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Incubator Q&A Closed loop on a side length 2 cube

Solution Process I start with a fairly symmetric placement which doesn't meet the constraints and make simple modifications until it does. We have two "single" and two "double" tiles per sid...

posted 3d ago by Peter Taylor‭

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#1: Initial revision by

Peter Taylor‭ · 2026-09-14T14:04:09Z (3 days ago)

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<details><summary>Solution</summary>

![Solution](https://proposals.codidact.com/uploads/abxhdvs5iqcpxzf6meeth5gl4pit)
</details>
<details><summary>Process</summary>
I start with a fairly symmetric placement which doesn't meet the constraints and make simple modifications until it does.

We have two "single" and two "double" tiles per side. We can place them to leave four vertices of the cube clear:

![Pick one vertex and then on each face which it touches pick the diagonally opposite vertex](https://proposals.codidact.com/uploads/do80fcc3m4umm1ep0z7bw0p0upa2)

Now place the double tiles in the remaining spaces:

![All in the same orientation](https://proposals.codidact.com/uploads/xsx6v6pbpgk0cpsgkvvvae0vsd93)

The only problem is that we have more than one loop. For each double tile in some arbitrary order, if rotating it 90 degrees will join two loops then do so.</details>

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