![]() ![]() ![]() Disk 1 would jump from the leftmost peg to the right, landing on the middle peg. Of course, for puzzles with an Even number of disks the movements would be reversed but would follow the same pattern. This completes the circle of movement and would once again allow Disk 1 to move left onto the middle peg and then back onto the leftmost peg again, ready to jump back around to the rightmost peg and start the sequence again. If Disk 1 is on the leftmost peg, moving it left would bring it back around to the right most peg. But what if it is already on the leftmost peg? As we can see in our movement graphic above, you may think of the Disk 1 movements across the board as a circular motion. And if it was instead resting on the middle peg it would move one peg to the left onto the leftmost peg. So if Disk 1 currently resides on the right most peg, it would move one peg to the left to the middle peg on its turn. ![]() For example, the odd algorithm has it moving one peg to the left on steps 1, 3, 5 and 7. The two algorithms share some notable similarities, particularly that the tiny Disk 1 is repositioned on every other move in an optimal solution. To solve their puzzle a player will perform the applicable 8-move algorithm to their board repeatedly until all of the disks have been transferred from the leftmost starting peg to the rightmost target peg. In our guide we'll be using the "odd" algorithm since our example puzzle contains seven disks. The leftmost column shows the move algorithm for puzzles with an odd number of disks, and the rightmost column details the solution for puzzles with an even number of starting disks. ![]() In the chart to the left you'll find the two optimal move algorithms for any Tower of Hanoi puzzles based on the total number of disks in your starting Tower. We'll now take a look at the algorithms used to solve the Tower of Hanoi and how these three focus disks will factor into each solution. The remaining disks of various colors are simply known as Big Disks, and numbering them is not necessary. Finally, the third disk down is called Disk 3 and is colored Yellow. It is the second smallest disk in the puzzle and is colored Orange in our examples. The second disk from the top is called Disk 2. It is colored Red in our graphic and is the smallest of all the disks. These three disks are moved around quite a bit in an optimal solution, so it will be necessary to become familiar with them. In our solution algorithms below we'll focus mainly on the top three disks of the Tower. In this guide we'll focus on solving a seven-disk Tower of Hanoi puzzle and we've provided an example of our puzzle board in the graphic above, complete with colored disks for reference purposes. The proper solution for a Tower of Hanoi puzzle is very similar for all of the various puzzles, but varies slightly based on whether or not the total number of disks in the puzzle is Odd or Even. The most common total of disks is seven, but you may have puzzles with more (or less) disks in play. Tower of Hanoi Puzzles may consist of any number of disks as long as they total three or more. In fact, the Tower of Hanoi solution provides two simple algorithms that allow players to optimally solve Tower of Hanoi puzzles with any number of disks when applied to the puzzle! Optimal Algorithms for Solving Tower of Hanoi Puzzles The puzzle was invented by the French mathematician Edouard Lucas in 1883 and is often described as a mathematical puzzle, although solving the Tower of Hanoi doesn't require any mathematical equations at all for a human player. The rules of the puzzle state that the player can only move one disk per turn and can never place a larger disk onto a smaller one at any time.īased on these guidelines, players attempt to move their initial Tower disk-by-disk towards the target third peg in a seemingly complex method of movement using any of the three available pegs until it is rebuilt onto the rightmost peg exactly as it was on the initial leftmost peg at the start of the puzzle. In the Tower of Hanoi puzzle a player attempts to move a large pile of disks, known as the Tower, from the leftmost peg to the rightmost on the puzzle board. The Tower of Hanoi is one of the truly classic puzzle games, challenging players with its seemingly simple but frustratingly difficult goal. ![]()
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