Conjecturing and generalising

problem
Two's company

Age

11 to 14

Challenge level

Seven balls are shaken. You win if the two blue balls end up touching. What is the probability of winning?
problem
Flippin' discs

Age

11 to 14

Challenge level

Discs are flipped in the air. You win if all the faces show the same colour. What is the probability of winning?
problem
Bishop's paradise

Age

11 to 14

Challenge level

Weekly Problem 37 - 2013
Which of the statements about diagonals of polygons is false?
problem
Board block challenge

Age

7 to 11

Challenge level

Choose the size of your pegboard and the shapes you can make. Can you work out the strategies needed to block your opponent?
problem
Triangle pin-down

Age

7 to 11

Challenge level

Use the interactivity to investigate what kinds of triangles can be drawn on peg boards with different numbers of pegs.
problem
Right angles

Age

11 to 14

Challenge level

Can you make a right-angled triangle on this peg-board by joining up three points round the edge?
problem
Subtended angles

Age

11 to 14

Challenge level

What is the relationship between the angle at the centre and the angles at the circumference, for angles which stand on the same arc? Can you prove it?
problem
Cubes within cubes revisited

Age

11 to 14

Challenge level

Imagine starting with one yellow cube and covering it all over with a single layer of red cubes, and then covering that cube with a layer of blue cubes. How many red and blue cubes would you need?
problem
Partitioning revisited

Age

11 to 14

Challenge level

We can show that (x + 1)² = x² + 2x + 1 by considering the area of an (x + 1) by (x + 1) square. Show in a similar way that (x + 2)² = x² + 4x + 4
problem
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?