Welcome to the staging ground for new communities! Each proposal has a description in the "Descriptions" category and a body of questions and answers in "Incubator Q&A". You can ask questions (and get answers, we hope!) right away, and start new proposals.
Are you here to participate in a specific proposal? Click on the proposal tag (with the dark outline) to see only posts about that proposal and not all of the others that are in progress. Tags are at the bottom of each post.
Post History
Answer4 amazons. Achieving the claimed result .A... ....A ..... A.... ...A. The claimed result is optimal If we have five amazons then every rank and file must have one. Consider the c...
#2: Post edited
by
trichoplax
·
2026-08-01T16:29:16Z (about 2 months ago)
Use backticks for code blocks to allow specifying no syntax highlighting
- <details><summary>Answer</summary>4 amazons.</details>
- <details><summary>Achieving the claimed result</summary>
.A.......A.....A.......A.- </details>
- <details><summary>The claimed result is optimal</summary>
- 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.
..A............??.????.??.......A............??.??............A............- </details>
- #### 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*](http://www.kotesovec.cz/books/kotesovec_non_attacking_chess_pieces_2013_6ed.pdf) (see section 7.1 for amazons, although it is slightly misleading on this particular problem).
- <details><summary>Answer</summary>4 amazons.</details>
- <details><summary>Achieving the claimed result</summary>
- ```txt
- .A...
- ....A
- .....
- A....
- ...A.
- ```
- </details>
- <details><summary>The claimed result is optimal</summary>
- 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.
- ```txt
- ..A..
- .....
- .....
- ??.??
- ??.??
- .....
- ..A..
- .....
- .....
- ??.??
- .....
- .....
- ..A..
- .....
- .....
- ```
- </details>
- #### 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*](http://www.kotesovec.cz/books/kotesovec_non_attacking_chess_pieces_2013_6ed.pdf) (see section 7.1 for amazons, although it is slightly misleading on this particular problem).
#1: Initial revision
by
Peter Taylor
·
2026-07-31T10:34:02Z (about 2 months ago)
<details><summary>Answer</summary>4 amazons.</details>
<details><summary>Achieving the claimed result</summary>
.A...
....A
.....
A....
...A.
</details>
<details><summary>The claimed result is optimal</summary>
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.
..A..
.....
.....
??.??
??.??
.....
..A..
.....
.....
??.??
.....
.....
..A..
.....
.....
</details>
#### 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*](http://www.kotesovec.cz/books/kotesovec_non_attacking_chess_pieces_2013_6ed.pdf) (see section 7.1 for amazons, although it is slightly misleading on this particular problem).