Countdown

Countdown is a draft programming task. It is not yet considered ready to be promoted as a complete task, for reasons that should be found in its talk page.

Given six numbers randomly selected from the list [1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 25, 50, 75, 100], calculate using only positive integers and four operations [+, -, *, /] a random number between 101 and 999.

Example:

Using: [3, 6, 25, 50, 75, 100]
Target: 952

Solution:

• 100 + 6 = 106
• 75 * 3 = 225
• 106 * 225 = 23850
• 23850 - 50 = 23800
• 23800 / 25 = 952

Origins

This is originally a 1972 French television game show. The game consists of randomly selecting six of the twenty-four numbers, from a list of: twenty "small numbers" (two each from 1 to 10), and four "large numbers" of 25, 50, 75 and 100. A random target number between 101 and 999 is generated. The players have 30 seconds to work out a sequence of calculations with the numbers whose final result is as close as possible to the target number. Only the four basic operations: addition, subtraction, multiplication and division can be used to create new numbers and not all six numbers are required. A number can only be used once. Division can only be done if the result has no remainder (fractions are not allowed) and only positive integers can be obtained at any stage of the calculation. (More info on the original game).

Extra challenge

The brute force algorithm is quite obvious. What is more interesting is to find some optimisation heuristics to reduce the number of calculations. For example, a rather interesting computational challenge is to calculate, as fast as possible, all existing solutions (that means 2'764'800 operations) for all possible games (with all the 13'243 combinations of six numbers out of twenty-four for all 898 possible targets between 101 and 999).

11l

Translation of: Python
```V best = 0
V best_out = ‘’
V target = 952
V nbrs = [100, 75, 50, 25, 6, 3]

F sol(target, nbrs, out = ‘’) -> N
I abs(target - :best) > abs(target - nbrs[0])
:best = nbrs[0]
:best_out = out
I target == nbrs[0]
print(out)
E I nbrs.len > 1
L(i1) 0 .< nbrs.len - 1
L(i2) i1 + 1 .< nbrs.len
V remains = nbrs[0 .< i1] [+] nbrs[i1 + 1 .< i2] [+] nbrs[i2 + 1 ..]
V (a, b) = (nbrs[i1], nbrs[i2])
I a > b
swap(&a, &b)
V res = b + a
V op = b‘ + ’a‘ = ’res‘ ; ’
sol(target, res [+] remains, out‘’op)
I b != a
res = b - a
op = b‘ - ’a‘ = ’res‘ ; ’
sol(target, res [+] remains, out‘’op)
I a != 1
res = b * a
op = b‘ * ’a‘ = ’res‘ ; ’
sol(target, res [+] remains, out‘’op)
I b % a == 0
res = Int(b / a)
op = b‘ / ’a‘ = ’res‘ ; ’
sol(target, res [+] remains, out‘’op)

sol(target, nbrs)
I best != target
print(‘Best solution ’String(best))
print(best_out)```
Output:
```100 + 6 = 106 ; 106 * 75 = 7950 ; 7950 * 3 = 23850 ; 23850 - 50 = 23800 ; 23800 / 25 = 952 ;
100 + 6 = 106 ; 106 * 3 = 318 ; 318 * 75 = 23850 ; 23850 - 50 = 23800 ; 23800 / 25 = 952 ;
100 + 6 = 106 ; 75 * 3 = 225 ; 225 * 106 = 23850 ; 23850 - 50 = 23800 ; 23800 / 25 = 952 ;
100 + 3 = 103 ; 103 * 75 = 7725 ; 7725 * 6 = 46350 ; 46350 / 50 = 927 ; 927 + 25 = 952 ;
100 + 3 = 103 ; 103 * 6 = 618 ; 618 * 75 = 46350 ; 46350 / 50 = 927 ; 927 + 25 = 952 ;
100 + 3 = 103 ; 75 * 6 = 450 ; 450 * 103 = 46350 ; 46350 / 50 = 927 ; 927 + 25 = 952 ;
100 + 3 = 103 ; 75 * 6 = 450 ; 450 / 50 = 9 ; 103 * 9 = 927 ; 927 + 25 = 952 ;
75 * 6 = 450 ; 450 / 50 = 9 ; 100 + 3 = 103 ; 103 * 9 = 927 ; 927 + 25 = 952 ;
75 * 6 = 450 ; 100 + 3 = 103 ; 450 * 103 = 46350 ; 46350 / 50 = 927 ; 927 + 25 = 952 ;
75 * 6 = 450 ; 100 + 3 = 103 ; 450 / 50 = 9 ; 103 * 9 = 927 ; 927 + 25 = 952 ;
75 * 3 = 225 ; 100 + 6 = 106 ; 225 * 106 = 23850 ; 23850 - 50 = 23800 ; 23800 / 25 = 952 ;
```

J

Brute force implementation:

