Problems
Why not send us your solutions?
Eggs in Baskets
Stage:1 Challenge Level:
There are three baskets, a brown one, a red one and a pink one, holding a total of 10 eggs. Can you use the information given to find out how many eggs are in each basket?
6 Beads
Stage:1 Challenge Level:
If you put three beads onto a tens/ones abacus you could make the numbers 3, 30, 12 or 21. What numbers can be made with six beads?
Month Mania
Stage:1 and 2 Challenge Level:
Can you design a new shape for the twenty-eight squares and arrange the numbers in a logical way? What patterns do you notice?
Taking a Die for a Walk
Stage:1 and 2 Challenge Level:
Investigate the numbers that come up on a die as you roll it in the direction of north, south, east and west, without going over the path it's already made.
Magic Vs
Stage:2 Challenge Level:
Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?
5 on the Clock
Stage:2 Challenge Level:
On a digital clock showing 24 hour time, over a whole day, how many times does a 5 appear? Is it the same number for a 12 hour clock over a whole day?
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?
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).
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 'sits' on a right-angled triangle, touches two sides of the triangle and has its centre on the hypotenuse of the triangle. Can you find and justify the relationship between x,. . . .
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.
Just Rolling Round
Stage:4 and 5 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?
Polycircles
Stage:4 and 5 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?
Circles Ad Infinitum
Stage:5 Challenge Level:
A circle is inscribed in an equilateral triangle. Smaller circles touch it and the sides of the triangle, the process continuing indefinitely. What is the sum of the areas of all the circles?
Catalyse That!
Stage:5 Challenge Level:
Can you work out how to produce the right amount of chemical in a temperature-dependent reaction?
Stats Statements
Stage:5 Challenge Level:
Are these statistical statements sometimes, always or never true? Or it is impossible to say?
Elsewhere...
Featured Solutions
Quadrilaterals
You found some very helpful ways of working on this problem. Some of you drew pictures while others used numbers to represent the circle's dots.
Legs Eleven
We received good solutions with clear explanations to why the numbers add up to multiples of 11.
Sixty-seven Squared
Playing with numbers leads to a conjecture for the solution. Place value and summing a geometric series gives proof of the conjecture.
Articles & Games
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.
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.
Student Guide to Getting Started with Rich Tasks
This article gives advice on getting started with exploring rich mathematical tasks.
