="color: #0000FF;">[</span><span style="color: #000000;">j</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">rj</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #000000;">res</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">join</span><span style="color: #0000FF;">(</span><span style="color: #000000;">rules</span><span style="color: #0000FF;">,</span><span style="color: #008000;">", "</span><span style="color: #0000FF;">)</span>
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"%d: %v ==> %s\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">n</span><span style="color: #0000FF;">,</span><span style="color: #000000;">sentences</span><span style="color: #0000FF;">,</span><span style="color: #000000;">res</span><span style="color: #0000FF;">})</span>
<span style="color: #000080;font-style:italic;">-- printf(1,"%d: %s\n",{n,res}) -- (maybe pref.)</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">res</span><span style="color: #0000FF;">!=</span><span style="color: #000000;">expected</span> <span style="color: #008080;">then</span> <span style="color: #0000FF;">?</span><span style="color: #000000;">9</span><span style="color: #0000FF;">/</span><span style="color: #000000;">0</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">procedure</span>
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"\nStep 2: convert sentences into structures/equations, and solve them:\n"</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">count</span> <span style="color: #008080;">do</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">words</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">split</span><span style="color: #0000FF;">(</span><span style="color: #000000;">lines</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">],{</span><span style="color: #008000;">"."</span><span style="color: #0000FF;">})</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">sentences</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{},</span>
<span style="color: #000000;">sentencii</span><span style="color: #0000FF;">,</span> <span style="color: #000080;font-style:italic;">-- (one ...but some still contain "and")</span>
<span style="color: #000000;">unknowns</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{}</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">w</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">words</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
<span style="color: #0000FF;">{</span><span style="color: #000000;">sentencii</span><span style="color: #0000FF;">,</span><span style="color: #000000;">unknowns</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">parse_sentence</span><span style="color: #0000FF;">(</span><span style="color: #000000;">words</span><span style="color: #0000FF;">[</span><span style="color: #000000;">w</span><span style="color: #0000FF;">],</span><span style="color: #000000;">unknowns</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">sentences</span> <span style="color: #0000FF;">&=</span> <span style="color: #000000;">sentencii</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">if</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">sentences</span><span style="color: #0000FF;">)></span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">unknowns</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span>
<span style="color: #000080;font-style:italic;">-- messy: puzzle has too much info!
-- (14 aka "33 coins" and 17 "Terry" with 38 coins,
-- eliminate wrongly and get a divide by zero...)
--
<span style="color: #000000;">sentences</span><span style="color: #0000FF;">[-</span><span style="color: #000000;">2</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">sentences</span><span style="color: #0000FF;">[-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]</span>
<span style="color: #000000;">sentences</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">sentences</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">..</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">unknowns</span><span style="color: #0000FF;">)]</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">if</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">sentences</span><span style="color: #0000FF;">)!=</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">unknowns</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span> <span style="color: #0000FF;">?</span><span style="color: #000000;">9</span><span style="color: #0000FF;">/</span><span style="color: #000000;">0</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">s</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">sentences</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
<span style="color: #000080;font-style:italic;">-- pad any short equations, eg 3 more nickels than dimes
-- needs a 0 for quarters, if were not mentioned
<span style="color: #004080;">sequence</span> <span style="color: #000000;">ss</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">sentences</span><span style="color: #0000FF;">[</span><span style="color: #000000;">s</span><span style="color: #0000FF;">]</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">padcode</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">ss</span><span style="color: #0000FF;">[$]</span>
<span style="color: #000000;">ss</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">ss</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">..$-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">shortlen</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">sentences</span><span style="color: #0000FF;">)+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">-</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">ss</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">shortlen</span> <span style="color: #008080;">then</span>
