msp729 · November 8, 2023 16:46 · Nov 8, 2023
diff --git a/Main.hs b/Main.hs
@@ -0,0 +1,43 @@
+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
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