### 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?

### Great Squares

Investigate how this pattern of squares continues. You could measure lengths, areas and angles.

### Square Areas

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

# Carpet Cuts

##### Stage: 3 Challenge Level:

Katherine from Maidstone Girls Grammar School made very good use of the Excel spreadsheet software to draw her solutions. .

To find the ten by ten foot carpet from a twelve by nine foot carpet with an eight by one foot hole exactly in the middle, I started by making a lot of grids (9 by 12 with an 8 by 1 foot hole hole exactly in the middle) so that I would be able to try different ways to make it a 10 by 10 foot carpet.

At first, I was cutting in straight lines trying to make them fit. Just out of interest, I counted the squares in the carpet, there were 100. This meant that I couldn't overlap the carpet in any way.

From this information, I thought that it would only be possible by cutting diagonally, so I started to cut going up then across one at a time, then I worked it out like this.

RESULT. I found the solution, but there were two. A left and a right handed solution, here they are.