<span style="color: #008080;">switch</span> <span style="color: #000000;">padcode</span> <span style="color: #008080;">do</span>
<span style="color: #008080;">case</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">:</span> <span style="color: #000000;">ss</span> <span style="color: #0000FF;">&=</span> <span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">shortlen</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">case</span> <span style="color: #000000;">1</span><span style="color: #0000FF;">:</span> <span style="color: #000000;">ss</span> <span style="color: #0000FF;">&=</span> <span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">shortlen</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">case</span> <span style="color: #008000;">'a'</span><span style="color: #0000FF;">:</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">u</span><span style="color: #0000FF;">=-</span><span style="color: #000000;">shortlen</span> <span style="color: #008080;">to</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">1</span> <span style="color: #008080;">do</span>
<span style="color: #004080;">string</span> <span style="color: #000000;">uu</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">unknowns</span><span style="color: #0000FF;">[</span><span style="color: #000000;">u</span><span style="color: #0000FF;">]</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">k</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">find</span><span style="color: #0000FF;">(</span><span style="color: #000000;">uu</span><span style="color: #0000FF;">,</span><span style="color: #000000;">assets</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">ss</span> <span style="color: #0000FF;">&=</span> <span style="color: #000000;">assetv</span><span style="color: #0000FF;">[</span><span style="color: #000000;">k</span><span style="color: #0000FF;">]</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">default</span><span style="color: #0000FF;">:</span> <span style="color: #0000FF;">?</span><span style="color: #000000;">9</span><span style="color: #0000FF;">/</span><span style="color: #000000;">0</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">switch</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #000000;">sentences</span><span style="color: #0000FF;">[</span><span style="color: #000000;">s</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">ss</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #000000;">solveN</span><span style="color: #0000FF;">(</span><span style="color: #000000;">i</span><span style="color: #0000FF;">,</span><span style="color: #000000;">sentences</span><span style="color: #0000FF;">,</span><span style="color: #000000;">unknowns</span><span style="color: #0000FF;">,</span><span style="color: #000000;">expectations</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">])</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">k</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">find</span><span style="color: #0000FF;">(</span><span style="color: #004600;">false</span><span style="color: #0000FF;">,</span><span style="color: #000000;">vused</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">k</span> <span style="color: #008080;">then</span> <span style="color: #0000FF;">?{</span><span style="color: #008000;">"unused vocab"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">vocab</span><span style="color: #0000FF;">[</span><span style="color: #000000;">k</span><span style="color: #0000FF;">]}</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<!--</syntaxhighlight>-->
{{out}}
You just gotta love this Pidgin English! The problem numbering system used below is mine alone.<br>
Line 1,339 ⟶ 1,732:
23: {{4525,25,10},{29,-1,1}} ==> quarters = 121, dimes = 150
24: {{12,1,1},{30,10,1}} ==> dimes = 2, pennies = 10
</pre>
=={{header|Wren}}==
{{trans|Go}}
{{libheader|Wren-dynamic}}
{{libheader|Wren-pattern}}
{{libheader|Wren-str}}
{{libheader|Wren-sort}}
{{libheader|Wren-fmt}}
<syntaxhighlight lang="wren">import "./dynamic" for Struct
import "./pattern" for Pattern
import "./str" for Str
import "./sort" for Sort
import "./fmt" for Fmt
var Kind = Struct.create("Kind", ["name", "value", "number"])
// variable1 = constant1 * variable2 + constant2
var Relation = Struct.create("Relation", ["variable1", "variable2", "constant1", "constant2"])
var nums = {
"one-half": "0 times", "one": "1", "two": "2", "three": "3", "four": "4", "five": "5",
"six": "6", "seven": "7", "eight": "8", "nine": "9", "ten": "10", "eleven": "11", "twelve": "12",
"thirteen": "13", "fourteen": "14", "fifteen": "15", "sixteen": "16", "seventeen": "17",
"eighteen": "18", "nineteen": "19", "twenty": "20", "thirty": "30", "forty": "40",
"fifty": "50", "sixty": "60", "seventy": "70", "eighty": "80", "ninety": "90", "hundred": "100"
}
var nums2 = {
"twenty-": "2", "thirty-": "3", "forty-": "4",
"fifty-": "5", "sixty-": "6", "seventy-": "7", "eighty-": "8", "ninety-": "9"
}
var coins = {
"pennies": 0.01, "nickels": 0.05, "dimes": 0.10, "quarters": 0.25, "half-dollars": 0.50,
"one-dollar": 1.00, "two-dollar": 2.00, "five-dollar": 5.00, "ten-dollar": 10.00
}
var bills = {
"$1": "one-dollar", "$2": "two-dollar", "$5": "five-dollar", "$10": "ten-dollar"
}
var rx1 = Pattern.new("[/$+1/f|+1/d¢]")
var rx2 = Pattern.new("[pennies|nickels|dimes|quarters|half-dollar|one-dollar|two-dollar|five-dollar|ten-dollar]")
var rx3 = Pattern.new("/s[+1/d]/s")
var rx4 = Pattern.new("[+1/d] times as many [+1/y] as [~she has |][+1/y]")
var rx5 = Pattern.new("[+1/d] more [+1/y] than [~she has |][+1/y]")
var rx6 = Pattern.new("[+1/d] less [+1/y] than [~she has |][+1/y]")
var rx7 = Pattern.new("[+1/d] dollars")
var spaced = Fn.new { |s| " %(s) " }
// Gets a sorted list of monetary values.