```deck=: (25*1+i.4),2#1+i.10
deal=: 6&((?#){])@deck
targ=: 101+?@899
Pi=: ,~((#:I.@,)</~)i.
Va=: {{
ok=. I#~(= 1>.>.)u&".&>/y{~|:I=. Pi N=.#y
(N-1){."1 (y{~ok-."1~i.N),.<@(u expr)"1 ok{y
}}
Pa=: {{ if. 1<#;:y do. '(',y,')' else. y end. }}
expr=: {{ (Pa A),(;u`''),Pa B['A B'=.y }}
arith=: [:; <@(+Va, -Va, *Va, %Va,(-Va, %Va)@|.)"1
all=: {{ A#~x=".@>A=.~.,arith^:5 ":each y}}

echo 'terms: ',":c=. /:~ deal ''
echo 'target: ',":t=. targ ''
echo '#solutions: ',":#a=. t all c
echo 'for example: ',;{.a
}}
```

Examples:

```   task''
terms: 2 3 3 6 9 50
target: 476
#solutions: 77
for example: (9*(3+50))-(6-(2+3))
terms: 1 4 6 7 8 9
target: 657
#solutions: 75
for example: 9*(8+((1+4)*(6+7)))
terms: 4 7 8 9 10 10
target: 300
#solutions: 495
for example: (10+(9*10))*((4+7)-8)
```

Julia

Brute force with a somewhat narrowed search space.

```using Combinatorics

const max_pick = 6
const fulllist = [1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 25, 50, 75, 100]
const oplist = [+, +, +, +, +, +,  -, -, -, -, -, -,  *, *, *, *, *, *, ÷, ÷, ÷, ÷, ÷, ÷]

function single_countdown_game(ilist, target)
candidates = [(0, "")]
for i in 1:max_pick, arr in permutations(ilist, i), ops in multiset_permutations(oplist, length(arr) - 1)
candidate = arr[1]
if !isempty(ops)
for (j, op) in pairs(ops)
((op == ÷) && candidate % arr[j + 1] != 0) && @goto nextops
candidate = op(candidate, arr[j + 1])
end
end
if abs(candidate - target) <= abs(candidates[1][1] - target)
if abs(candidate - target) < abs(candidates[1][1] - target)
empty!(candidates)
end
sops = push!(map(string, ops), "")
push!(candidates, (candidate, prod(" \$(arr[i]); \$(sops[i])" for i in eachindex(arr))))
end
@label nextops
end
return unique(candidates)
end

for (terms, target) in [([2, 3, 3, 6, 9, 50], 476), ([1, 4, 6, 7, 8, 9], 657), ([4, 7, 8, 9, 10, 10], 300)]
sols = single_countdown_game(terms, target)
println("\$(length(sols)) solutions for terms \$terms, target \$target.")
println("  Example: \$(sols[1][2])= \$(sols[1][1])\n")
end
```
Output:
```24 solutions for terms [2, 3, 3, 6, 9, 50], target 476.
Example:  3; + 50; * 9; + 2; - 3; = 476

42 solutions for terms [1, 4, 6, 7, 8, 9], target 657.
Example:  4; + 6; * 8; - 7; * 9; = 657

223 solutions for terms [4, 7, 8, 9, 10, 10], target 300.
Example:  7; - 4; * 10; * 10; = 300
```

Nim

Here is, with some minor modifications, a program I already wrote to solve this game. It gets the six values and the target value from the command line.

The program uses brute force, but no recursion, to find one of the best solutions.

```import std/[os, strutils, tables]

type
Operator = enum opAdd = "+", opSub = "-", opMul = "×", opDiv = "/", opNone = ""
Operation = tuple[op1, op2: int; op: Operator; r: int]

func result(values: seq[int]; target: int): tuple[val: int; ops: seq[Operation]] =

type Results = Table[seq[int], seq[Operation]]

var results: Results
results[values] = @[]
var terminated = false
while not terminated:
terminated = true
var next: Results
for vals, ops in results:
var v1 = vals
for i1, val1 in vals:
v1.delete i1
var v2 = v1
for i2, val2 in v1:
v2.delete i2
let newVal = case op
of opSub: (if val1 > val2: val1 - val2 else: 0)
of opMul: val1 * val2
of opDiv: (if val1 mod val2 == 0: val1 div val2 else: 0)
of opNone: val1
if newVal > 0:
if v2.len > 1: terminated = false
let newOps = if op != opNone: ops & (val1, val2, op, newVal) else: ops
if v2 notin next or newOps.len < next[v2].len:
next[v2] = newOps
v2 = v1
v1 = vals
results = move next

var best = int.high
var bestOps: seq[Operation]
for vals, ops in results:
let val = vals[0]
if val == target: return (val, ops)
if abs(val - target) < abs(best - target):
best = val
bestOps = ops
result = (best, bestOps)

let params = commandLineParams()
if params.len != 7:
quit "Six values + the target value are expected.", QuitFailure
var values: seq[int]
for param in params:
var val: int
try:
val = parseInt(param)
if val <= 0:
raise newException(ValueError, "")
except ValueError:
quit "Wrong value: " & param, QuitFailure

let target = values.pop()
let (val, ops) = result(values, target)
echo "Target value: ", target
echo "Nearest value computed: ", val
echo "Operations:"
for (op1, op2, op, r) in ops:
echo "  ", op1, " ", op, " ", op2, " = ", r
```
Output:

Using command `./countdown 3 6 25 50 75 100 952`, we get the following result:

