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Incubator Q&A Packing a 3-dimensional object with 3-dimensional L-shaped pieces

Consider the following L-shaped 3-dimensional object consisting of 3 unit cubes joined at their faces: Is it possible to use six of the above L-shaped pieces to form the following 3-dimensiona...

1 answer · posted 5mo ago by will.octagon.gibson‭ · last activity 4mo ago by will.octagon.gibson‭

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#2: Post edited by

will.octagon.gibson‭ · 2026-04-24T06:23:33Z (5 months ago)
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Consider the following L-shaped 3-dimensional object consisting of 3 unit cubes joined at their faces:
![3-dimensional L-shape](https://proposals.codidact.com/uploads/df8hqkx66ngzs6f9rftxhwx4mp36)
---
Is it possible to use six of the above L-shaped pieces to form the following 3-dimensional object (whose volume is 18 unit cubes)?
![Staircase-like 3-dimensional shape](https://proposals.codidact.com/uploads/uz9hrdgdr0knvitwrwjpkwpwdpbj)
---
If yes, show how the object can be formed.
~~If no, why not.~~

Consider the following L-shaped 3-dimensional object consisting of 3 unit cubes joined at their faces:
![3-dimensional L-shape](https://proposals.codidact.com/uploads/df8hqkx66ngzs6f9rftxhwx4mp36)
---
Is it possible to use six of the above L-shaped pieces to form the following 3-dimensional object (whose volume is 18 unit cubes)?
![Staircase-like 3-dimensional shape](https://proposals.codidact.com/uploads/uz9hrdgdr0knvitwrwjpkwpwdpbj)
---
If yes, show how the object can be formed.
If no, explain why not.

#1: Initial revision by

will.octagon.gibson‭ · 2026-04-23T16:10:23Z (5 months ago)

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Packing a 3-dimensional object with 3-dimensional L-shaped pieces

Consider the following L-shaped 3-dimensional object consisting of 3 unit cubes joined at their faces:

![3-dimensional L-shape](https://proposals.codidact.com/uploads/df8hqkx66ngzs6f9rftxhwx4mp36)

---

Is it possible to use six of the above L-shaped pieces to form the following 3-dimensional object (whose volume is 18 unit cubes)?

![Staircase-like 3-dimensional shape](https://proposals.codidact.com/uploads/uz9hrdgdr0knvitwrwjpkwpwdpbj)

---

If yes, show how the object can be formed.  

If no, why not.

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