Take a look at the video below:

Charlie asks James and Caroline for sets of five numbers.

For each set of numbers they give, Charlie picks out a set of three numbers which add together to give a multiple of $3$.

**Can you come up with a set of five numbers that doesn't include three which add up to a multiple of $3$?**

**If not, can you come up with an argument to convince someone else that no such set exists?**

Now that you've thought about choosing three numbers from a set of five, you might like to consider the following:

Can you always choose two numbers from a set of three whose total is a multiple of two?

Can you always choose four numbers from a set of seven whose total is a multiple of four?