### Calendar Capers

Choose any three by three square of dates on a calendar page...

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!

### Rotating Triangle

What happens to the perimeter of triangle ABC as the two smaller circles change size and roll around inside the bigger circle?

# What Numbers Can We Make Now?

##### Stage: 3 Challenge Level:

This problem follows on from What Numbers Can We Make?

The interactivity below creates sets of bags similar to those in What Numbers Can We Make?

Investigate what numbers you can make when you choose three numbers from the bags. Once you think you know what is special about the numbers you can check your answer.

You can also find what is special when you choose four, five or six numbers.

When you have an efficient strategy, test it by choosing 99 or 100 numbers.

Always enter the biggest possible multiple. The "plus" number may include zero.

Choose numbers from the bags and find their total.

The answer is always than a multiple of