Problems
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?
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.
Stats Statements
Stage: 5 Challenge Level:
Are these statistical statements sometimes, always or never true? Or it is impossible to say?
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?
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
Advent Calendar 2008
Our 2008 Advent Calendar has a 'Making Maths' activity for every day in the run-up to Christmas.
Tiling in Ludlow
What is the same and what is different about these tiling patterns and how do they contribute to the floor as a whole?
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.
Stemnrich
stemNRICH is a section of the NRICH site devoted to the mathematics underlying scientific contexts.
