How the Game Works
The Tower of Hanoi game begins with a number of discs stacked from largest to smallest on the first pole. The game can be played with any amount of discs starting on the first pole. The goal of the game is to get all the discs from the first pole to the third pole in the least amount of moves possible. A larger disc is to never be placed on a smaller disc, and only one disc may be moved at a time. There is one pole between the first pole and third pole where the discs can be temporarily placed (chess). Based on these guidelines, players attempt to move the discs to the third pole using any complex method of movement so that the original Tower of discs that was built on the first pole is exactly rebuilt on the third pole. Recognizing the pattern is the key to solving the puzzle to Tower of Hanoi. Without recognizing the pattern from the start, the game may seem very complex (and frustrating, resulting in quite the headache…). The pattern to the game is to move the discs in a clockwise direction, continuing to repeat the pattern for each disc and remembering not to place a larger disc on a smaller disc (entertainment). Here is an example of how to solve the puzzle with three discs starting on the first pole (mathforum). Pole A represents the first pole, Pole B represents the second pole and Pole C represents the third pole.
Generally, if there is a stack of an odd number on Pole A, move the first disc to Pole C, continuing along the pattern of each time you move a bigger disc, move each disc of smaller size on top of it. If you're starting with a stack of an even number, move the first disc to Pole B and continue. If you have an odd number on Pole B, move the first disc to Pole C, and if you have an even number on Pole B, move the first disc to Pole A. If you have an odd number on Pole C, move the first disc to Pole B. If you have an even number on Pole C, move the first disc to Pole A. Thinking about these tips is the most efficient and reasonable way to do the puzzle in the minimum number of moves.
Go clockwise! No matter how many discs are on the first pole at the start of the game, following this same pattern will be the solution to solving the puzzle. Tower of Hanoi takes a lot of strategy, yet there of course is mathematical evidence that this pattern works.
- begin with three discs on Pole A
- move the smallest disc clockwise from Pole A to Pole C
- move the next largest disc from Pole A to Pole B
- move the smallest disc from Pole C to Pole B (on top of the disc one size larger)
- move the remaining (and largest) disc from Pole A to Pole C
- move the smallest disc from Pole B to Pole A
- move the next largest disc from Pole B to Pole C (on top of the largest disc)
- finally, move the smallest disc from Pole A to Pole C, where you will have rebuilt the Tower on Pole C
Generally, if there is a stack of an odd number on Pole A, move the first disc to Pole C, continuing along the pattern of each time you move a bigger disc, move each disc of smaller size on top of it. If you're starting with a stack of an even number, move the first disc to Pole B and continue. If you have an odd number on Pole B, move the first disc to Pole C, and if you have an even number on Pole B, move the first disc to Pole A. If you have an odd number on Pole C, move the first disc to Pole B. If you have an even number on Pole C, move the first disc to Pole A. Thinking about these tips is the most efficient and reasonable way to do the puzzle in the minimum number of moves.
Go clockwise! No matter how many discs are on the first pole at the start of the game, following this same pattern will be the solution to solving the puzzle. Tower of Hanoi takes a lot of strategy, yet there of course is mathematical evidence that this pattern works.