### Repeaters

Choose any 3 digits and make a 6 digit number by repeating the 3 digits in the same order (e.g. 594594). Explain why whatever digits you choose the number will always be divisible by 7, 11 and 13.

### Oh! Hidden Inside?

Find the number which has 8 divisors, such that the product of the divisors is 331776.

### Like Powers

Investigate $1^n + 19^n + 20^n + 51^n + 57^n + 80^n + 82^n$ and $2^n + 12^n + 31^n + 40^n + 69^n + 71^n + 85^n$ for different values of n.

# Multiples Sudoku

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

In the third row, 30 and 18 appear on adjacent border lines. Which set of three numbers could be placed in the first three cells of that row?

In the fifth row, 8 and 18 appear on adjacent border lines. Which set of three numbers could be placed in the last three cells of that row?

Alison and Charlie kept a record of the order in which they filled the Sudoku.

They filled the cell marked 1 first, then the cell marked 2, then the cell marked 3...

You might like to retrace their route to fill in the cells in the same order, though this is just one possible route through the problem.

You can print their journey here.