Problems
3 Rings
Stage: 2 Challenge Level: 
If you have three circular objects, you could arrange them so that they are separate, touching, overlapping or inside each other. Can you investigate all the different possibilities?
Two Egg Timers
Stage: 2 Challenge Level:
You have two egg timers. One takes 4 minutes exactly to empty and the other takes 7 minutes. What times in whole minutes can you measure and how?
Towers
Stage: 3 Challenge Level:
A tower of squares is built inside a right angled isosceles triangle. The largest square stands on the hypotenuse. What fraction of the area of the triangle is covered by the series of squares?
Crossing the Atlantic
Stage: 3 Challenge Level:
Every day at noon a boat leaves Le Havre for New York while another boat leaves New York for Le Havre. The ocean crossing takes seven days. How many boats will each boat cross during their journey?
Dozens
Stage: 3 Challenge Level:
Use the digits 1, 3, 4, 5 and one more digit and, with these digits, make the largest possible 5-digit number which is divisible by 12.
A Shade Crossed
Stage: 4 Challenge Level:
Find the area of the shaded region created by the two overlapping triangles in terms of a and b?
Shrink
Stage: 4 Challenge Level:
X is a moveable point on the hypotenuse, and P and Q are the feet of the perpendiculars from X to the sides of a right angled triangle. What position of X makes the length of PQ a minimum?
From All Corners
Stage: 4 Challenge Level:
Straight lines are drawn from each corner of a square to the mid points of the opposite sides. Express the area of the octagon that is formed at the centre as a fraction of the area of the square.
Clickety Click and All the Sixes
Stage: 5 Challenge Level:
What is the sum of: 6 + 66 + 666 + 6666 ............+ 666666666...6 where there are n sixes in the last term?
