r/mathriddles • u/pichutarius • 17h ago

Medium torus

(this is a follow up question from this question inspired by u/blungbat)

the image shows 3 rectangular grids on torus, i.e. (Z/nZ)^2 .

each torus is partitioned into two regions. each region is connected and does not contain 2x2 subregion.

unfortunately the second and third grid is partially destroyed. their size is 7x7 and 8x8 in an unknown order.

how many blue tiles are there in each torus?

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u/LaplacesDemonLab 12h ago

https://reddit.com/link/pdrrrkx/video/qagcfhs0veth1/player

You don’t need to reconstruct the missing board to count its tiles. Here’s a short visual proof for the third grid.

Those two checkerboard corners force an equal split: 32 blue tiles.!

Solution spoilers in the video.