Hyperswap

This CAD model was designed by Oskar van Deventer, copyright (c), 8 November 2024.

Hyperswap is a failed attempt to design a hyper-exponential puzzle. The puzzle is operated by moving the slider up and down, park one of the numbered tiles there, and swap it with a neighboring tile, similar to bubblesort. The goal is to swap the ten numbered tiles. The number of states of this puzzle is ten factorial, and increases hyper-exponentially with the number of tiles. However, the diameter of the state space and hence the number of moves to solve does not. The diameter of bubblesort grows quadratically with the number of tiles. The diameter of this puzzle grows much more rapidly because of a limitation where which tiles can swap, indicated by the numbers at the right. Tile 1 can swap everywhere. Tile 2 can swap only at an even distance from the center. Etcetera. All tiles can swap at the center. Tiles can only be passed by higher-numbered ones, not lower-numbered. Jaap Scherphuis analysed that the number of moves for the shortest solution is 269 for the ten-tile version. There are many longer solutions, as the state graph is still well-connected. Jaap Scherphuis' analysis concluded that the puzzle is at most exponential, with a base lower than 2. Perhaps it is phinary. More analysis is needed.

The .zip file contains six versions of the puzzle, with 2, 4, 6, 8, 10, and 12 tiles. The table below provides the minimum number opf moves to solve each one.
The puzzle uses cylindrical magnets withe 3-mm diameter and 2-mm thickness: https://www.supermagnete.de/eng/disc-magnets-neodymium/disc-magnet-3mm-2mm_S-03-02-N

Here are some links about this design.
https://www.youtube.com/watch?v=Y75a-WDYpKo
https://i.materialise.com/en/shop/item/hyperswap
https://i.materialise.com/forum/t/hyperswap-by-oskar/3861
https://twistypuzzles.com/forum/viewtopic.php?t=40082

Feel free to 3D-print an extra sample to give to a friend, as long as you mention the designer and don't charge money.

If you are planning to sell some samples, then please contact me for a license agreement. The royalty fee is 10% of your selling price.

Please do not upload the design to a commercial service, or redistribute the design in any way other than linking to the YouTube video: https://www.youtube.com/watch?v=Y75a-WDYpKo

Enjoy!

Oskar
22 March 2025

Contact: 
https://oskarvandeventer.nl/index_contact.php?subject=Print%20It%20Yourself

Tiles: Moves
2:	1
4:	12
6:	51
8:	134
10:	269
12:	494

