How to solve Queens

How to solve Queens: techniques that work

Start with the smallest color region. A region that only spans one row or one column must hold its crown there, which immediately bans that row or column for every other region. This "region forcing" move is the engine of most Queens solves: each placement removes a row, a column and a color from the pool, so the puzzle shrinks fast.

When a region's remaining cells all sit in the same row (or column) — even if the region is larger — you can still cross that row off for everyone else. You don't need to know which exact cell the crown lands on to use the information.

Around every placed crown, mark the eight surrounding cells as impossible. The no-touching rule is stricter than chess: two crowns can never be orthogonally or diagonally adjacent, even across region borders. Combine this with a pigeonhole count — if three regions only have cells left in the same two rows, something upstream is wrong — and you can solve every board without guessing.

Common mistakes

The classic error is reading Queens as chess: crowns here do not attack along whole diagonals, only the eight neighbouring cells are forbidden. Players eliminate far too many cells and conclude the board is broken.

The second is guessing early. Every board we generate has exactly one solution reachable by pure deduction, so a dead end always means a missed forcing move — usually a one-row region you haven't noticed.

From easy to hard

Easy boards are small with chunky regions, so region forcing does most of the work. Hard boards stretch regions across many rows, forcing you to chain several eliminations before the first crown is safe to place. If you time yourself, sub-two-minutes on hard is a genuinely strong result.