Bicolor Tower of Hanoi

Blue and red disks alternate in one tower. Send the blue disks to the last peg and the red ones to the middle peg. With 4, 6, 8 and 10 disks the fewest moves are 11, 45, 182 and 731.

The rules

• The tower starts on the first peg, with blue and red disks taking turns from the top.
• Finish with every blue disk on the last peg and every red disk on the middle peg.
• One disk at a time, only the top disk, never a larger disk on a smaller one.

What is different

In the classic puzzle the whole tower moves to another peg. Here the tower has to be taken apart: the blue disks (1st, 3rd, 5th… from the top) go to the last peg and the red ones (2nd, 4th, 6th…) go to the middle peg. Each colour ends up as a tower of its own, smallest on top, and the two goals mirror each other, so neither colour is the harder one.

How many moves

That is about 70% of the classic count for the same number of disks. If you are stuck, the first move is always the smallest disk to the last peg; the Bicolor solver shows the rest.