The fourth round of Hanoi

In the four-peg variant of the Towers of Hanoi game, it is well known that N disks can be transferred from a column to another in 2(del 0) + 2(del 1) + ... + 2(del)(N-1) moves, where del n denotes the largest integer p such that p(p + 1)/2 <= n, and it was conjectured that this number of moves was the minimum possible. We shall see, in this article, that is is indeed the case.