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Incubator Q&A Closed loop on an octahedron

Solution Process An easy observation is that every triangle has an edge which the line does not pass through, so we're really tiling with four diamonds: I placed the red diamond arbitraril...

posted 2d ago by Peter Taylor‭

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#1: Initial revision by

Peter Taylor‭ · 2026-09-15T14:36:15Z (2 days ago)

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<details><summary>Solution</summary>

![The path winds through the central four triangles and slices off the corners of the four triangles in the net with two edges exposed](https://proposals.codidact.com/uploads/nylizw4s5cs9sxjaqbw7e4i4oakf)
</details>
<details><summary>Process</summary>
An easy observation is that every triangle has an edge which the line does not pass through, so we're really tiling with four diamonds:

![Similar but recoloured](https://proposals.codidact.com/uploads/k89fy869j7twnk25fl2kdacujxco)

I placed the red diamond arbitrarily due to symmetry. Since the top half of the red diamond couldn't be part of a cycle of length 4 around the vertex I placed the blue diamond to break that cycle. The other two diamonds are now forced.
</details>

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