### 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?

# What Two ...?

##### Stage: 2 Short Challenge Level:

Louise of Headington Junior School gives the answer of 237 and 238.

"I worked this out by finding the square root of 56,406 and then wrote down the whole number (237) and rounded it up to 238".

Class 7P from Loretto Junior, Musselburgh apporached this problem using trial and improvement which is a very useful strategy:

Kitty said let's try 600 x 600 = 360000 and that is too big!
Angus said let's try 100 x 100 = 10000 and that is too small.
Ashleigh thought 200 x 200 was 40000 which was a little too small.
Graeme knew that 250 x 250 was 62,500 - close!
Sophie offered 230 x 230 which is 52,900 - getting there.
Gair now tried 240 x 240 and got 57,600.
Tom provided the masterstroke and said our number 56406 should be in the high 230s , so we looked at 236x 237 but the last digit is a 2 because 6x7 = 42.
Finally Caitlin shouted in excitement 'try 237x 238 as the last digit will be a 6'. The answer therefore is 237 x 238.