The problem of list order

numbers.hs

import Data.List (delete)

squarable x = x `elem` [y^2 | y <- [2..x] ]

nexts x rest = foldr check [] rest
    where check v good = if squarable (x + v) then v:good
                                              else good

search ls [] = [ls]
search ls rs = nexts (last ls) rs >>= \v -> search (ls ++ [v]) (delete v rs)

result = search [16] [1..15]

main = putStrLn $ "Result: " ++ show result

def test(pool, res):
   for i in pool:
       if res[-1] != i and res[-1] + i in (4, 9, 16, 25):
           return i
   assert False

pool = list(reversed(range(1,16)))
res = [16,]
while pool:
   i = test(pool, res)
   pool.remove(i)
   res.append(i)