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Tower of Brahma


The minimum number of moves required to solve a Tower of Brahma puzzle can be calculated according to the number of puzzle pieces.
How it works
Move all discs from one peg to another peg, using certain rules and within a minimum number of moves.
Things to try or ask around the exhibit
- If you follow the puzzle rules, can you transfer the stack of discs to another peg in a certain number of moves?
- Is there a mathematical pattern for solving the puzzle with three, then four discs?
- How many moves would you need for five discs?
Background
When you solve the Tower of Brahma puzzle, you need at least:
- 7 moves for 3 discs
- 15 moves for 4 discs
- moves for 5 discs.
The solution can be represented by a mathematical formula, where n equals the number of discs and the minimum number of moves needed to solve the puzzle is 2n - 1. This formula used to calculate the least number of moves is known as a Recurrence Relation.
Finding the science in your world
Psychologists sometimes use the Tower of Brahma puzzle as a test for dementia and problem-solving abilities, because the problem is relatively simple and steps in the solution can be traced and recorded.