var getValues = Fn.new { |q|
var ss = rx1.findAll(q).map { |m| m.text.trimEnd(".") }.toList
if (ss.count == 0) return []
var res = []
for (s in ss) {
if (s == "") continue
if (s[0] == "$") {
s = s[1..-1]
} else {
s = "." + s[0..-3] // '¢' is 2 bytes
}
var f = Num.fromString(s)
res.add(f)
}
res.sort()
return res
}
// Gets a sorted slice of non-monetary integers.
var getNumbers = Fn.new { |q|
var ns = rx3.findAll(q).map { |m| m.text }.toList
if (ns.count == 0) return null
var res = []
for (n in ns) {
var i = Num.fromString(n)
res.add(i)
}
res.sort()
return res
}
// Gets the 'kinds' for the problem.
var getKinds = Fn.new { |a|
var num = Num.fromString(a[1])
var kinds = [Kind.new(a[2], 0, 0), Kind.new(a[4], 0, 0)]
var areCoins = false
for (i in 0...kinds.count) {
var v = coins[kinds[i].name]
if (v) {
kinds[i].value = v
areCoins = true
}
}
if (!areCoins) return [0, null]
return [num, kinds]
}
// Checks if the problem involves 3 coins and
// also returns their names and the names of the coins which occur most.
var hasThreeCoins = Fn.new { |q|
q = q.replace(".", "").replace(",", "")
var words = q.split(" ")
var coinMap = {}
for (word in words) {
if (coins.containsKey(word)) {
var v = coinMap[word]
if (v) {
coinMap[word] = v + 1
} else {
coinMap[word] = 1
}
}
}
if (coinMap.count != 3) return [null, "", false]
var maxNum = 0
var maxNames = []
var names = []
for (me in coinMap) {
names.add(me.key)
if (me.value > maxNum) {
maxNum = me.value
maxNames = [me.key]
} else if (me.value == maxNum) {
maxNames.add(me.key)
}
}
return [names, maxNames, true]
}
var errorMsg = Fn.new { |p|
System.print(p)
System.print("*** CAN'T SOLVE THIS ONE ***\n")
}
var printAnswers = Fn.new { |p, kinds|
System.print(p)
System.write("ANSWER:")
var i = 0
for (kind in kinds) {
if (i > 0) System.write(",")
System.write(" %(kind.number) %(kind.name)")
i = i + 1
}
System.print("\n")
}
// Processes a problem which involves 3 coins.