```Target value: 952
Nearest value computed: 952
Operations:
6 + 100 = 106
3 × 75 = 225
106 × 225 = 23850
23850 - 50 = 23800
23800 / 25 = 952
```

Perl

Translation of: Raku
```use v5.36;
use builtin 'indexed';
use experimental qw(builtin for_list);

sub countdown (\$target, @numbers) {
return 0 if 1 == scalar(@numbers);

for my (\$n0k,\$n0v) (indexed @numbers) {
my @nums1 = @numbers;
splice(@nums1,\$n0k,1);
for my(\$n1k,\$n1v) (indexed @nums1) {
my @nums2 = @nums1;
splice(@nums2,\$n1k,1);
my @numsNew;
if (\$n1v >= \$n0v) {
@numsNew = @nums2;
push @numsNew, my \$res = \$n1v + \$n0v;
if (\$res == \$target or countdown(\$target, @numsNew)) {
say "\$res = \$n1v + \$n0v" and return 1
}
if (\$n0v != 1) {
@numsNew = @nums2;
push @numsNew, my \$res = \$n1v * \$n0v;
if (\$res == \$target or countdown(\$target, @numsNew)) {
say "\$res = \$n1v * \$n0v" and return 1
}
}
if (\$n1v != \$n0v) {
@numsNew = @nums2;
push @numsNew, my \$res = \$n1v - \$n0v;
if (\$res == \$target or countdown(\$target, @numsNew)) {
say "\$res = \$n1v - \$n0v" and return 1
}
}
if (\$n0v != 1 and 0==(\$n1v%\$n0v)) {
@numsNew = @nums2;
push @numsNew, my \$res = int(\$n1v / \$n0v);
if (\$res == \$target or countdown(\$target, @numsNew)) {
say "\$res = \$n1v / \$n0v" and return 1
}
}
}
}
}
return 0
}

my @numbersList = ([3,6,25,50,75,100], [100,75,50,25,6,3], [8,4,4,6,8,9]);
my @targetList  =  <952                 952                 594>;

for my \$i (0..2) {
my \$numbers = \$numbersList[\$i];
say "Using : ", join ' ', @\$numbers;
say "Target: ", my \$target  = \$targetList[\$i];
say "No exact solution found" unless countdown(\$target, @\$numbers);
say '';
}
```
Output:
```Using : 3 6 25 50 75 100
Target: 952
952 = 23800 / 25
23800 = 23850 - 50
23850 = 225 * 106
106 = 100 + 6
225 = 75 * 3

Using : 100 75 50 25 6 3
Target: 952
952 = 23800 / 25
23800 = 23850 - 50
23850 = 7950 * 3
7950 = 106 * 75
106 = 100 + 6

Using : 8 4 4 6 8 9
Target: 594
594 = 66 * 9
66 = 64 + 2
64 = 16 * 4
2 = 6 - 4
16 = 8 + 8
```

Phix

```--
-- demo/Countdown.exw
--
-- solves the numbers game from countdown.
--
with javascript_semantics
constant n = 6,
ops = "+-*/"

sequence chosen = repeat(0,n), -- original numbers <-> partial sums
expression = repeat(0,n), -- the operations tried so far
solution -- (a/best snapshot of expression)

int len,    -- n+1 means no solution yet found
maxlev, -- recursion limit (5, drops as solns found)
near,   -- nearest answer (in solution) out by this
lenn,   -- length of ""         ""
target

procedure countdown(int level=1)
--
-- Recursive search - takes two numbers, performs an op (storing result), checks
-- for target value, and calls itself. All solutions are stored, to find shortest,
-- so that, for example, 100+1 is chosen instead of 100+(75/25)-1-1.
-- Optimizations are made to ensure commutative operations are only performed one
-- way round, division is only performed when no remainder, and */1 are skipped.
--
for i=1 to n do
integer sti = chosen[i] -- speedwise/save
if sti!=0 then
for j=1 to n do
integer stj = chosen[j] -- ""
if i!=j and stj!=0 then
if (operation<DIV or mod(sti,stj)=0)
and (operation<MUL or stj!=1)
and (sti>=stj) then
-- worth doing...
integer ci = sti
switch operation do
case SUB: ci -= stj
case MUL: ci *= stj
case DIV: ci /= stj
end switch
chosen[i] = ci
chosen[j] = 0
/* store operands and operator */
expression[level] = {sti,ops[operation],stj,ci}

