### Building Tetrahedra

Can you make a tetrahedron whose faces all have the same perimeter?

A 1 metre cube has one face on the ground and one face against a wall. A 4 metre ladder leans against the wall and just touches the cube. How high is the top of the ladder above the ground?

Four rods are hinged at their ends to form a convex quadrilateral. Investigate the different shapes that the quadrilateral can take. Be patient this problem may be slow to load.

# CD Heaven

##### Age 14 to 16 Challenge Level:

All CD Heaven stores were given the same number of a popular CD to sell for £24.

In their two week sale each store reduces the price of the CD by 25% and any further reductions are then left to the discretion of the store managers.

Towards the end of the two week sale one store still had 30 CDs left and the manager decided to try to clear the remainder by reducing the price by a further $\frac{1}{3}$ but still did not manage to sell them all. The total sales for the CDs was £2010. If the store had managed to sell all its CDs by the end of the two week sale period it would have received £2370.

Another store sold the same number of CDs before and during the first two weeks of the sale as the first store but in reverse order (the number they sold for £24 was the same as the number sold in the two weeks of the sale by the first store and vice versa). At the end of the two weeks the shop manager decided to reduce the price of the CDs by a further 50% and managed to sell all the remaining 30 CDs making her total sales £2010.

How many CDs did the first store sell at each price?