#### 23 Mar 2003 Bram»(Master)

Building a Pentultimate

I have long been fascinated by the pentultimate. Could one actually be built? I have a general design which I'm fairly confident is workable.

Imagine two blocks which you wish to slide along each other in a straight line. If you cut a slot along their boundary, you can put a disc in the middle which will rotate as they move. You can add teeth to the disc and notches to the edges of the slot, thus forcing the gear to rotate and move exactly half as much as each block does relative to the other one. A more esoteric trick is to add circular notches to the faces of the disc and grooves to the sides of the slot for those notches to move in. This will have the same effect in terms of how the disc moves, but has the additional property that the two blocks can't be pulled apart while the disc is inside.

If we bend things a bit we can make the slot be circular, and the blocks then rotate. My trick for making a pentultimate is to cut grooves of this form along the hidden sides of each visible piece and have a disc sit under each boundary between a triangular and pentagonal piece. The discs keep the puzzle from being taken apart, but allow rotation along the cuts. Every time a rotation is done around a cut, it moves a fifth of a complete rotation, making each of the ten discs beneath move half that distance, resulting in each of them moving to the next position along and the puzzle once again being in a rotatable position.

The details of course must be hashed out, but I'm confident a real physical pentultimate which is robust enough to play with could be made using this technique.

An interesting possibility this internal mechanism raises is that the outside of the the puzzle could be made transparent, and the puzzle would then be to position and orient the internal discs.

There are many other fascinating Rubik-type puzzles, but I think the pentultimate would be by far the most compelling toy.