#### You may also like

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!

### Have You Got It?

Can you explain the strategy for winning this game with any target?

### Counting Factors

Is there an efficient way to work out how many factors a large number has?

# Expanding Zeros

##### Age 11 to 14 Short Challenge Level:

The following sequence continues indefinitely:

27 = 3 x 3 x 3
207 = 3 x 3 x 23
2 007 = 3 x 3 x 223
20 007 = 3 x 3 x 2223.......

Which of the following integers is a multiple of 81?

a) 20 000 007
b) 2 000 000 007
c) 200 000 000 007
d) 20 000 000 000 007

If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.

This problem is taken from the UKMT Mathematical Challenges.
You can find more short problems, arranged by curriculum topic, in our short problems collection.