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Pascal's triangle/Puzzle: Difference between revisions
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[18, 0, 73]
</lang>
=={{header|Ruby}}==
<lang ruby># uses [[Reduced row echelon form#Ruby]]
require 'rref'
pyramid = [
[ 151],
[nil,nil],
[40,nil,nil],
[nil,nil,nil,nil],
["x", 11,"y", 4,"z"]
]
p pyramid
equations = [[1,-1,1,0]] # y = x + z
def parse_equation(str)
eqn = [0] * 4
lhs, rhs = str.split("=")
eqn[3] = rhs.to_i
for term in lhs.split("+")
case term
when "x": eqn[0] += 1
when "y": eqn[1] += 1
when "z": eqn[2] += 1
else eqn[3] -= term.to_i
end
end
eqn
end
-2.downto(-5) do |row|
pyramid[row].each_index do |col|
val = pyramid[row][col]
sum = "%s+%s" % [pyramid[row+1][col].to_s, pyramid[row+1][col+1].to_s]
if val.nil?
pyramid[row][col] = sum
else
equations << parse_equation(sum + "=#{val}")
end
end
end
reduced = convert_to(reduced_row_echelon_form(equations), :to_i)
for eqn in reduced
if eqn[0] == 1 and eqn[1] == 0 and eqn[2] == 0: x = eqn[3]
elsif eqn[0] == 0 and eqn[1] == 1 and eqn[2] == 0: y = eqn[3]
elsif eqn[0] == 0 and eqn[1] == 0 and eqn[2] == 1: z = eqn[3]
else
fail "no solution? #{equations.inspect} ==> #{reduced.inspect}"
end
end
puts "x == #{x}"
puts "y == #{y}"
puts "z == #{z}"
answer = []
for row in pyramid
answer << row.collect {|cell| eval cell.to_s}
end
p answer</lang>
<pre>[[151], [nil, nil], [40, nil, nil], [nil, nil, nil, nil], ["x", 11, "y", 4, "z"]]
x == 5
y == 13
z == 8
[[151], [81, 70], [40, 41, 29], [16, 24, 17, 12], [5, 11, 13, 4, 8]]</pre>
=={{header|Tcl}}==
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