### Pebbles

Place four pebbles on the sand in the form of a square. Keep adding as few pebbles as necessary to double the area. How many extra pebbles are added each time?

### Adding All Nine

Make a set of numbers that use all the digits from 1 to 9, once and once only. Add them up. The result is divisible by 9. Add each of the digits in the new number. What is their sum? Now try some other possibilities for yourself!

### GOT IT Now

For this challenge, you'll need to play Got It! Can you explain the strategy for winning this game with any target?

# Inclusion Exclusion

##### Stage: 3 Challenge Level:

How many integers between 1 and 1200 are multiples of 2?

How many integers between 1 and 1200 are multiples of 3?

How many integers between 1 and 1200 are multiples of 5?

Some integers are multiples of both 2 and 3, of both 2 and 5, of both 3 and 5...

Some integers are multiples of 2, 3 and 5...

Can the Venn diagram in the question help, if you consider that the multiples of 2, 3 and 5 each correspond to one of the sets (circles)?