-- check for solution
if ci==target then
if level<len then
/* solution is shortest so far - store it */
len = level
maxlev = level-1
near = 0
solution = deep_copy(expression)
end if
else
--store closest?
integer offby = abs(target-ci)
if offby<near then
near = offby
lenn = level
solution = deep_copy(expression)
end if
-- if not at required level, recurse
if level<maxlev then
countdown(level+1)
end if
end if
-- undo
chosen[i] = sti
chosen[j] = stj
end if
end for
end if
end for
end if
end for
end procedure

procedure test(sequence list, int dest)
len = n+1
maxlev = 5
near = dest
target = dest
chosen = deep_copy(list)
countdown()
/* process solution into printable form */
string off = "exact"
if len=n+1 then
off = sprintf("off by %d",near)
len = lenn
end if
string soln = join(apply(true,sprintf,{{"%d%c%d=%d"},solution[1..len]}),", ")
printf(1,"Target %d from %18v: %s (%s)\n",{dest,list,soln,off})
end procedure

atom t0 = time()
test({75,50,25,100,8,2},737)
test({3,6,25,50,75,100},952)
test({100,75,50,25,6,3},952)
test({50,100,4,2,2,4},203)
test({25,4,9,2,3,10},465)
test({9,8,10,5,9,7},241)
test({3,7,6,2,1,7},824)
test({75,50,25,100,8,2},125)
test({8,4,4,6,8,9},594)
test({2,4,9,10,3,5},363)
--test(shuffle(tagset(10)&tagset(10)&tagstart(25,4,25))[1..6],100+rand(899))
?time()-t0

{} = wait_key()
```
Output:
```Target 737 from {75,50,25,100,8,2}: 75/25=3, 50-3=47, 100-2=98, 98*8=784, 784-47=737 (exact)
Target 952 from {3,6,25,50,75,100}: 75*3=225, 100+6=106, 225*106=23850, 23850-50=23800, 23800/25=952 (exact)
Target 952 from {100,75,50,25,6,3}: 100+6=106, 106*75=7950, 7950*3=23850, 23850-50=23800, 23800/25=952 (exact)
Target 203 from   {50,100,4,2,2,4}: 50*4=200, 200+4=204, 2/2=1, 204-1=203 (exact)
Target 465 from    {25,4,9,2,3,10}: 25-10=15, 9*3=27, 27+4=31, 31*15=465 (exact)
Target 241 from     {9,8,10,5,9,7}: 9+9=18, 8+5=13, 18*13=234, 234+7=241 (exact)
Target 824 from      {3,7,6,2,1,7}: 7+3=10, 10*6=60, 60-1=59, 59*2=118, 118*7=826 (off by 2)
Target 125 from {75,50,25,100,8,2}: 75+50=125 (exact)
Target 594 from      {8,4,4,6,8,9}: 8*8=64, 64-4=60, 60+6=66, 66*9=594 (exact)
Target 363 from     {2,4,9,10,3,5}: 9*4=36, 36*10=360, 360+3=363 (exact)
1.797
```

Prolog

```/* given numbers & target */

n(100,1). n(75,2). n(50,3). n(25,4). n(6,5). n(3,6).
ok(Res) :- Res = 952.

/* four operations with strictly positive integers and N1 >= N2 */

r(N1,N2,Res,'+') :-                         Res is N1 + N2.
r(N1,N2,Res,'-') :- N1 > N2,                Res is N1 - N2.
r(N1,N2,Res,'*') :- N2 > 1,                 Res is N1 * N2.
r(N1,N2,Res,'/') :- N2 > 1, 0 is N1 mod N2, Res is N1 div N2.

/* concatenation */

concaten([],L,L).
concaten([H|L1],L2,[H|L3]) :- concaten(L1,L2,L3).

/* four operations & print solution management */

ra(N1,N2,Res,Lout1,Lout2,NewLout) :-
concaten(Lout1,Lout2,Lout),
N1 >= N2,
r(N1,N2,Res,Ope),
concaten(Lout,[N1,Ope,N2,Res|[]],NewLout).

/* print result */

lout([]) :- nl.
lout([N1,Ope,N2,Res|Queue]) :-
out(N1,Ope,N2,Res),
lout(Queue).
out(N1,Ope,N2,Res) :-
write(N1), write(Ope), write(N2), write('='), write(Res), nl.

/* combine two last numbers & result control */

c(N1,N2,Lout1,Lout2) :-
ra(N1,N2,Res,Lout1,Lout2,NewLout),
ok(Res),
lout(NewLout).

