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Hanoi towers pattern how to#
Hanoi towers pattern full#

Of course, if we want the tower to end up on a specific pole, we may have to reorder the $6$ steps depending on if the initial tower has an even or an odd number of disks. Lets name the pegs A, B, and C, and lets number the disks from 1, the smallest disk, to, the largest disk.

Hanoi towers pattern full#

If we completely unroll step 1), then we see that the full move sequence for solving the Towers of Hanoi is just repeating this pattern of $6$ steps over and over until we are done. You are given a set of three pegs and disks, with each disk a different size. So you need to move all the disks from the first tower over to the last. A larger disk can not be placed on a smaller disk. While moving the disks, certain rules must be followed.

Move the $n-2$ tower from pole B onto pole CĪside from step 1), the other steps involve moving a single disk (the only legal move) at a time between the poles in a pattern indicated by the iterative solution. Move all the disks stacked on the first tower over to the last tower using a helper tower in the middle.

Move the $n-1$ disk that's left on pole A to pole C.

Move the $n-2$ pieces from pole A to pole B.

Of course step 1) is much more involved than the other steps! Let's unroll step 1) and see what patterns we notice.

Move the $n-1$ tower you left on pole C back on top of pole B.

Move the remaining disk on pole A to pole B.

Move $n-1$ pieces from pole A to pole C.

In short, getting the EXACT replica of the ring pattern.

Hanoi towers pattern how to#

If you know how to move a tower with $n-1$ pieces then you can figure out how to move a tower with $n$ pieces. First holding the selected rings, middle pole as a helper pole, and the last one as the target pole. This will give you 5 pieces for our Hanoi Tower. Do the same procedure making more circles with 3 cm, 2 cm, and 1 cm radius. Now repeat the process but this time measure the radius of 4 cm. Cut the circle from styrofoam or cardboard using the scalpel or scissors.

In one version of the puzzle Brahmin priests are completing the puzzle with 64 golden. Draw a circle on the styrofoam or cardboard. Tool/Solver to generate moves for The Tower of Hanoi game, a kind of puzzle-game using increasing size stacked discs that the player need to move following. So we now have a formula for the minimum moves with the Tower of Hanoi. The Iterative Solution basically relies on the principle of induction. Can we see a pattern in the following list of minimum number of moves: 1,3,7,15,31,63, They are actually powers of 2 with one subtracted : 2 N-1. In doing so, the aim is to collect data, look for patterns, make conjectures. If you're interested, I explain how to solve the Tower of Hanoi (plus induction proofs) in this video. The Tower of Hanoi game is a great puzzle that everyone can have a go at.