### 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?

### Towers

A tower of squares is built inside a right angled isosceles triangle. What fraction of the area of the triangle is covered by the squares?

### Framed

Seven small rectangular pictures have one inch wide frames. The frames are removed and the pictures are fitted together like a jigsaw to make a rectangle of length 12 inches. Find the dimensions of the pictures.

# Warmsnug Double Glazing

##### Age 11 to 14 Challenge Level:

Warmsnug calculate the prices of their windows according to the area of glass used and the length of frame needed.

Can you work out how Warmsnug arrived at the prices of the windows below?
Which window has been given an incorrect price?

The information is available on a printable worksheet here.

This spreadsheet generates prices for the windows according to different pricing rules.
Can you find an efficient strategy for finding how the prices were calculated?

This problem is based on the original Warmsnug Double Glazing problem which appeared in The Language of Functions and Graphs produced by the Shell Centre for Mathematical Education and the Joint Matriculation Board.