Place four black queens and one black bishop so every square on the board is under attack, leaving no safe square for a white king.
Key Takeaways
Attributed to Kempelen, creator of the 18th-century Mechanical Chess Player, framed as one of his hardest combinatorial problems.
Constraint: all 64 squares must be covered; the white king must have no legal placement anywhere on the board.
Only five pieces total, but the bishop’s color constraint and queen interaction make full coverage non-obvious.
The puzzle is interactive: drag or tap pieces onto the board, tap a placed piece to remove it.
Hacker News Comment Review
Brute-force enumeration found 388 total solutions; after removing rotational and reflective symmetry, only 49 distinct solutions exist, with 18 unique queen layouts and bishop placement varying 1-5 ways per layout.
Counterintuitive structure: some solutions cluster three queens on the same row, invalidating the instinct to spread queens across unique rows and columns for maximum reach.
A practical human strategy: place the first queen in a corner, then greedily place each next piece on the square with the most uncovered neighbors; the bishop fills gaps last.
Notable Comments
@tromp: flags a precise error in the puzzle wording: the correct term is “check” not “checkmate,” since a king adjacent to an unprotected queen can capture it.
@tiffanyh: ChatGPT solved it in 6 seconds; Claude Opus exhausted a full day’s token quota and failed.
