### 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!

### Have You Got It?

Can you explain the strategy for winning this game with any target?

# Stair Climb

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

Boris has to run up $99$ steps, and runs up $5$ in each unit of time, so it takes him $99 \div 5 = 19\frac{4}{5}$ units of time to reach the top.

Spike has to run up $78$ steps, and runs up $4$ in each unit of time, so it takes him $78 \div 4 = 19\frac{1}{2}$ units of time.

Percival has to run up $61$ steps, and runs up $3$ in each unit of time, so it takes him $61 \div 3 = 20\frac{1}{3}$ units of time.

Therefore they finish in the order Spike, Boris Percival.

This problem is taken from the UKMT Mathematical Challenges.