[Jack Hydrazine]

http://en.wikipedia.org/wiki/Tower_of_Hanoi

[DuncanWaring]

Note this guy seems to have solved the “Four Peg” version:

http://en.wikipedia.org/wiki/Tower_of_Hanoi#With_four_pegs_and_beyond

[Hillarys Gate Cult]

I can solve the Tower of Hanoi problem in one move. A B-52 airstrike.

[Lancey Howard]

Although the three-peg version has a simple recursive solution as outlined above, the optimal solution for the Tower of Hanoi problem with four pegs (called Reve's puzzle), let alone more pegs, is still an open problem. This is a good example of how a simple, solvable problem can be made dramatically more difficult by slightly loosening one of the problem constraints.

The fact that the problem with four or more pegs is an open problem does not imply that no algorithm exists for finding (all of) the optimal solutions.