Being curious

Start with two numbers and generate a sequence where the next number is the mean of the last two numbers...

Semi-regular tessellations combine two or more different regular polygons to fill the plane. Can you find all the semi-regular tessellations?

These clocks have only one hand, but can you work out what time they are showing from the information?

The Man is much smaller than us. Can you use the picture of him next to a mug to estimate his height and how much tea he drinks?

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

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

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

Place the numbers from 1 to 9 in the squares below so that the difference between joined squares is odd. How many different ways can you do this?

If there are 3 squares in the ring, can you place three different numbers in them so that their differences are odd? Try with different numbers of squares around the ring. What do you notice?

Choose four of the numbers from 1 to 9 to put in the squares so that the differences between joined squares are odd.