Sliced
Age 14 to 16
Challenge Level 
An irregular tetrahedron has two opposite sides the same length ($a$ say) and the line joining their midpoints is perpendicular to these two edges and is of length $b$. What is the volume of the tetrahedron?
You may also like
Just Rolling Round
P is a point on the circumference of a circle radius r which rolls, without slipping, inside a circle of radius 2r. What is the locus of P?
Coke Machine
The coke machine in college takes 50 pence pieces. It also takes a certain foreign coin of traditional design...
Just Opposite
A and C are the opposite vertices of a square ABCD, and have coordinates (a,b) and (c,d), respectively. What are the coordinates of the vertices B and D? What is the area of the square?