### 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?

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!

### N000ughty Thoughts

Factorial one hundred (written 100!) has 24 noughts when written in full and that 1000! has 249 noughts? Convince yourself that the above is true. Perhaps your methodology will help you find the number of noughts in 10 000! and 100 000! or even 1 000 000!

# Expanding Zeros

##### Stage: 3 and 4 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: 200,007
B: 20,000,007
C: 2,000,000,007
D: 200,000,000,007
E: 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.
View the archive of all weekly problems grouped by curriculum topic

View the previous week's solution
View the current weekly problem