var threeCoins = Fn.new { |p, q, names, maxNames|
var relations = []
var am = rx4.findAll(q).map { |m| [m.text] + m.capsText }.toList
for (i in 0...am.count) {
var res = getKinds.call(am[i])
var mult = res[0]
var kinds = res[1]
relations.add(Relation.new(kinds[0].name, kinds[1].name, mult, 0))
}
var mt = rx5.findAll(q).map { |m| [m.text] + m.capsText }.toList
for (i in 0...mt.count) {
var res = getKinds.call(mt[i])
var plus = res[0]
var kinds = res[1]
relations.add(Relation.new(kinds[0].name, kinds[1].name, 1, plus))
}
var lt = rx6.findAll(q).map { |m| [m.text] + m.capsText }.toList
for (i in 0...lt.count) {
var res = getKinds.call(lt[i])
var minus = res[0]
var kinds = res[1]
relations.add(Relation.new(kinds[0].name, kinds[1].name, 1, -minus))
}
var le = relations.count
if (le > 2) {
errorMsg.call(p)
return
}
if (le == 0) { // numbers of each coin must be the same
var sum = 0
for (name in names) sum = sum + coins[name]
var tv = getValues.call(q)[-1]
var n = (tv/sum + 0.5).floor
var kinds = []
for (name in names) kinds.add(Kind.new(name, 0, n))
printAnswers.call(p, kinds)
} else {
var totalValue = getValues.call(q)[-1]
for (maxName in maxNames) {
for (i in 0...le) {
if (relations[i].constant1 == 0) {
relations[i].constant1 = 0.5 // deals with 'one-half' cases
}
if (le == 2 && maxName == relations[i].variable1) {
var v = relations[i].variable2
relations[i].variable1 = v
relations[i].variable2 = maxName
relations[i].constant1 = 1 / relations[i].constant1
relations[i].constant2 = -relations[i].constant2
}
}
var tv = totalValue
var v1 = ""
var v2 = ""
var v3 = ""
var n1 = 0
var n2 = 0
var n3 = 0
if (le == 2) {
var tmc = coins[relations[0].variable1] * relations[0].constant1 +
coins[relations[1].variable1] * relations[1].constant1 + coins[maxName]
tv = tv - coins[relations[0].variable1] * relations[0].constant2 -
coins[relations[1].variable1] * relations[1].constant2
v1 = maxName
v2 = relations[0].variable1
v3 = relations[1].variable1
n1 = (tv/tmc + 0.5).floor
n2 = (relations[0].constant1*n1 + relations[0].constant2 + 0.5).floor
n3 = (relations[1].constant1*n1 + relations[1].constant2 + 0.5).floor
} else {
var tn = getNumbers.call(q)[-1]
v1 = relations[0].variable1
v2 = relations[0].variable2
for (name in names) {
if (name != v1 && name != v2) {
v3 = name
break
}
}
var mult1 = coins[v1]
var mult2 = coins[v2]
var mult3 = coins[v3]
n2 = (((tn-relations[0].constant2)*mult3-tv+relations[0].constant2*mult1)/
((relations[0].constant1+1)*mult3-relations[0].constant1*mult1-mult2) + 0.5).floor
n1 = (n2*relations[0].constant1 + relations[0].constant2 + 0.5).floor
n3 = tn.floor - n1 - n2
}
var calcValue = n1 * coins[v1] + n2 * coins[v2] + n3 * coins[v3]
if ((totalValue - calcValue).abs <= 1e-14) {
var kinds = [Kind.new(v1, 0, n1), Kind.new(v2, 0, n2), Kind.new(v3, 0, n3)]
printAnswers.call(p, kinds)
return
}
}
errorMsg.call(p)
}
}
var ps = [
"If a person has three times as many quarters as dimes and the total amount of money is $5.95, find the number of quarters and dimes.",
"A pile of 18 coins consists of pennies and nickels. If the total amount of the coins is 38¢, find the number of pennies and nickels.",
"A small child has 6 more quarters than nickels. If the total amount of coins is $3.00, find the number of nickels and quarters the child has.",
"A child's bank contains 32 coins consisting of nickels and quarters. If the total amount of money is $3.80, find the number of nickels and quarters in the bank.",
"A person has twice as many dimes as she has pennies and three more nickels than pennies. If the total amount of the coins is $1.97, find the numbers of each type of coin the person has.",
"In a bank, there are three times as many quarters as half dollars and 6 more dimes than half dollars. If the total amount of the money in the bank is $4.65, find the number of each type of coin in the bank.",
"A person bought 12 stamps consisting of 37¢ stamps and 23¢ stamps. If the cost of the stamps is $3.74, find the number of each type of the stamps purchased.",
"A dairy store sold a total of 80 ice cream sandwiches and ice cream bars. If the sandwiches cost $0.69 each and the bars cost $0.75 each and the store made $58.08, find the number of each sold.",
