### 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?

### Adding All Nine

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?

# Magical Products

##### Stage: 3 Short Challenge Level:

 $3$ $\frac{1}{6}$ $2$ $\frac{2}{3}$ $1$ $\frac{3}{2}$ $\frac{1}{2}$ $6$ $\frac{1}{3}$

This is one answer (seven others are possible by rotation and reflection).

This problem is taken from the UKMT Mathematical Challenges.