## Tuesday, 23 June 2015

### Towers of Hanoi

We've been investigating the Towers of Hanoi puzzle. Usually this is done with disks.

But we used Cuisenaire rods.
We started with just three rods.
The aim is to move a whole pile of rods, but in a certain way. Bigger rods can never be on top of smaller ones. You can only move the top rod in the pile. You can never put a big rod on top of a small one. You can only have one pile in a circle.

The challenge was, not just to do the puzzle, but to be able to find a way to write down what we had done. We found lots of different ways:
Then we moved onto four rods:
Some of us shared our ways with the whole class.

It was interesting to look at the pattern in the minimum number of moves necessary for different sized piles of rods at the start:
Here's a slideshow:

PS The next day Rod brought in his own Towers of Hanoi:
We also returned to that doubling series (called "powers of two" - but we don't need to remember that, do we). Some of us kept on doubling for quite a while...
And we went the other way too: halving. We halved a circle: ½  ¼  ⅛...