"An office supply store sells college-ruled notebook paper for $1.59 a ream and wide-ruled notebook paper for $2.29 a ream. If a student purchased 9 reams of notebook paper and paid $15.71, how many reams of each type of paper did the student purchase?",
"A clerk is given $75 in bills to put in a cash drawer at the start of a workday. There are twice as many $1 bills as $5 bills and one less $10 bill than $5 bills. How many of each type of bill are there?",
"A person has 8 coins consisting of quarters and dimes. If the total amount of this change is $1.25, how many of each kind of coin are there?",
"A person has 3 times as many dimes as he has nickels and 5 more pennies than nickels. If the total amount of these coins is $1.13, how many of each kind of coin does he have?",
"A person bought ten greeting cards consisting of birthday cards costing $1.50 each and anniversary cards costing $2.00 each. If the total cost of the cards was $17.00, find the number of each kind of card the person bought.",
"A person has 9 more dimes than nickels. If the total amount of money is $1.20, find the number of dimes the person has.",
"A person has 20 bills consisting of $1 bills and $2 bills. If the total amount of money the person has is $35, find the number of $2 bills the person has.",
"A bank contains 8 more pennies than nickels and 3 more dimes than nickels. If the total amount of money in the bank is $3.10, find the number of dimes in the bank.",
"Your uncle walks in, jingling the coins in his pocket. He grins at you and tells you that you can have all the coins if you can figure out how many of each kind of coin he is carrying. You're not too interested until he tells you that he's been collecting those gold-tone one-dollar coins. The twenty-six coins in his pocket are all dollars and quarters, and they add up to seventeen dollars in value. How many of each coin does he have?",
"A collection of 33 coins, consisting of nickels, dimes, and quarters, has a value of $3.30. If there are three times as many nickels as quarters, and one-half as many dimes as nickels, how many coins of each kind are there?",
"A wallet contains the same number of pennies, nickels, and dimes. The coins total $1.44. How many of each type of coin does the wallet contain?",
"Suppose Ken has 25 coins in nickels and dimes only and has a total of $1.65. How many of each coin does he have?",
"Terry has 2 more quarters than dimes and has a total of $6.80. The number of quarters and dimes is 38. How many quarters and dimes does Terry have?",
"In my wallet, I have one-dollar bills, five-dollar bills, and ten-dollar bills. The total amount in my wallet is $43. I have four times as many one-dollar bills as ten-dollar bills. All together, there are 13 bills in my wallet. How many of each bill do I have?",
"Marsha has three times as many one-dollar bills as she does five dollar bills. She has a total of $32. How many of each bill does she have?",
"A vending machine has $41.25 in it. There are 255 coins total and the machine only accepts nickels, dimes and quarters. There are twice as many dimes as nickels. How many of each coin are in the machine?",
"Michael had 27 coins in all, valuing $4.50. If he had only quarters and dimes, how many coins of each kind did he have?",
"Lucille had $13.25 in nickels and quarters. If she had 165 coins in all, how many of each type of coin did she have?",
"Ben has $45.25 in quarters and dimes. If he has 29 less quarters than dimes, how many of each type of coin does he have?",
"A person has 12 coins consisting of dimes and pennies. If the total amount of money is $0.30, how many of each coin are there?"
]
for (p in ps) {
var q = Str.lower(p).replace("twice", "two times").replace(" does ", " has ")
for (d in ["half", "one", "two", "five", "ten"]) {
q = q.replace(d + " dollar", d + "-dollar")
}
for (me in nums) {
q = q.replace(spaced.call(me.key), spaced.call(me.value))
}
for (me in nums2) {
q = q.replace(me.key, me.value)
}
for (me in nums) {
q = q.replace(me.key + " ", me.value + " ")
}
for (me in bills) {
q = q.replace(me.key + " ", me.value + " ")
}
q = q.replace(" bills", "").replace(" bill", "")
// check if there are 3 coins involved
