### 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!

### Counting Factors

Is there an efficient way to work out how many factors a large number has?

# Have You Got It?

##### Stage: 3 Challenge Level:

Work backwards.

Simplify the game by choosing a smaller target and working out a winning strategy.

Investigate complements of $6$.

Play the game against the computer and think about the computer's strategy.