Sally is making spinners. She has divided two circles into 3 equal parts.
Now she is going to put 1s, 2s and 3s stickers in the spaces on the circles. But she finds that she only has two 1s stickers, two 2s stickers, and two 3s stickers.
Where should she put the numbers so that when she spins the two spinners the total of 5 comes up as often as possible?
Solution
The only way that Sally can get a total of 5 is if there is a 2 on one spinner and a 3 on the other. If she has a 2 and a 3 on each of the spinners, then she’ll get two possible totals of 5. If she has two 2s on one spinner and a 3 on the other, that will give her two ways of getting 5 too. However, if she has two 2s on one spinner and two 3s on the other she has found four ways to get a total of 5.
It’s not possible for her to find five ways of getting 5 though. So the spinners must look like this.
Extension
If Sally has found a lot of different sticker numbers, how could she number her two spinners so that she gets totals of 7, 8, 9, 10 and 11? (There are still only three spaces for numbers on each spinner.)