Tower of Brahma

A yellow surface with 3 chrome pegs of which one has five red and blue discs threaded onto it from largest to smallest disc.
A blue and yellow exhibit table, with a green, white and orange information panel on top, sitting in front of a green and a blue wall. On the yellow tabel top are three chrome pegs, of which one has five red and blue discs that are threaded onto the peg, and arranged from largest to smallest.

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.