There must be millions of people who have heard of the Tower of Hanoi puzzle and the simple algorithm that generates the simplest solution. But what happens when you are playing the game not with three pegs, as in the original puzzle, but with 4, 5, 6 etc. pegs? Hardly anybody seems to know that there are also really really beautiful solutions which are believed to be optimal but whose optimality has only been proved for four pegs. Even less people know that you can boil down all these optimal solutions into simple no-brainer recipes that allow you to effortless execute these solutions from scratch. Clearly a job for the Mathologer. Get ready to dazzle your computer science friends 🙂

I also talk about 466/885, the Power of Hanoi constant and a number of other Hanoi facts off the beaten track. And the whole thing has a Dr Who hook which is also very cute.

00:00​ Intro
01:58​ Chapter 1: The doctor vs. the toymaker
14:27​ Chapter 2: Hanoi constant
21:21​ Chapter 3: The Reve’s puzzle
28:04​ A beautiful shortest solution for 10 discs and 4 pegs (discs and super-disks)
30:23​ Chapter 4: Unprovable algorithm
35:43​ A beautiful shortest solution for 10 discs and 5 pegs (discs, super-discs and super-super-discs)
37:17​ Supporters

Here are some references for you to check out:

Andreas M. Hinz et al. – The Tower of Hanoi – Myths and Maths, 2nd edition (2018, Birkhäuser Basel) That’s the book I mentioned in the video.

The Dr Who episode (well the part that’s not been lost) https://www.dailymotion.com/video/x11…​%5B…%5D