Being curious

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

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

Six balls are shaken. You win if at least one red ball ends in a corner. What is the probability of winning?

Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the dot affects its speed at each stage.

A 2 by 3 rectangle contains 8 squares and a 3 by 4 rectangle contains 20 squares. What sizes of rectangle contain exactly 100 squares? Can you find them all?

Explore the effect of reflecting in two intersecting mirror lines.

Take a look at the multiplication square. The first eleven triangle numbers have been identified. Can you see a pattern? Does the pattern continue?

Take a look at the video and try to find a sequence of moves that will untangle the ropes.

Here's a chance to work with large numbers...

Can you recreate squares and rhombuses if you are only given a side or a diagonal?