Working systematically

Find out about the lottery that is played in a far-away land. What is the chance of winning?

This cube has ink on each face which leaves marks on paper as it is rolled. Can you work out what is on each face and the route it has taken?

How many models can you find which obey these rules?

My coat has three buttons. How many ways can you find to do up all the buttons?

Take three whole numbers. The differences between them give you three new numbers. Find the differences between the new numbers and keep repeating this. What happens?

Move your counters through this snake of cards and see how far you can go. Are you surprised by where you end up?

Can you order the digits from 1-3 to make a number which is divisible by 3 so when the last digit is removed it becomes a 2-figure number divisible by 2, and so on?

Lauren and Thomas tell their ages in terms of sums of squares. Can you work out how old they really are?

What could be the scores from five throws of this dice?

Can you find a number and its double using the digits $1$ to $9$ only once each?