You may also like

problem icon

Plum Tree

Label this plum tree graph to make it totally magic!

problem icon

Magic W

Find all the ways of placing the numbers 1 to 9 on a W shape, with 3 numbers on each leg, so that each set of 3 numbers has the same total.

problem icon

2-digit Square

A 2-Digit number is squared. When this 2-digit number is reversed and squared, the difference between the squares is also a square. What is the 2-digit number?

Three Four Five

Age 14 to 16 Challenge Level:

3 semicircles
As shown in the diagram, two semi-circles (each of radius $1/2$) touch each other, and a semi-circle of radius 1 touches both of them. Find the radius of the circle which touches all three semi-circles, and find a 3-4-5 triangle in the diagram.