 This is a mathematical snack from the Association of Teachers of Mathematics. This is a puzzle called the Tower of Hanoi. There are three spaces on the piece of paper in front of me and I have a number of discs of different sizes. I have three here. I've made a tower in order of size with the smallest on the top and I've put the tower in the starting space. The challenge is to move the tower to the finishing space in the fewest number of moves possible. The rules are move only one disc at a time and never put a larger disc on a smaller one. So here we go. One, two, three, four, five, six, seven, eight, nine, 10, 11. I'm going to see if I can do it in fewer moves so I'm going to go back to the beginning. One, two, three, four, five, six, seven. I think that might be the fewest number of moves I need. Seven. I'm not going to try and do this with four discs so I've brought a larger disc and I've got a new tower now with four discs and I'm going to try and move it across. Same rules. One, two, three, four, five, six, seven, eight, nine, 10, 11, 12, 13, 14, 15. I think that might be the smallest. I'm not sure. I'd need to try it out more times but I'm going to write 15 there in brackets. So what about five? What about six? Can you spot a pattern? Can you predict what five and six might be?