Have you ever introduced the classic Tower of Hanoi game to your kids ? It consists of 3 pegs and a number of disks of different sizes, which can be stacked onto any peg. The game starts with all the disks stacked in ascending order of size on the first peg, with the smallest disk at the top. The goal is to move all the disks from first peg to the third peg in the smallest number of moves possible, according to the following rules.
- Only one disk can be moved at a time.
- A larger disk can never be on top of the smaller one
- Only the upper disk from one of the stacks can be moved and placed on top of another stack or an empty peg
The name of the puzzle Tower of Hanoi , also known as Tower of Brahma originated based on a myth, that somewhere in one of the ancient Indian Temple and Vietnamese Monastery, the priests and monks are shuffling 64 golden disks between three pillars for centuries. According to the legend, when the priests would finish transferring all of the disks, the world will end. Should we worry ?
Instead of investing in a tower of Hanoi puzzle , I gave my kids different size circles cut out from the foam sheets of varying colors, to play with. My kids were engaged for a good enough time trying it with different number of disks.
Tower of Hanoi with 3 Disks
Tower of Hanoi with 4 Disks
When there are even number of disks involved, you would be moving the first disk to the middle peg whereas in odd number of disks, you would be moving the first disk to the last peg. Did you notice that difference.
Can you find out how many minimum number of steps are required if there are 6 ,7… n disks ? There are 7 minimum steps required for 3 disks, 15 steps for 4 disks, 31 steps for 5 disks and so on. Let me know in the comments section.
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