Comments on: More Gnomes
https://blog.tanyakhovanova.com/2022/06/more-gnomes/
Mathematics, applications of mathematics to life in general, and my life as a mathematician.Tue, 18 Oct 2022 18:44:15 +0000
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By: Tanya Khovanova's Math Blog » Blog Archive » Gnomes Solution
https://blog.tanyakhovanova.com/2022/06/more-gnomes/#comment-13588
Tue, 18 Oct 2022 18:44:15 +0000https://blog.tanyakhovanova.com/?p=1653#comment-13588[…] I recently posted a gnome puzzle by Alexander Gribalko. […]
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By: JBL
https://blog.tanyakhovanova.com/2022/06/more-gnomes/#comment-13477
Wed, 29 Jun 2022 11:53:16 +0000https://blog.tanyakhovanova.com/?p=1653#comment-13477So I thought the second one would be a long case-bash, and was pleasantly surprised. Oddly, the fact that it was a chessboard and not any old 3-by-3 grid was helpful. The numbers work out nicely for an n-by-n grid whenever n is 0 or 3 modulo 4 (then n(n + 1)/4 boards gives you a total of exactly n^2 choose 2 pairs of adjacent gnomes, so you are looking to get each pair adjacent exactly once). I would guess that this can be done for n > 3, but finding an example for 16 gnomes and five 4-by-4 boards seems hard by hand.
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By: Ivan
https://blog.tanyakhovanova.com/2022/06/more-gnomes/#comment-13472
Wed, 22 Jun 2022 20:26:51 +0000https://blog.tanyakhovanova.com/?p=1653#comment-13472With respect to the first puzzle, I think a more interesting question is “What is the minimal number of knaves on a N x N chessboard, where N>3?” Answering it will not only give an answer to the puzzle, but will also lead to a new OEIS sequence.
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By: Mathematical Gnome problem – The nth Root
https://blog.tanyakhovanova.com/2022/06/more-gnomes/#comment-13471
Sun, 19 Jun 2022 23:01:13 +0000https://blog.tanyakhovanova.com/?p=1653#comment-13471[…] I recently posted a cute Shapovalovâ€™s puzzle about gnomes. Here is another easier gnome puzzle, also by Alexander Shapovalov. … (Tanya Khovanova’s Math Blog) […]
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