var res = hasThreeCoins.call(q)
if (res[2]){
threeCoins.call(p, q, res[0], res[1])
continue
}
var am = rx4.findAll(q).map { |m| [m.text] + m.capsText }.toList
if (am.count == 1) {
var res = getKinds.call(am[0])
var mult = res[0]
var kinds = res[1]
if (!kinds) {
errorMsg.call(p)
continue
}
var tv = getValues.call(q)[-1]
kinds[1].number = (tv/(mult*kinds[0].value + kinds[1].value) + 0.5).floor
kinds[0].number = kinds[1].number * mult
printAnswers.call(p, kinds)
continue
}
var mt = rx5.findAll(q).map { |m| [m.text] + m.capsText }.toList
if (mt.count == 1) {
var res = getKinds.call(mt[0])
var plus = res[0]
var kinds = res[1]
if (!kinds) {
errorMsg.call(p)
continue
}
var tv = getValues.call(q)[-1]
kinds[1].number = ((tv-plus*kinds[0].value)/(kinds[0].value + kinds[1].value) + 0.5).floor
kinds[0].number = kinds[1].number + plus
printAnswers.call(p, kinds)
continue
}
var lt = rx6.findAll(q).map { |m| [m.text] + m.capsText }.toList
if (lt.count == 1) {
var res = getKinds.call(lt[0])
var minus = res[0]
var kinds = res[1]
if (!kinds) {
errorMsg.call(p)
continue
}
var tv = getValues.call(q)[-1]
kinds[1].number = ((tv+minus*kinds[0].value)/(kinds[0].value + kinds[1].value) + 0.5).floor
kinds[0].number = kinds[1].number - minus
printAnswers.call(p, kinds)
continue
}
res = getValues.call(q)
var tv = 0
if (res.count > 0) {
tv = res[-1]
} else {
var res3 = rx7.findAll(q).map { |m| [m.text] + m.capsText }.toList
tv = Num.fromString(res3[0][1])
}
var tn = getNumbers.call(q)[-1]
var coinNames = rx2.findAll(q).map { |m| m.text }.toList
Sort.insertion(coinNames)
var kinds = []
if (coinNames.count > 0) {
kinds.add(Kind.new(coinNames[0], coins[coinNames[0]], 0))
for (i in 1...coinNames.count) {
if (coinNames[i] != coinNames[i-1]) {
kinds.add(Kind.new(coinNames[i], coins[coinNames[i]], 0))
}
}
if (kinds.count != 2) {
errorMsg.call(p)
continue
}
} else if (res.count >= 3) {
kinds.add(Kind.new(Fmt.swrite("$$$.2f item", res[0]), res[0], 0))
for (i in 1...res.count-1) {
if (res[i] != res[i-1]) {
kinds.add(Kind.new(Fmt.swrite("$$$.2f item", res[i]), res[i], 0))
}
}
if (kinds.count!= 2) {
errorMsg.call(p)
continue
}
} else {
errorMsg.call(p)
continue
}
kinds[0].number = ((tv-tn*kinds[1].value)/(kinds[0].value-kinds[1].value) + 0.5).floor
kinds[1].number = tn - kinds[0].number
printAnswers.call(p, kinds)
}</syntaxhighlight>
{{out}}
<pre>
If a person has three times as many quarters as dimes and the total amount of money is $5.95, find the number of quarters and dimes.
ANSWER: 21 quarters, 7 dimes
A pile of 18 coins consists of pennies and nickels. If the total amount of the coins is 38¢, find the number of pennies and nickels.
ANSWER: 5 nickels, 13 pennies
A small child has 6 more quarters than nickels. If the total amount of coins is $3.00, find the number of nickels and quarters the child has.
ANSWER: 11 quarters, 5 nickels
A child's bank contains 32 coins consisting of nickels and quarters. If the total amount of money is $3.80, find the number of nickels and quarters in the bank.
ANSWER: 21 nickels, 11 quarters
A person has twice as many dimes as she has pennies and three more nickels than pennies. If the total amount of the coins is $1.97, find the numbers of each type of coin the person has.
ANSWER: 7 pennies, 14 dimes, 10 nickels
In a bank, there are three times as many quarters as half dollars and 6 more dimes than half dollars. If the total amount of the money in the bank is $4.65, find the number of each type of coin in the bank.
ANSWER: 3 half-dollars, 9 quarters, 9 dimes
A person bought 12 stamps consisting of 37¢ stamps and 23¢ stamps. If the cost of the stamps is $3.74, find the number of each type of the stamps purchased.
ANSWER: 5 $0.23 item, 7 $0.37 item
A dairy store sold a total of 80 ice cream sandwiches and ice cream bars. If the sandwiches cost $0.69 each and the bars cost $0.75 each and the store made $58.08, find the number of each sold.
ANSWER: 32 $0.69 item, 48 $0.75 item
An office supply store sells college-ruled notebook paper for $1.59 a ream and wide-ruled notebook paper for $2.29 a ream. If a student purchased 9 reams of notebook paper and paid $15.71, how many reams of each type of paper did the student purchase?
