42
Today my 6-years old son came with a math homework. The stated goal was to learn the different ways to make 10 out of smaller numbers. I was impressed. Immediately, I wondered
how many ways are there to make 10 out of smaller numbers?
This is one of the beauties of maths: a very simple problem, which a 6-years old can understand, may actually be quite fundamental. If you want to solve this in the general case, for any number instead of 10, you end up with the partition function. And in order to find this, you will probably learn recurrence relations. So what is the answer for 10?
42
Then I looked at one exercise they did in class, which was simply to find different ways to pay 10 euros with bills of 10, 5 and coins of 2 and 1 euro(s).