Background Information

The Tumbler Puzzle is made by Nintendo. It is in the shape of a barrel, the bulk of which is transparent. Around the barrel are five columns of coloured beads (four of each colour) and three black beads. The barrel also slides up and down, three 'pegs' shift the beads in the corresponding columns (whilst the other two columns are unaffected). The barrel also has two sections (each two beads high) that are rotated around it, moving 10 of the beads at a time. The solution is to have a different colour in each column except for the top position where the 'pegs' are, these should contain the three black beads.

I can't remember now how the subject first came up but Phil and myself were discussing how such an apparently simple puzzle had defeated us. Also, in its now muddled state it was virtually impossible to figure anything out as with only a couple of lifts/drops and twists virtually every bead is affected.

It then struck us that the thing to do was write a program that would sequence through the possible moves to search for the solution. This was a relatively trivial exercise in recursion. The program only knew four moves; raise the tumbler, lower the tumbler, rotate the top barrel left and rotate the bottom barrel left. We figured that rotating to the right would simply be represented as four rotations to the left. We defined the current state of the beads and set the program running.

The program stored the current position in a file. From this file we could monitor progress. We quickly realised that despite a very high number of moves being performed, it was going to take years to find a solution. Also, even if we were presented with the sequence of moves that had to be performed to complete the puzzle, we would not have a reusable solution.

We changed the program to restrict the depth of recursion and added move to rotate the barrel sections to the right. We also changed the bead definition so that every bead was unique (there are only 23 beads so each was represented by a different letter). We then modified the program to stop if 8 or less beads had been affected. The idea was to look for sequences of moves that had a very isolated effect.

We then ran the program gradually increasing the depth of recursion. It found the three move sequences detailed on these pages. Obviously there are many more, however, we can be confident that these are the shortest sequences that have useful effects.

Note that we did not encounter any sequences that had an impact on the top row or the two bottom rows, however, we were confident that will a little trial and error these rows are not that difficult to complete. Hence the starting position. If people are having trouble with this then I'll resurrect the program and search for some suitable moves.

Tumbler Puzzle Contents | Starting Position | Steve Martin's Home Page
Solution © Phil Seeley, Steve Martin 1994
Web Page design © Steve Martin, 1999