Editing Tower of Hanoi (section)

=== Iterative solution ===
[[File:Iterative algorithm solving a 6 disks Tower of Hanoi.gif|thumb|Animation of an iterative algorithm-solving 6-disk problem]]
A simple solution for the toy puzzle is to alternate moves between the smallest piece and a non-smallest piece. When moving the smallest piece, always move it to the next position in the same direction (to the right if the starting number of pieces is even, to the left if the starting number of pieces is odd). If there is no tower position in the chosen direction, move the piece to the opposite end, but then continue to move in the correct direction. For example, if you started with three pieces, you would move the smallest piece to the opposite end, then continue in the left direction after that. When the turn is to move the non-smallest piece, there is only one legal move. Doing this will complete the puzzle in the fewest moves.<ref>{{cite journal |last=Troshkin |first=M. |title=Doomsday Comes: A Nonrecursive Analysis of the Recursive Towers-of-Hanoi Problem |journal=Focus |volume=95 |issue=2 |pages=10–14 |language=ru }}</ref>

==== Simpler statement of iterative solution ====
{{More citations needed section|date=January 2024}}
The iterative solution is equivalent to repeated execution of the following sequence of steps until the goal has been achieved:
* Move one disk from peg A to peg B or vice versa, whichever move is legal.
* Move one disk from peg A to peg C or vice versa, whichever move is legal.
* Move one disk from peg B to peg C or vice versa, whichever move is legal.
Following this approach, the stack will end up on peg B if the number of disks is odd and peg C if it is even.