##### Year 3 to Year 6: Finding Fifteen

Tim had nine cards, each with a different number from 1 to 9 on it.

He put the cards into three piles so that the total in each pile was 15.

How could he have done this?

Can you find all the different ways Tim could have done this?

Thank you for the many solutions to this problem. It was interesting to see that some of you presumed there had to be three cards in each pile which totalled 15. In fact, the question simply said there had to be three PILES, which makes the problem a little trickier than it looks at first.

Let’s be systematic by looking for other ways to make a number, for example 7. So we made 6+1, 3+4, 5+2 and 7 on its own and put 8 with it each time. It was good because then there were more solutions to make 15. Here are some solutions to make 15 (reading across the table for the three piles):