Date: 11 Aug 1982 2204-PDT From: ISAACS at SRI-KL Subject: Tsukuda's Square To: CUBE-LOVERS at MIT-MC Just got a new group-theory puzzle, called Tsukuda's Square. It's sort of like the 15/16 puzzle, but harder. It consists of a 4x4 matrix in the center with the numbers from 1 to 16. On the left side are 4 plungers, one for each row. At the top is one plunger, which pushes down columns 2, 3, and 4, all at once. Both the top and the side plungers push the rows or columns over 1 square; releasing them causes the same row(s) or columns to slide back. When the top plunger is pushed down, the number 1 row plunger cannot be pushed because of interference; that is the only interference. A typical move, for instance, would be to push in the #2 row plunger, push the top, release the #2, release the top. This would change 1 2 3 4 5 6 7 8 (only looking at the top 2 rows) to 1 3 4 8 2 5 6 7. You can push 2 or 3 (or even4) side plungers at once. Pushing an adjacent pair is even useful in solving this thing. At any rate, it has the normal even parity problem - that is, you cannot exchange a single pair, but you can exchange 2 pairs, or permute three squares. Because of the limited moves, it is not nearly so simple as it looks. I can permute 3 in one specific position, and it takes me 12 moves to do so (where a move is a push of 1 or more side plungers, then push the top, then release them, or the reverse [push the top first]). Can anyone develop some more efficient algorithms? -- Stan -------