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Eight Queens, No Truce

brainteaser
Place eight queens on a standard 8×8 chessboard. Every queen attacks along its row, its column, and both diagonals. Your placement must leave every pair of queens unable to attack each other. Count arrangements by exact square positions: rotating or reflecting a placement usually produces a different arrangement and should be counted separately. The board is fixed in place, with its rows and columns distinguished. Since no two queens may share a row, a successful arrangement necessarily has exactly one queen in each row. How many distinct valid arrangements are possible?

Hints

Hint 1
Hint 2
Hint 3

Solution

Commit an attempt to unseal the proof. Write your answer — right or wrong, thinking it through is the point.

How many valid eight-queen arrangements are there?

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