/* unique list */

uniqueList([]).
uniqueList([H|T]) :- \+(member(H,T)), uniqueList(T).

/* all possible arrangements */

c1 :-
n(Nb,_),                                             /* a                  */
ok(Nb),
write(Nb).

c2 :-
n(N1,I1), n(N2,I2),                                  /* (ab)               */
I1\=I2,
c(N1,N2,[],[]).

c3 :-
n(N1,I1), n(N2,I2), n(N3,I3),
I1\=I2, I1\=I3, I2\=I3,
ra(N1,  N2,  Res1,[],   [],   Lout1),            /* (ab) c             */
c(Res1,N3,       Lout1,[]).

c4 :-
n(N1,I1), n(N2,I2), n(N3,I3), n(N4,I4),
uniqueList([I1,I2,I3,I4]),
ra(N1,  N2,  Res1,[],   [],   Lout1),            /* (ab) (cd)          */
((  ra(N3,  N4,  Res2,[],   [],   Lout2),
c(Res1,Res2,     Lout1,Lout2));                 /* ((ab) c) d         */
(   ra(Res1,N3,  Res2,Lout1,[],   Lout2),
c(Res2,N4,       Lout2,[]))).

c5 :-
n(N1,I1), n(N2,I2), n(N3,I3), n(N4,I4), n(N5,I5),
uniqueList([I1,I2,I3,I4,I5]),
ra(N1,  N2,  Res1,[],   [],   Lout1),            /* ((ab) (cd)) e      */
((  ra(N3,  N4,  Res2,[],   [],   Lout2),
ra(Res1,Res2,Res3,Lout1,Lout2,Lout3),
c(Res3,N5,       Lout3,[]));                    /* ((ab) c) (de)      */
(   ra(Res1,N3,  Res2,Lout1,[],   Lout2),
ra(N4,  N5,  Res3,[],   [],   Lout3),
c(Res2,Res3,     Lout2,Lout3));                 /* (((ab) c) d) e     */
(   ra(Res1,N3,  Res2,Lout1,[],   Lout2),
ra(Res2,N4,  Res3,Lout2,[],   Lout3),
c(Res3,N5,       Lout3,[]))).

c6 :-
n(N1,I1), n(N2,I2), n(N3,I3), n(N4,I4), n(N5,I5), n(N6,I6),
uniqueList([I1,I2,I3,I4,I5,I6]),
ra(N1,  N2,  Res1,[],   [],   Lout1),            /* ((ab) (cd)) (ef)   */
((  ra(N3,  N4,  Res2,[],   [],   Lout2),
ra(Res1,Res2,Res3,Lout1,Lout2,Lout3),
ra(N5,  N6,  Res4,[],   [],   Lout4),
c(Res3,Res4,     Lout3,Lout4));                 /* ((ab) c) ((de) f)  */
(   ra(Res1,N3,  Res2,Lout1,[],   Lout2),
ra(N4,  N5,  Res3,[],   [],   Lout3),
ra(Res3,N6,  Res4,Lout3,[],   Lout4),
c(Res2,Res4,     Lout2,Lout4));                 /* (((ab) c) d) (ef)  */
(   ra(Res1,N3,  Res2,Lout1,[],   Lout2),
ra(Res2,N4,  Res3,Lout2,[],   Lout3),
ra(N5,  N6,  Res4,[],   [],   Lout4),
c(Res3,Res4,     Lout3,Lout4));                 /* ((((ab) c) d) e) f */
(   ra(Res1,N3,  Res2,Lout1,[],   Lout2),
ra(Res2,N4,  Res3,Lout2,[],   Lout3),
ra(Res3,N5,  Res4,Lout3,[],   Lout4),
c(Res4,N6,       Lout4,[]))).

/* solution */

solution :- c1 ; c2 ; c3 ; c4 ; c5 ; c6.
```
Output:
```100+6=106
106*75=7950
7950*3=23850
23850-50=23800
23800/25=952

yes
```

Python

```best = 0
best_out = ""
target = 952
nbrs = [100, 75, 50, 25, 6, 3]

def sol(target, nbrs, out=""):
global best, best_out
if abs(target - best) > abs(target - nbrs[0]):
best = nbrs[0]
best_out = out
if target == nbrs[0]:
print(out)
elif len(nbrs) > 1:
for i1 in range(0, len(nbrs)-1):
for i2 in range(i1+1, len(nbrs)):
remains = nbrs[:i1] + nbrs[i1+1:i2] + nbrs[i2+1:]
a, b = nbrs[i1], nbrs[i2]
if a > b: a, b = b, a
res = b + a
op = str(b) + " + " + str(a) + " = " + str(res) + " ; "
sol(target, [res] + remains, out + op)
if b != a:
res = b - a
op = str(b) + " - " + str(a) + " = " + str(res) + " ; "
sol(target, [res] + remains, out + op)
if a != 1:
res = b * a
op = str(b) + " * " + str(a) + " = " + str(res) + " ; "
sol(target, [res] + remains, out + op)
if b % a == 0:
res = int(b / a)
op = str(b) + " / " + str(a) + " = " + str(res) + " ; "
sol(target, [res] + remains, out + op)

