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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?

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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!

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Have You Got It?

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

Ben's Game

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

The total number they were using must be divisible by $3$.

Ben's counters must initially have been divisible by $3$, Jack's by $4$ and Emma's by $5$.

It might help to work out the maximum each could have started with - e.g. Emma could not have started with $25$ counters. Can you work out why?

How many counters could each of them have started with?

Try some possible numbers.