In turn 4 people throw away three nuts from a pile and hide a
quarter of the remainder finally leaving a multiple of 4 nuts. How
many nuts were at the start?

Three semi-circles have a common diameter, each touches the other
two and two lie inside the biggest one. What is the radius of the
circle that touches all three semi-circles?

Sums of Squares

Age 16 to 18 Challenge Level:

Try some examples of your own.

What do you notice about the squares?

If you think there is a pattern can you prove that it will always
work out that way?