sol(target, nbrs)
if best != target:
print("Best solution " + str(best))
print(best_out)
```
Output:
```100 + 6 = 106 ; 106 * 75 = 7950 ; 7950 * 3 = 23850 ; 23850 - 50 = 23800 ; 23800 / 25 = 952 ;
100 + 6 = 106 ; 106 * 3 = 318 ; 318 * 75 = 23850 ; 23850 - 50 = 23800 ; 23800 / 25 = 952 ;
100 + 6 = 106 ; 75 * 3 = 225 ; 225 * 106 = 23850 ; 23850 - 50 = 23800 ; 23800 / 25 = 952 ;
100 + 3 = 103 ; 103 * 75 = 7725 ; 7725 * 6 = 46350 ; 46350 / 50 = 927 ; 927 + 25 = 952 ;
100 + 3 = 103 ; 103 * 6 = 618 ; 618 * 75 = 46350 ; 46350 / 50 = 927 ; 927 + 25 = 952 ;
100 + 3 = 103 ; 75 * 6 = 450 ; 450 * 103 = 46350 ; 46350 / 50 = 927 ; 927 + 25 = 952 ;
100 + 3 = 103 ; 75 * 6 = 450 ; 450 / 50 = 9 ; 103 * 9 = 927 ; 927 + 25 = 952 ;
75 * 6 = 450 ; 450 / 50 = 9 ; 100 + 3 = 103 ; 103 * 9 = 927 ; 927 + 25 = 952 ;
75 * 6 = 450 ; 100 + 3 = 103 ; 450 * 103 = 46350 ; 46350 / 50 = 927 ; 927 + 25 = 952 ;
75 * 6 = 450 ; 100 + 3 = 103 ; 450 / 50 = 9 ; 103 * 9 = 927 ; 927 + 25 = 952 ;
75 * 3 = 225 ; 100 + 6 = 106 ; 225 * 106 = 23850 ; 23850 - 50 = 23800 ; 23800 / 25 = 952 ;
```

Quorum

```use Libraries.Containers.List
use Libraries.Containers.Iterator
use Libraries.System.DateTime

action Main
DateTime datetime
number start = datetime:GetEpochTime()
List<integer> numbers
if not Solution(952,numbers)
output "No exact solution found."
end
number stop = datetime:GetEpochTime()
output stop-start + " ms"
end

action Solution(integer target, List<integer> numbers) returns boolean
if numbers:GetSize() > 1
// All couple of numbers
Iterator<integer> it0 = numbers:GetIterator()
repeat while it0:HasNext()
integer n0 = it0:Next()
List<integer> numbers1 = cast(List<integer>, numbers:Copy())
numbers1:Remove(n0)
Iterator<integer> it1 = numbers1:GetIterator()
repeat while it1:HasNext()
integer n1 = it1:Next()
List<integer> numbers2 = cast(List<integer>, numbers1:Copy())
numbers2:Remove(n1)
// All four operations
integer res = 0
List<integer> numbersNew
if n1 >= n0 // Both case are generated
res = n1 + n0
numbersNew = cast(List<integer>, numbers2:Copy())
if res = target or Solution(target, numbersNew)
output res + " = " + n1 + " + " + n0
return true
end
if n0 not= 1
res = n1 * n0
numbersNew = cast(List<integer>, numbers2:Copy())
if res = target or Solution(target, numbersNew)
output res + " = " + n1 + " * " + n0
return true
end
end
if n1 not= n0
res = n1 - n0
numbersNew = cast(List<integer>, numbers2:Copy())
if res = target or Solution(target, numbersNew)
output res + " = " + n1 + " - " + n0
return true
end
end
if n0 not= 1 and n1 mod n0 = 0
res = n1 / n0
numbersNew = cast(List<integer>, numbers2:Copy())
if res = target or Solution(target, numbersNew)
output res + " = " + n1 + " / " + n0
return true
end
end
end // n1 >= n0
end // it1
end // it0
end // if numbers:GetSize() > 1
return false
end```
Output:
```952 = 23800 / 25
23800 = 23850 - 50
23850 = 225 * 106
225 = 3 * 75
106 = 6 + 100
218.0 ms
```

