Hi iMaterialise fans,
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.
Tiles: Moves
2: 1
4: 12
6: 51
8: 134
10: 269
12: 494
Watch the YouTube video.
Download the CAD file to print-it-yourself.
Buy the puzzle at my iMaterialise Shop.
Read more at the Non-Twisty Puzzles Forum.
Check out the photos below.
Enjoy!
Oskar
