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?
Best Answer
Actually, this is no longer an open problem, even at the time of the OP. The Frame-Stewart bound was proved optimal by Thierry Bousch in La quatrième tour de Hanoï which appeared in the Bulletin of the Belgian Mathematical Society - Simon Stevin in 2014.