### 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?

### It Figures

Suppose we allow ourselves to use three numbers less than 10 and multiply them together. How many different products can you find? How do you know you've got them all?

### Bracelets

Investigate the different shaped bracelets you could make from 18 different spherical beads. How do they compare if you use 24 beads?

##### Stage: 2 Challenge Level:

Well done to those of you who had a good attempt at this problem.

George of Ardingly College says :

You just have to make the numbers on the right hand-side add up to the same total as the left hand side.

Congratulations to Jessica and Emily of Aldermaston CE primary School who found many different solutions to the problem.

In order to work out this problem we decided we should do a chart, so we could track how many answers we could come up with. We both did our tally chart, Emily did one using 4 weights and Jessica did one using less than 4 weights.

At the end we both helped each other. Emily's chart had more answers than Jessica's chart. One of the ways that Emily worked some out was splitting one of Jessica's numbers to 2 numbers and then she would get more solutions.

Tally chart for making 24 with 4 weights:

Tally Chart for ways to make 24 with less than 4 weights:

It is impossible to do it with only 2 weights because there is no 12 hook and 2 12s would make 24.