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

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-sha...

1 answer · posted 5mo ago by will.octagon.gibson‭ · last activity 3d ago by trichoplax‭

Question puzzles tiling

#2: Post edited by

will.octagon.gibson‭ · 2026-09-14T15:00:32Z (3 days ago)
Added tiling tag

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puzzles tiling

#1: Initial revision by

will.octagon.gibson‭ · 2026-04-22T16:59:33Z (5 months ago)

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Tiling a 5x9 rectangle with L-shaped pieces

Consider the following L-shaped piece made of three unit squares joined at their edges:

![L-shaped piece made from three unit squares](https://proposals.codidact.com/uploads/dotpm7rd61wt2p0g9l3gsw1k6x1a)

Allowing rotations of the L-shaped pieces, you can easily tile a 2x3 rectangle with two of the above L-shaped pieces:

<details>
<summary>Click here to reveal 2x3 tiling</summary>

![Tiling of a 2x3 rectangle using two L-shaped pieces](https://proposals.codidact.com/uploads/0i4a8ucpviikny3642bvunnjqmkw)

</details>

---

## 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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