##### Level 1Level 2Level 3Level 4Level 5Level 6Level 7Level 8Level 9Level 10More Puzzles

The objective of this puzzle is to move the discs, one at a time, from start to finish.

You are not allowed to put a disc on top of a smaller disk though.

You will be awarded a trophy if you can complete the puzzle in the minimum number of moves.

Start by moving this disk.

You can't put a disc on top of a smaller disc.

The objective of this puzzle is to move the discs, one at a time, from start to finish.

You are not allowed to put a disc on top of a smaller disk though.

You will be awarded a trophy if you can complete the puzzle in the minimum number of moves.

## Investigation

Complete the first five levels of this puzzle and keep your results in a table. Can you work out how the minimum number of moves is related to the number of discs? Could you fill in the rest of the table without doing levels 6 to 10 of the puzzle?

 Number of discs Minimum Moves 1 2 3 4 5 6 7 8 9 10 1

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The Tower of Hanoi (also called the Tower of Brahma or Lucas' Tower) was invented by the French mathematician Ă‰douard Lucas in 1883.

There is a story about an Indian temple which contains a large room with three old posts and 64 golden disks. Brahmin priests, acting out the command of an ancient prophecy, have been moving these disks for countless years. According to the legend, when the last move of the puzzle will be completed, the world will end!

Level 10 of this puzzle featured in an episodeIn the 1966 Doctor Who story called The Celestial Toymaker. The villain forces the Doctor to work on a ten-piece Tower of Hanoi puzzle (which they call The Trilogic Game) and if the Doctor manages to complete the puzzle, the Toymaker's domain will disappear.

The Math Book,

Sunday, August 11, 2019

"Simple algorithms exist for solutions involving three pegs, and the game is often used in computer programming classes to teach recursive algorithms. However, the optimal solution for the Tower of Hanoi problem with four or more pegs is still unknown!"

Bridget Lindley, UK

Saturday, October 31, 2020

"I have a plastic Tower of Hanoi from 1950s with 8 discs, but with only two colours (yellow and blue). Much easier to keep track of your moves than with lots of colours especially when so close in size."

Ella, Home Schooling

Tuesday, January 26, 2021

"This is quite hard but really fun and I have the whole family involved (even the cat). I always enjoy completing Transum tasks and can't wait to see more like this!"

Bernie Westacott, Twitter

Friday, February 19, 2021

The solutions to this and other Transum puzzles, exercises and activities are available here when you are signed in to your Transum subscription account. If you do not yet have an account and you are a teacher, tutor or parent you can apply for one by completing the form on the Sign Up page.

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