The peaceable queens problem is to determine the maximum number m such that one can place m queens of each colour on an n by n chessboard without any queens of opposite colours attacking each other. On an 11 by 11 chessboard, it is possible to do this with 17 queens of each colour, as shown above. Furthermore, 17 is the largest possible number that works on an 11 by 11 board.
Interesting! I'm very familiar with the Eight Queens problem, but this is the first I've heard of gaggles of peaceable queens. I like the toroidal patterns. I'm somehow a bit surprised the solution doesn't come in integer form when it seems like an integer problem -- N rows and columns, N possible positions. But I'm a math tyro with little math intuition to call my own.
Thanks for your comment! The problem isn’t really solved, and Ainley’s bound is not known to be the best possible solution in general, so it might be the case that the best solution does involve integers (or, at least, rational numbers).
Yeah, or a rational solution — a countable solution rather than something in the uncountable domain. Though I guess a real solution makes sense as a bound. Probably a log in there or something.
Took a quick look at your linked page. Saved for when I have more time (I’ll be checking out your posts in general). I have a WordPress blog with a 13-year anniversary on the 4th, so I’ve got my hands full for a bit.
The picture of the Queen on the tile floor along with the caption may be the funniest thing I’ve seen today. Thanks for the laugh!
Thanks, Roger! The mathematics in this post is recreationally motivated as far as I can tell, but sometimes this sort of thing turns out to have connections with other areas that at first seem unrelated.
Interesting! I'm very familiar with the Eight Queens problem, but this is the first I've heard of gaggles of peaceable queens. I like the toroidal patterns. I'm somehow a bit surprised the solution doesn't come in integer form when it seems like an integer problem -- N rows and columns, N possible positions. But I'm a math tyro with little math intuition to call my own.
Thanks for your comment! The problem isn’t really solved, and Ainley’s bound is not known to be the best possible solution in general, so it might be the case that the best solution does involve integers (or, at least, rational numbers).
Here’s another post I did on arranging queens on a chessboard from a couple of months ago: https://apieceofthepi.substack.com/p/arranging-queens-on-a-chessboard
Yeah, or a rational solution — a countable solution rather than something in the uncountable domain. Though I guess a real solution makes sense as a bound. Probably a log in there or something.
Took a quick look at your linked page. Saved for when I have more time (I’ll be checking out your posts in general). I have a WordPress blog with a 13-year anniversary on the 4th, so I’ve got my hands full for a bit.
The picture of the Queen on the tile floor along with the caption may be the funniest thing I’ve seen today. Thanks for the laugh!
Chess is an ideal framing to explore mathematical analyses. Thank you for the post!
Thanks, Roger! The mathematics in this post is recreationally motivated as far as I can tell, but sometimes this sort of thing turns out to have connections with other areas that at first seem unrelated.