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What is the maximum number of Amazons that can be placed on a 5x5 chessboard so that no piece attacks another? Question
An Amazon is a fairy chess piece that can move like a queen or a knight.
What is the maximum number of Amazons that can be placed on a 5x5 chessboard so that no piece attacks another?
Attribution:
Puzzle: me
Image of Amazon: Wikipedia
1 answer
The following users marked this post as Works for me:
| User | Comment | Date |
|---|---|---|
| will.octagon.gibson | (no comment) | Jul 31, 2026 at 12:40 |
Answer
4 amazons.Achieving the claimed result
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The claimed result is optimal
If we have five amazons then every rank and file must have one. Consider the central file. Up to symmetry there are three squares where we can place an amazon, and each of them permits at most two more non-attacking amazons.
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Comments
The solution is unique up to symmetries of the square.
I'm not certain where I saw this problem first: I think it was MathOverflow, but I can't find the relevant Q&A. A mathematical resource on non-attacking chess and fairy chess pieces is Kotěšovec, Non-attacking chess pieces (see section 7.1 for amazons, although it is slightly misleading on this particular problem).
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