## Towers of Hanoi (3 ACTS)

I really should have waited to do this until after Movember (mustache month for charity), but felt like getting stuck in.

Act 1 – Any Questions?

Questions

1. What’s the minimum number of moves to transfer all 10 disks to the 3rd column?

(Make a guess you know is too low and one that you know is too high)

2. How would you even go about doing the 10 disk problem? What strategies are there which would break the problem up into manageable chunks?

Sequel

1. It took me 33 minutes to complete the 10 disk puzzle. Working at the same speed, approximately how long would it take me to solve a 50 disk puzzle?

2. As the number of disks increase, the number of moves increase in a certain way. Can you find any other problems or real life phenomenon that increase in the same or a similar way?

a. NCTM Applet to help investigate it (It would be great to get them working out strategies as a homework task with this applet. Any strategies that they notice you could get them to email to you before the next lesson).

b. Connection with the Sierpinski Triangle.

c. Robot that can solve the Towers of Hanoi puzzle.

Related Problems:

a. A Geogebra Applet on Bacterial Growth.

b. Nrich Task – Modelling an Epidemic (Nice kinaesthetic starter).

c. Grains of Rice on a Chessboard Problem (The video is quite old but I love it).

d. Compound Interest – Would you rather have £1000000 today or £1 today, £2 tomorrow, £4 the next day, £8 the day after that, with this sequence continuing for 30 days?

e. Paper Folding TED Talk.

f. Dan Meyer’s Domino SkyScraper.