Raku

Translation of: Wren
```# 20221021 Raku programming solution

sub countdown (\$target, @numbers) {
return False if @numbers.elems == 1;
for @numbers.kv -> \n0k,\n0v {
(my @nums1 = @numbers).splice(n0k,1);
for @nums1.kv -> \n1k,\n1v {
(my @nums2 = @nums1).splice(n1k,1);
if n1v >= n0v {
(my @numsNew = @nums2).append: my \$res = n1v + n0v;
if (\$res == \$target or countdown(\$target, @numsNew)) {
say "\$res = ",n1v,' + ',n0v andthen return True
}
if n0v != 1 {
(my @numsNew = @nums2).append: my \$res = n1v * n0v;
if (\$res == \$target or countdown(\$target, @numsNew)) {
say "\$res = ",n1v,' * ',n0v andthen return True
}
}
if n1v != n0v {
(my @numsNew = @nums2).append: my \$res = n1v - n0v;
if (\$res == \$target or countdown(\$target, @numsNew)) {
say "\$res = ",n1v,' - ',n0v andthen return True
}
}
if n0v != 1 and n1v %% n0v {
(my @numsNew = @nums2).append: my \$res = n1v div n0v;
if (\$res == \$target or countdown(\$target, @numsNew)) {
say "\$res = ",n1v,' / ',n0v andthen return True
}
}
}
}
}
return False
}

my @allNumbers  = < 1 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 9 9 10 10 25 50 75 100 >;
my @numbersList = <3 6 25 50 75 100>  ,   <100 75 50 25 6 3>,
<8 4 4 6 8 9>       ,   @allNumbers.pick(6);
my @targetList  = 952, 952, 594, (101..1000).pick;

for (0..^+@numbersList) -> \i {
say "Using : ", my @numbers = |@numbersList[i];
say "Target: ", my \$target  = @targetList[i];
say "No exact solution found" unless countdown \$target, @numbers;
say()
}
```
Output:
```Using : [3 6 25 50 75 100]
Target: 952
952 = 23800 / 25
23800 = 23850 - 50
23850 = 225 * 106
106 = 100 + 6
225 = 75 * 3

Using : [100 75 50 25 6 3]
Target: 952
952 = 23800 / 25
23800 = 23850 - 50
23850 = 7950 * 3
7950 = 106 * 75
106 = 100 + 6

Using : [8 4 4 6 8 9]
Target: 594
594 = 66 * 9
66 = 64 + 2
64 = 16 * 4
2 = 6 - 4
16 = 8 + 8

Using : [100 9 50 2 9 8]
Target: 599
599 = 590 + 9
590 = 59 * 10
10 = 8 + 2
59 = 109 - 50
109 = 100 + 9```

Rebol

```REBOL [
Title: "CountDown"
Date: 1-May-2008
]

target: 952
list: [ 3 6 25 50 75 100 ]

op: [+ - * /]
sb: func[x y][x - y]
ml: func[x y][if error? try [return x * y][0]]
dv: func[x y][either (x // y) = 0 [x / y][0]]
calculs: func[x y][make block! [(ad x y) (sb x y) (ml x y) (dv x y)]]
nwlist: func[list j i res][sort append head remove at head remove at copy list j i res]

sol: function[list size][ol][
for i 1 (size - 1) 1 [
for j (i + 1) size 1 [
ol: reduce calculs list/:j list/:i
for k 1 4 1 [
if any [(ol/:k = target) all [(ol/:k <> 0) (size > 1) (s: sol (nwlist list j i ol/:k) (size - 1))]] [
return rejoin [list/:j op/:k list/:i "=" ol/:k newline s]
] ] ] ]
return false
]

print rejoin [ceb list length? list]
```
Output:
```75*3=225
100+6=106
225*106=23850
23850-50=23800
23800/25=952
false
```

Scala

Translation of: Python
Library: Scala

My son made this translation for me.

```var best = 0
var best_out = ""
val target = 952
val nbrs = List(100, 75, 50, 25, 6, 3)

def sol(target: Int, xs: List[Int], out: String): Unit = {
if ((target - best).abs > (target - xs.head).abs) {
best_out = out
}
println(out)
else
0 until (xs.size-1) foreach { i1 =>
(i1+1) until xs.size foreach { i2 =>
val remains = xs.patch(i2, Nil, 1).patch(i1, Nil, 1)
val (n1, n2) = (xs(i1), xs(i2))
val (a, b) = (n1 min n2, n1 max n2)
def loop(res: Int, op: Char) =
sol(target, res :: remains, s"\$out\$b \$op \$a = \$res ; ")
loop(b + a, '+')
if (b != a)
loop(b - a, '-')
if (a != 1) {
loop(b * a, '*')
if (b % a == 0)
loop(b / a, '/')
}
}
}
}

