# Slide and Swap on Cubic Graphs

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Slide and Swap is a tile-sliding permutation game played on cubic (3-regular) graphs, similar to the familiar 15 Puzzle and its generalization to arbitrary graphs. In Slide and Swap, you may slide any adjacent tile into the open space (just click the tile you want to slide), but the other two neighbors of the tile you slide will be swapped as well. When the hole returns to its initial vertex after a sequence of slides, the numbered tiles will have been permuted, and these permutations of the tiles form a group under composition.

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Contributed by: Jacob A. Siehler (August 2011)

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

References

[1] A. F. Archer, "A Modern Treatment of the 15 Puzzle," *American Mathematical Monthly*, 106, 1999 pp. 793–799.

[2] R. M. Wilson, "Graph Puzzles, Homotopy, and the Alternating Group," *Journal of Combinatorial Theory Series B*, 16, 1974 pp. 86–96.

[3] Wikipedia, "PSL (2,7)." (Aug 17, 2011) http://en.wikipedia.org/wiki/PSL%282,7%29.

## Permanent Citation

"Slide and Swap on Cubic Graphs"

http://demonstrations.wolfram.com/SlideAndSwapOnCubicGraphs/

Wolfram Demonstrations Project

Published: August 23 2011