ANSWER: 7 $1.59 item, 2 $2.29 item
A clerk is given $75 in bills to put in a cash drawer at the start of a workday. There are twice as many $1 bills as $5 bills and one less $10 bill than $5 bills. How many of each type of bill are there?
ANSWER: 5 five-dollar, 10 one-dollar, 4 ten-dollar
A person has 8 coins consisting of quarters and dimes. If the total amount of this change is $1.25, how many of each kind of coin are there?
ANSWER: 5 dimes, 3 quarters
A person has 3 times as many dimes as he has nickels and 5 more pennies than nickels. If the total amount of these coins is $1.13, how many of each kind of coin does he have?
ANSWER: 3 nickels, 9 dimes, 8 pennies
A person bought ten greeting cards consisting of birthday cards costing $1.50 each and anniversary cards costing $2.00 each. If the total cost of the cards was $17.00, find the number of each kind of card the person bought.
ANSWER: 6 $1.50 item, 4 $2.00 item
A person has 9 more dimes than nickels. If the total amount of money is $1.20, find the number of dimes the person has.
ANSWER: 11 dimes, 2 nickels
A person has 20 bills consisting of $1 bills and $2 bills. If the total amount of money the person has is $35, find the number of $2 bills the person has.
ANSWER: 5 one-dollar, 15 two-dollar
A bank contains 8 more pennies than nickels and 3 more dimes than nickels. If the total amount of money in the bank is $3.10, find the number of dimes in the bank.
ANSWER: 17 nickels, 25 pennies, 20 dimes
Your uncle walks in, jingling the coins in his pocket. He grins at you and tells you that you can have all the coins if you can figure out how many of each kind of coin he is carrying. You're not too interested until he tells you that he's been collecting those gold-tone one-dollar coins. The twenty-six coins in his pocket are all dollars and quarters, and they add up to seventeen dollars in value. How many of each coin does he have?
ANSWER: 14 one-dollar, 12 quarters
A collection of 33 coins, consisting of nickels, dimes, and quarters, has a value of $3.30. If there are three times as many nickels as quarters, and one-half as many dimes as nickels, how many coins of each kind are there?
ANSWER: 18 nickels, 6 quarters, 9 dimes
A wallet contains the same number of pennies, nickels, and dimes. The coins total $1.44. How many of each type of coin does the wallet contain?
ANSWER: 9 pennies, 9 dimes, 9 nickels
Suppose Ken has 25 coins in nickels and dimes only and has a total of $1.65. How many of each coin does he have?
ANSWER: 8 dimes, 17 nickels
Terry has 2 more quarters than dimes and has a total of $6.80. The number of quarters and dimes is 38. How many quarters and dimes does Terry have?
ANSWER: 20 quarters, 18 dimes
In my wallet, I have one-dollar bills, five-dollar bills, and ten-dollar bills. The total amount in my wallet is $43. I have four times as many one-dollar bills as ten-dollar bills. All together, there are 13 bills in my wallet. How many of each bill do I have?
ANSWER: 8 one-dollar, 2 ten-dollar, 3 five-dollar
Marsha has three times as many one-dollar bills as she does five dollar bills. She has a total of $32. How many of each bill does she have?
ANSWER: 12 one-dollar, 4 five-dollar
A vending machine has $41.25 in it. There are 255 coins total and the machine only accepts nickels, dimes and quarters. There are twice as many dimes as nickels. How many of each coin are in the machine?
ANSWER: 90 dimes, 45 nickels, 120 quarters
Michael had 27 coins in all, valuing $4.50. If he had only quarters and dimes, how many coins of each kind did he have?
ANSWER: 15 dimes, 12 quarters
Lucille had $13.25 in nickels and quarters. If she had 165 coins in all, how many of each type of coin did she have?
ANSWER: 140 nickels, 25 quarters
Ben has $45.25 in quarters and dimes. If he has 29 less quarters than dimes, how many of each type of coin does he have?
ANSWER: 121 quarters, 150 dimes
A person has 12 coins consisting of dimes and pennies. If the total amount of money is $0.30, how many of each coin are there?
ANSWER: 2 dimes, 10 pennies
</pre>
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