problem
Favourite
Arithmagons
Age
11 to 16
Challenge level
Can you find the values at the vertices when you know the values on the edges?
problem
Favourite
More Twisting and Turning
Age
11 to 16
Challenge level
It would be nice to have a strategy for disentangling any tangled ropes...
problem
Favourite
Take Three From Five
Age
11 to 16
Challenge level
Caroline and James pick sets of five numbers. Charlie tries to find three that add together to make a multiple of three. Can they stop him?
problem
Favourite
Who is the fairest of them all ?
Age
11 to 14
Challenge level
Explore the effect of combining enlargements.
problem
Favourite
Differences
Age
11 to 14
Challenge level
Can you guarantee that, for any three numbers you choose, the product of their differences will always be an even number?
problem
Favourite
Speeding boats
Age
14 to 16
Challenge level
Two boats travel up and down a lake. Can you picture where they will cross if you know how fast each boat is travelling?
problem
Favourite
Circles in quadrilaterals
Age
14 to 16
Challenge level
Explore when it is possible to construct a circle which just touches all four sides of a quadrilateral.
problem
Favourite
A little light thinking
Age
14 to 16
Challenge level
Here is a machine with four coloured lights. Can you make two lights switch on at once? Three lights? All four lights?
problem
Favourite
Which is cheaper?
Age
14 to 16
Challenge level
When I park my car in Mathstown, there are two car parks to choose from. Can you help me to decide which one to use?
problem
Favourite
Hollow Squares
Age
14 to 16
Challenge level
Which armies can be arranged in hollow square fighting formations?
problem
Favourite
Pair Products
Age
14 to 16
Challenge level
Choose four consecutive whole numbers. Multiply the first and last numbers together. Multiply the middle pair together. What do you notice?
problem
Favourite
Painted Cube
Age
14 to 16
Challenge level
Imagine a large cube made from small red cubes being dropped into a pot of yellow paint. How many of the small cubes will have yellow paint on their faces?
problem
Favourite
Multiplication square
Age
14 to 16
Challenge level
Pick a square within a multiplication square and add the numbers on each diagonal. What do you notice?
problem
Favourite
Perpendicular lines
Age
14 to 16
Challenge level
Position the lines so that they are perpendicular to each other. What can you say about the equations of perpendicular lines?
problem
Favourite
For richer for poorer
Age
14 to 16
Challenge level
Charlie has moved between countries and the average income of both has increased. How can this be so?
problem
Favourite
At right angles
Age
14 to 16
Challenge level
Can you decide whether two lines are perpendicular or not? Can you do this without drawing them?
problem
Favourite
Mystic Rose
Age
14 to 16
Challenge level
Use the animation to help you work out how many lines are needed to draw mystic roses of different sizes.
problem
Favourite
Filling the gaps
Age
14 to 16
Challenge level
Which numbers can we write as a sum of square numbers?
problem
Favourite
Plus Minus
Age
14 to 16
Challenge level
Can you explain the surprising results Jo found when she calculated
the difference between square numbers?
problem
Favourite
Of all the areas
Age
14 to 16
Challenge level
Can you find a general rule for finding the areas of equilateral triangles drawn on an isometric grid?
problem
Favourite
Fair Shares?
Age
14 to 16
Challenge level
A mother wants to share a sum of money by giving each of her
children in turn a lump sum plus a fraction of the remainder. How
can she do this in order to share the money out equally?
problem
Favourite
What's Possible?
Age
14 to 16
Challenge level
Many numbers can be expressed as the difference of two perfect squares. What do you notice about the numbers you CANNOT make?
problem
Favourite
Attractive Tablecloths
Age
14 to 16
Challenge level
Charlie likes tablecloths that use as many colours as possible, but insists that his tablecloths have some symmetry. Can you work out how many colours he needs for different tablecloth designs?
problem
Favourite
Pick's Theorem
Age
14 to 16
Challenge level
Polygons drawn on square dotty paper have dots on their perimeter (p) and often internal (i) ones as well. Find a relationship between p, i and the area of the polygons.
problem
Favourite
Harmonic Triangle
Age
14 to 16
Challenge level
Can you see how to build a harmonic triangle? Can you work out the next two rows?