Problems
Cops and Robbers
Stage: 2 and 3 Challenge Level: 
Can you find a reliable strategy for choosing coordinates that will locate the robber in the minimum number of guesses?
M, M and M
Stage: 3 Challenge Level:
If you are given the mean, median and mode of five positive whole numbers, can you find the numbers?
Searching for Mean(ing)
Stage: 3 Challenge Level:
Imagine you have a large supply of 3kg and 8kg weights. How many of each weight would you need for the average (mean) of the weights to be 6kg? What other averages could you have?
Grid Lockout
Stage: 4 Challenge Level:
What remainders do you get when square numbers are divided by 4?
Just Opposite
Stage: 4 Challenge Level:
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?
Sitting Pretty
Stage: 4 Challenge Level:
A circle of radius r touches two sides of a right angled triangle, sides x and y, and has its centre on the hypotenuse. Can you prove the formula linking x, y and r?
Just Rolling Round
Stage: 4 Challenge Level:
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?
Giant Holly Leaf
Stage: 4 Challenge Level:
Find the perimeter and area of a holly leaf that will not lie flat (it has negative curvature with 'circles' having circumference greater than 2πr).
Polycircles
Stage: 4 Challenge Level:
Show that for any triangle it is always possible to construct 3 touching circles with centres at the vertices. Is it possible to construct touching circles centred at the vertices of any polygon?
Golden Thoughts
Stage: 4 Challenge Level:
Rectangle PQRS has X and Y on the edges. Triangles PQY, YRX and XSP have equal areas. Prove X and Y divide the sides of PQRS in the golden ratio.
Elsewhere...
Featured Solution
Legs Eleven
We received good solutions with clear explanations to why the numbers add up to multiples of 11.
Articles & Games
Geometry: A History from Practice to Abstraction
This article for students and teachers gives a brief history of the development of Geometry.
LCM Sudoku II
You are given the Lowest Common Multiples of sets of digits. Find the digits and then solve the Sudoku.
Slippery Snail
A game for 2 people. Take turns to move the counters 1, 2 or 3 spaces. The player to remove the last counter off the board wins.
