### 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!

### GOT IT Now

For this challenge, you'll need to play Got It! Can you explain the strategy for winning this game with any target?

##### Stage: 3 Challenge Level:

Please note: Although it involves only elementary mathematical ideas, this problem is very difficult and will probably take a long time to solve!

A mathematician goes into a supermarket and buys four items.

It has been a while since she has used a calculator and she multiplies the cost (in pounds, using the decimal point for the pence) instead of adding them.

At the checkout she says, "So that's £7.11" and the checkout man, correctly adding the items, agrees.

Find four possible prices of the items.

Extension: Prove that the costs giving rise to £7.11 are unique.