Useful Maneuvers

With a few basic maneuvers together with rotations of the whole puzzle by multiples of 72° all variants of the puzzle can be solved. The maneuvers only use the left and right disk L and R which intersect in two adjacent tiles. The maneuvers - found by computer search - are optimal in the metric which counts a rotation of arbitrary size as one move.

L = a clockwise rotation of the left disk by 36°
Lx = a clockwise rotation by x times 36°
L' = an anticlockwise rotation by 36°
Lx' = an anticlockwise rotation by x times 36°


1. Double pair swap L R' L' R (4)

By doing some move sequence M, applying the double pair swap and then undoing M all swaps can be managed in priciple, since there are indistinguishable tiles in all versions of the puzzle..


2. Single pair swap R3 L4 R2 L2 R3 L4 R2 L4 R3 L2 R2 L4 (12)

The single pair swap is interesting mainly from a theoretical point of view. If center rotation is enabled additionally the center of the right disk is rotated by 180°. In any case this maneuver is quite handy in some situtations.


3. Single pair twist R L R L' R' L R' L' R L' R L2 R' L2' R' L (16)

If orientations are enabled this maneuver is the basis to restore all orientations. Just move tiles into these positions, do the pair twist and move the tiles to their old positions again to rotate tiles by 72°.


In the program these 3 maneuvers are implemented as macros so they are easy to apply if you want.

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© 2020  Herbert Kociemba