### 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.

# Magic Potting Sheds

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

Mr McGregor has a magic potting shed. Overnight, the number of plants in it doubles. He would like to put the same number of plants in each of three gardens, planting one garden each day.

On the first day he puts some plants in the shed. Overnight, they double.
The next day he plants some in one of the gardens. The remaining plants double overnight.
The next day he plants some in a second garden, and again the remaining plants double overnight.
On the final day he plants all the remaining plants in the third garden.

Use the interactivity below to help you work out how many plants he should put in the potting shed on the first day, and how many he should plant in each garden.
Can you find more than one solution?
What do the solutions have in common?
Can you find the smallest number of plants he could use?

If you have enjoyed this problem, you might like to move on to More Magic Potting Sheds .