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Incubator Q&A Tiling a 5x9 rectangle with L-shaped pieces

Spoiler As already demonstrated, a pair of tiles fills a 2x3 (or 3x2) space. I began by trying to lay out as many of those as I could (reduce to a simpler problem); these are shown as the large...

posted 5mo ago by Monica Cellio‭ · edited 3d ago by trichoplax‭

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#2: Post edited by

trichoplax‭ · 2026-09-14T17:40:18Z (3 days ago)
Typo (I think - please revert if I've misinterpreted)

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<details><summary>Spoiler</summary>
![solution](https://proposals.codidact.com/uploads/c2ti6opbctk1qkc7iimpe6p1crj4)
As already demonstrated, a pair of tiles files a 2x3 (or 3x2) space. I began by trying to lay out as many of those as I could (reduce to a simpler problem); these are shown as the larger blocks with blue lines for the individual tiles within them. With a 9x5 grid I believe that five of the six-square blocks is the maximum that can fit. I say this based on experimentation; I can't formally prove it. The challenge, then, is to lay them out so that the remaining 15 squares can fit L-shaped tiles.
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<details><summary>Spoiler</summary>
![solution](https://proposals.codidact.com/uploads/c2ti6opbctk1qkc7iimpe6p1crj4)
As already demonstrated, a pair of tiles fills a 2x3 (or 3x2) space. I began by trying to lay out as many of those as I could (reduce to a simpler problem); these are shown as the larger blocks with blue lines for the individual tiles within them. With a 9x5 grid I believe that five of the six-square blocks is the maximum that can fit. I say this based on experimentation; I can't formally prove it. The challenge, then, is to lay them out so that the remaining 15 squares can fit L-shaped tiles.
</details>

#1: Initial revision by

Monica Cellio‭ · 2026-05-03T02:10:00Z (5 months ago)

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<details><summary>Spoiler</summary>

![solution](https://proposals.codidact.com/uploads/c2ti6opbctk1qkc7iimpe6p1crj4)

As already demonstrated, a pair of tiles files a 2x3 (or 3x2) space.  I began by trying to lay out as many of those as I could (reduce to a simpler problem); these are shown as the larger blocks with blue lines for the individual tiles within them.  With a 9x5 grid I believe that five of the six-square blocks is the maximum that can fit.  I say this based on experimentation; I can't formally prove it.  The challenge, then, is to lay them out so that the remaining 15 squares can fit L-shaped tiles.

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