Comments on: Polyomino Cutting
https://blog.tanyakhovanova.com/2023/11/polyomino-cutting/
Mathematics, applications of mathematics to life in general, and my life as a mathematician.Sun, 19 Nov 2023 14:49:24 +0000
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By: JBL
https://blog.tanyakhovanova.com/2023/11/polyomino-cutting/#comment-13842
Sun, 19 Nov 2023 14:49:24 +0000https://blog.tanyakhovanova.com/?p=1969#comment-13842Is there a polyomino for which it is only possible to divide it into two congruent unions of squares if the pieces are not connected?
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By: Murat
https://blog.tanyakhovanova.com/2023/11/polyomino-cutting/#comment-13841
Sat, 18 Nov 2023 04:21:48 +0000https://blog.tanyakhovanova.com/?p=1969#comment-13841Does it have a solution?
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By: tanyakh
https://blog.tanyakhovanova.com/2023/11/polyomino-cutting/#comment-13831
Mon, 06 Nov 2023 17:24:42 +0000https://blog.tanyakhovanova.com/?p=1969#comment-13831Mauro, the cut should be along the grid.
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By: Mauro
https://blog.tanyakhovanova.com/2023/11/polyomino-cutting/#comment-13830
Mon, 06 Nov 2023 14:23:22 +0000https://blog.tanyakhovanova.com/?p=1969#comment-13830What is the definition of a cut? One connected path? Can it be along the edges?
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By: Lazar Ilic
https://blog.tanyakhovanova.com/2023/11/polyomino-cutting/#comment-13829
Mon, 06 Nov 2023 13:32:24 +0000https://blog.tanyakhovanova.com/?p=1969#comment-13829XXXXO
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By: Ivan
https://blog.tanyakhovanova.com/2023/11/polyomino-cutting/#comment-13826
Sat, 04 Nov 2023 10:52:49 +0000https://blog.tanyakhovanova.com/?p=1969#comment-13826Let us imagine this shape as 2 intersecting quadrilaterals: upper left green quadrilateral A (4 rows, 5 columns) and lower right blue quadrilateral B (4 rows, 6 columns). Their intersection is the yellow quadrilateral C (3 rows, 4 columns), which can be divided into two congruent polyominoes. In order to divide the whole shape into two congruent polyominoes, the green and blue remainders have to be added to the respective halves of the yellow quadrilateral in a symmetric fashion, which is impossible.
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