### Square Areas

Can you work out the area of the inner square and give an explanation of how you did it?

### Dissect

What is the minimum number of squares a 13 by 13 square can be dissected into?

### 2001 Spatial Oddity

With one cut a piece of card 16 cm by 9 cm can be made into two pieces which can be rearranged to form a square 12 cm by 12 cm. Explain how this can be done.

# Coloured Edges

##### Age 11 to 14Challenge Level

Laura Turner and Laura Malarkey from the Mount School have explained how they worked out the answer to this problem:

n is equal to the number of tiles along one side.

We can calculate the number of edges in two different ways:

Method 1 - In total there are $n ²$ tiles on $4n ²$ edges.

Method 2 - There are a total of $2n$ green edges which implies there are a total of $20n$ edges of all colours.

Therefore:

$20n = 4n ²$

$5n = n ²$ (divide by $4$)

$5 = n$ (divide by $n$)

So there are $25$ tiles in the set.