  In this paper, our aim is to prove that our recursive algorithm to solve the
"Reve's puzzle" (four- peg Tower of Hanoi) is the optimal solution according to
minimum number of moves. Here we used Frame's five step algorithm to solve the
"Reve's puzzle", and proved its optimality analyzing all possible strategies to
solve the problem. Minimum number of moves is important because no one ever
proved that the "presumed optimal" solution, the Frame-Stewart algorithm,
always gives the minimum number of moves. The basis of our proof is Bifurcation
Theorem. In fact, we can solve generalized "Tower of Hanoi" puzzle for any pegs
(three or more pegs) using Bifurcation Theorem. But our scope is limited to the
"Reve's puzzle" in this literature, but lately, we would discuss how we can
reach our final destination, the Generalized Tower of Hanoi Strategy. Another
important point is that we have used only induction method to prove all the
results throughout this literature. Moreover, some simple theorems and lemmas
are derived through logical perspective or consequence of induction method.
Lastly, we will try to answer about uniqueness of solution of this famous
puzzle.
