2026-09-22
Futoshiki is a Latin square: fill each row and column with 1–n exactly once. What makes it different from Sudoku is the inequality signs between cells — and beginners consistently under-use them. The signs aren't constraints to check at the end; they're the first thing to read.
Any cell that must be greater than a neighbour can never be 1. Any cell less than a neighbour can never be n (the grid size). That instantly prunes candidates. On a 5×5 grid, a cell with > on both sides is at least 3; a cell with < on both sides is at most 3.
Inequalities chain: if A > B > C > D on a 5×5 grid, then A is at least 4 and D is at most 2. A chain of length n forces the ends completely. Before you place a single digit, trace every chain on the board — the long ones solve themselves.
Once the inequalities restrict a row, count what's missing. If a row needs {1,4,5} in three cells and one cell can only be 1 (it must be less than a neighbour holding 2), that's a free placement. Every placement refreshes the scarcity counts for both its row and column.
Players get so absorbed in the signs they forget the base rule: no repeats in a row or column. When a candidate survives the inequality test, check it against the digits already placed in its row and column. A digit that satisfies the sign but duplicates a row entry is still wrong.
The whole game is one habit: inequalities first, scarcity second. Try it on Futoshiki, then take the same "greater/less than" instinct into Skyscraper, where the edge clues are really just inequalities about visibility.