To start off, we have coins arranged in the following order:
..C.. A
F.. D.. B
..E.. G
The goal of this game is to return these letters into alphabetical order: A, B then C, D, E then F, G in the rows from top to bottom. On each move you may rotate any triangular block of letters, such as the blocks ADB or DEG, by one or two rotations clockwise. For example, if we rotate the block ADB by one rotation clockwise, our coins would look like:
..C.. D
F.. B.. A
..E.. G
What is the least number of moves required, with justification?
I found a way to do it in three moves: CAFDBEG ADFCBEG ADCEBFG ABCDEFG
It cannot be done in 2 moves since only D and G are in their aphabetic positions, and any two triangles will leave at least one of the 5 others outside it unmoved.