I recently had a homework about tower of hanoi that ended a derivative of four pegs, called Reve's puzzle.
The Stewart algorithm seems to be the optimal solution to solve it with the least moves number possible, cutting the initial tower in two intermediate ones of k and n - k sizes, with n the number of disks to move and k an integer between 1 and n - 1.
I understood how to explain this algorithm, except on one point: the optimal k choice appears to be 
, rounded minus 1.
Why is it the optimal solution?
According to A007664 the Stewart algorithm has been proven optimal for $n \le 30$. One implementation is at The Reve's Puzzle.
Whether it is optimal for 31 disks, 32 disks, and so on is still an open problem.