Problems
Constant Counting
Stage: 1 Challenge Level: 
You can make a calculator count for you by any number you choose. You can count by ones to reach 24. You can count by twos to reach 24. What else can you count by to reach 24?
Mrs Beeswax
Stage: 1 Challenge Level:
In how many ways could Mrs Beeswax put ten coins into her three puddings so that each pudding ended up with at least two coins?
Sweets in a Box
Stage: 2 Challenge Level:
How many different shaped boxes can you design for 36 sweets in one layer? Can you arrange the sweets so that no sweets of the same colour are next to each other in any direction?
Tom's Number
Stage: 2 Challenge Level:
Work out Tom's number from the answers he gives his friend. He will only answer 'yes' or 'no'.
Pies
Stage: 2 Challenge Level:
Grandma found her pie balanced on the scale with two weights and a quarter of a pie. So how heavy was each pie?
World of Tan - Celebrations
Stage: 2 Challenge Level:
Can you fit the tangram pieces into the outline of Little Ming and Little Fung dancing?
Paving Paths
Stage: 3 Challenge Level:
How many different ways can I lay 10 paving slabs, each 2 foot by 1 foot, to make a path 2 foot wide and 10 foot long from my back door into my garden, without cutting any of the paving slabs?
Plutarch's Boxes
Stage: 3 Challenge Level:
According to Plutarch, the Greeks found all the rectangles with integer sides, whose areas are equal to their perimeters. Can you find them? What rectangular boxes, with integer sides, have. . . .
Where Can We Visit?
Stage: 3 Challenge Level:
Charlie and Lynne put a counter on 42. They wondered if they could visit all the other numbers on their 1-100 board, moving the counter using just these two operations: x2 and -5. What do you think?
On the Road
Stage: 4 Challenge Level:
Four vehicles travelled on a road with constant velocities. The car overtook the scooter at 12 o'clock, then met the bike at 14.00 and the motorcycle at 16.00. The motorcycle met the scooter at. . . .
Triangle Incircle Iteration
Stage: 4 Challenge Level:
Start with any triangle T1 and its inscribed circle. Draw the triangle T2 which has its vertices at the points of contact between the triangle T1 and its incircle. Now keep repeating this. . . .
Why 24?
Stage: 4 Challenge Level:
Take any prime number greater than 3, square it, subtract one and divide by 24. Make a statement about what you notice about dividing by 24 (a conjecture) and prove that what you say is always true.
Code to Zero
Stage: 5 Challenge Level:
Find all 3 digit numbers such that by adding the first digit, the square of the second and the cube of the third you get the original number, for example 1 + 3^2 + 5^3 = 135.
Four Points on a Cube
Stage: 5 Challenge Level:
What is the surface area of the tetrahedron with one vertex at O the vertex of a unit cube and the other vertices at the centres of the faces of the cube not containing O?
Little and Large
Stage: 5 Challenge Level:
A point moves around inside a rectangle. What are the least and the greatest values of the sum of the squares of the distances from the vertices?
Squash
Stage: 5 Challenge Level:
If the score is 8-8 do I have more chance of winning if the winner is the first to reach 9 points or the first to reach 10 points?
Elsewhere...
Featured Solutions
Articles & Games
Frogs
You can solve frogs on the computer, using counters, or acting it out. Start with frogs in a line on one side, and toads on the other, with a space in between. They need to change places.