sol(target, nbrs, "")
if (best != target) {
println("Best solution " + best)
println(best_out)
}
```
Output:
```100 + 6 = 106 ; 106 * 75 = 7950 ; 7950 * 3 = 23850 ; 23850 - 50 = 23800 ; 23800 / 25 = 952 ;
100 + 6 = 106 ; 106 * 3 = 318 ; 318 * 75 = 23850 ; 23850 - 50 = 23800 ; 23800 / 25 = 952 ;
100 + 6 = 106 ; 75 * 3 = 225 ; 225 * 106 = 23850 ; 23850 - 50 = 23800 ; 23800 / 25 = 952 ;
100 + 3 = 103 ; 103 * 75 = 7725 ; 7725 * 6 = 46350 ; 46350 / 50 = 927 ; 927 + 25 = 952 ;
100 + 3 = 103 ; 103 * 6 = 618 ; 618 * 75 = 46350 ; 46350 / 50 = 927 ; 927 + 25 = 952 ;
100 + 3 = 103 ; 75 * 6 = 450 ; 450 * 103 = 46350 ; 46350 / 50 = 927 ; 927 + 25 = 952 ;
100 + 3 = 103 ; 75 * 6 = 450 ; 450 / 50 = 9 ; 103 * 9 = 927 ; 927 + 25 = 952 ;
75 * 6 = 450 ; 450 / 50 = 9 ; 100 + 3 = 103 ; 103 * 9 = 927 ; 927 + 25 = 952 ;
75 * 6 = 450 ; 100 + 3 = 103 ; 450 * 103 = 46350 ; 46350 / 50 = 927 ; 927 + 25 = 952 ;
75 * 6 = 450 ; 100 + 3 = 103 ; 450 / 50 = 9 ; 103 * 9 = 927 ; 927 + 25 = 952 ;
75 * 3 = 225 ; 100 + 6 = 106 ; 225 * 106 = 23850 ; 23850 - 50 = 23800 ; 23800 / 25 = 952 ;
```

Wren

Translation of: Quorum
Library: Wren-fmt
```import "random" for Random
import "./fmt" for Fmt

var countdown // recursive function
countdown = Fn.new { |target, numbers|
if (numbers.count == 1) return false
for (n0 in numbers) {
var nums1 = numbers.toList
nums1.remove(n0)
for (n1 in nums1) {
var nums2 = nums1.toList
nums2.remove(n1)
if (n1 >= n0) {
var res = n1 + n0
var numsNew = nums2.toList
if (res == target || countdown.call(target, numsNew)) {
Fmt.print("\$d = \$d + \$d", res, n1, n0)
return true
}
if (n0 != 1) {
res = n1 * n0
numsNew = nums2.toList
if (res == target || countdown.call(target, numsNew)) {
Fmt.print("\$d = \$d * \$d", res, n1, n0)
return true
}
}
if (n1 != n0) {
res = n1 - n0
numsNew = nums2.toList
if (res == target || countdown.call(target, numsNew)) {
Fmt.print("\$d = \$d - \$d", res, n1, n0)
return true
}
}
if (n0 != 1 && n1 % n0 == 0) {
res = (n1/n0).truncate
numsNew = nums2.toList
if (res == target || countdown.call(target, numsNew)) {
Fmt.print("\$d = \$d / \$d", res, n1, n0)
return true
}
}
}
}
}
return false
}

var allNumbers = [1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 25, 50, 75, 100]
var rand = Random.new()
var numbersList = [
[3, 6, 25, 50, 75, 100],
[100, 75, 50, 25, 6, 3], // see if there's much difference if we reverse the first example
[8, 4, 4, 6, 8, 9],
rand.sample(allNumbers, 6)
]
var targetList = [952, 952, 594, rand.int(101, 1000)]
for (i in 0...numbersList.count) {
System.print("Using : %(numbersList[i])")
System.print("Target: %(targetList[i])")
var start = System.clock
var done = countdown.call(targetList[i], numbersList[i])
System.print("Took %(((System.clock - start) * 1000).round) ms")
if (!done) System.print("No exact solution found")
System.print()
}
```
Output:

Sample output (as the fourth example is random):

```Using : [3, 6, 25, 50, 75, 100]
Target: 952
952 = 23800 / 25
23800 = 23850 - 50
23850 = 225 * 106
106 = 100 + 6
225 = 75 * 3
Took 173 ms

Using : [100, 75, 50, 25, 6, 3]
Target: 952
952 = 23800 / 25
23800 = 23850 - 50
23850 = 7950 * 3
7950 = 106 * 75
106 = 100 + 6
Took 378 ms

Using : [8, 4, 4, 6, 8, 9]
Target: 594
594 = 66 * 9
66 = 64 + 2
64 = 16 * 4
2 = 6 - 4
16 = 8 + 8
Took 2 ms

Using : [7, 2, 1, 8, 5, 3]
Target: 436
436 = 109 * 4
109 = 112 - 3
4 = 5 - 1
112 = 56 * 2
56 = 8 * 7
Took 11 ms
```