logic puzzle

puzzle.hs

#!/usr/bin/env nix-shell
#! nix-shell -p "ghc"
#! nix-shell -i "runghc"

-- https://www.zhihu.com/question/23999095/answer/2254625328

import Control.Monad (guard)

brain_states :: (Int, Int) -> [Int]
brain_states (x, y) = [z | z <- [x + y, abs(x - y)], z > 0]

unsure :: [a] -> Bool
unsure xs = length xs > 1

solution = do
    x <- [1..200]
    y <- [1..200]
    z <- [144]

    let info1 = \(x, y, z) -> unsure (brain_states (y, z))
    let info2 = \(x, y, z) -> unsure ([y | y <- brain_states (x, z), info1 (x, y, z)])
    let info3 = \(x, y, z) -> unsure ([z | z <- brain_states (x, y), info1 (x, y, z), info2 (x, y, z)])
    let info4 = \(x, y, z) -> unsure ([x | x <- brain_states (y, z), info2 (x, y, z), info3 (x, y, z)])
    let info5 = \(x, y, z) -> unsure ([y | y <- brain_states (x, z), info1 (x, y, z), info3 (x, y, z), info4 (x, y, z)])
    let info6 = \(x, y, z) -> ([z | z <- brain_states (x, y), info1 (x, y, z), info2 (x, y, z), info4 (x, y, z), info5 (x, y, z)]) == [144]

    guard $ info1 (x, y, z)
    guard $ info2 (x, y, z)
    guard $ info3 (x, y, z)
    guard $ info4 (x, y, z)
    guard $ info5 (x, y, z)
    guard $ info6 (x, y, z)

    pure (x, y, z)

main = print solution