Better Split Towers of Hanoi

Surprisingly, our solution to split the towers generates much more moves than our solution to interleave them. As both problems are symmetric, this should not be.

Disks amountInterleavedРозділити
5 пар 62 ходи 88 ходів
6 пар 126 ходів 183 ходи
7 пар 254 ходи 374 ходи

Can you make the split tower as efficient as the interleaved one?

The source of discrepancy is an inefficient problem decomposition. Satisfied that it merely worked, we looked no futher for a better solution. Keeping the disks of the interleaved tower in the correct order during every move is unnecessary. In fact, we can avoid moving the interleaved tower at all. A better problem decomposition splits the pair of disks into two colored towers as they are removed from the interleaved tower.


If someone could split the (n-1) pairs of disks beforehand, could you split the remaining pair?