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Comments on Tiling a 5x9 rectangle with L-shaped pieces
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Tiling a 5x9 rectangle with L-shaped pieces Question
Consider the following L-shaped piece made of three unit squares joined at their edges:
Allowing rotations of the L-shaped pieces, you can easily tile a 2x3 rectangle with two of the above L-shaped pieces:
Click here to reveal 2x3 tiling
Main question:
Allowing rotations of the L-shaped pieces, can you tile a 5x9 rectangle with 15 of the above L-shaped pieces?
If yes, construct a tiling.
If no, explain why not.
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The following users marked this post as Works for me:
| User | Comment | Date |
|---|---|---|
| will.octagon.gibson | (no comment) | May 3, 2026 at 02:50 |
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 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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