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-- Integer right triangles
--
-- Problem 39
-- If p is the perimeter of a right angle triangle with integral length sides,
-- {a,b,c}, there are exactly three solutions for p = 120.
--
-- {20,48,52}, {24,45,51}, {30,40,50}
--
-- For which value of p ≤ 1000, is the number of solutions maximised?
import Data.List(maximumBy)
-- 4m20s stucks
main = do
print (maximumBy (\(_, xs) (_, ys) -> compare (length xs) (length ys)) [
(p,
[(a, b, p - a - b) | a <- [1..p], b <- [1..(p-a)],
validRightTriangle a b (p - a - b)])
| p <- [1..1000]
])
validRightTriangle :: Int -> Int -> Int -> Bool
validRightTriangle a b c = a ^ 2 + b ^ 2 == c ^ 2
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