Rotos consists of frame made from two overlapping circular disks. There are 10 round moving pieces held inside, visible through holes in the puzzle frame. Each disk holds 7 of the pieces - one in the centre of the disk and 6 arranged around the rim. Each disk can be turned (by multiples of 60 degrees), so that 6 pieces are cycled around by a move. There are holes on both sides of the frame, and on one side the pieces are numbered from 0 to 9 while on the other there are three red, three green and four yellow pieces. In the solved position the top row has red pieces or the numbers 1-3, the middle row is yellow or 4-7, the bottom row is green or shows 890.
This puzzle was made in East Germany in the early eighties and is quite rare. At first glance it seems related to other two-disk puzzles such as Turnstile/puzzler and Rashkey. It is in fact related more closely to Rubik's Rings and Hungarian Rings. Whereas those have rings with 34 or 38 pieces and intersections 6 or 5 pieces apart, Rotos has rings of 6 pieces with intersection points 2 pieces apart.
There are 10 pieces, so there are at most 10! = 3,628,800 positions. On the numbered side all these positions are attainable. On the coloured side of the puzzle the pieces fall into groups of 3, 4 and 3 identical ones, so then there are only 10!/(3!4!3!) = 4,200 distinct positions.
I have done a computer analysis of the puzzle in order to find God's Algorithm for them. The results are in the tables below. Analogous to the Rubik's cube, there are two ways to count the moves. The Face Turn Metric means that a turn of either disk by any amount is a single move. The Sixth Turn Metric means that every 60 degree turn counts as a single move.
|Face turn metric|
This shows the coloured side can be solved in 8 moves (4.9905 on average), or 10 sixth turns (7.2938 on average). The two positions at distance 8 in the face turn metric are shown below, and are reached by the move sequence R5 L5 R L R2 L R5 L and its mirror image.
|Face turn metric|
This shows the numbered side can be solved in 15 moves (9.5509 on average), or 19 sixth turns (14.206 on average).
Let a clockwise 60 degree rotation of the left disk be denoted by L. Rotations of 120, 180, 240, 300 degrees are then denoted by L2, L3, L4 and L5. Note that L5 can also be considered an anti-clockwise 60 degree turn, and is therefore also denoted by L'. Turns of the right disk are denoted in the same way, but using the letter R.
Phase 2: Separate the red and green pieces.
Phase 3: (Optional) Swap the red and green pieces.
Phase 1: Solve pieces 3, 5 and 0.
Phase 2: Solve pieces 1, 6 and 8.
Note that in this phase we turn the R disk only through 120 degrees. This way 3, 5, 0 remain in their positions, except possibly cycled around. Once 1, 6, 8 are correct, a single turn can put 3, 5, 0 back again.
Phase 3: Solve pieces 2, 4, 7 and 9.