module Main (main) where

import Text.Printf (printf)

lq :: [(Int, Int)]
lq = [(i, 10 - i) | i <- [1 .. 9]]

lqjk :: [(Int, Int, Int, Int)]
lqjk = do
    (l, q) <- lq -- take l and q values from the lq list
    jpk <- [9 - l, 18 - l] -- the sum of j and k
    (j, k) <- [(i, jpk - i) | i <- [1 .. min 9 jpk]] -- possible values of j and k
    if 8 * l + 9 /= 10 * j + k -- if the equality is not satisfied
        then [] -- we do not have a solution
        else return (l, q, j, k) -- otherwise, success!

xyzlqjk :: [(Int, Int, Int, Int, Int, Int, Int)]
xyzlqjk = do
    (l, q, j, k) <- lqjk
    let zyx = 3 * (10 * l + q)
    let (zy, x) = divMod zyx 10
    let (z, y) = divMod zy 10
    if z > 0 && z < 10 -- making sure that there is a third digit and not a fourth one
        then [(x, y, z, l, q, j, k)] -- it's an actual three-digit number :)
        else [] -- :(

xyzprlqjk :: [(Int, Int, Int, Int, Int, Int, Int, Int, Int)]
xyzprlqjk = do
    (x, y, z, l, q, j, k) <- xyzlqjk
    let pqr = 6 * (10 * l + q)
    let (pq, r) = divMod pqr 10
    let (p, q) = divMod pq 10
    if p > 0 && p < 10 -- same thing, just need to guarantee that PQR is, in fact, a three-digit number
        then [(x, y, z, p, r, l, q, j, k)]
        else []

main :: IO ()
main = sequence_ $ do
    (x, y, z, p, r, l, q, j, k) <- xyzprlqjk -- take every possible collection of values
    if 100 * z + 10 * y + x /= 3 * (10 * l + q) then [] -- if ZYX/3 ≠ LQ, we do not have a solution
    else if 100 * p + 10 * q + r /= 6 * (10 * l + q) then [] -- if PQR/6 ≠ LQ, same issue
    else if 100 * j + 10 * k + l /= 9 * (10 * l + q) then [] -- again with JKL/9 ≠ LQ; these checks shuold be redundant
    else return $ printf "%d%d%d / 3 = %d%d%d / 6 = %d%d%d / 9 = %d%d" z y x p q r j k l l q -- but i don't want to report fake solutions