A bag contains coloured marbles. How many need to be taken out to ensure that at least three are of the same colour?

If two of these unusually numbered dice are thrown, how many different sums are possible?

Two of the four small triangles are to be painted black. In how many ways can this be done?

What is the probability that two pieces of rope are tied together, when Pat ties two loose ends together?

How many routes are there in this diagram from S to T?

What is the smallest number of jelly babies Tom must take, to be certain that he gets at least one of each flavour?

The 30 students in a class have 25 different birthdays between them. What is the largest number that can share any birthday?

Our school dinners offer the same choice each day, and each day I try a new option. How long will it be before I eat the same meal again?

Pizza, Indian or Chinese takeaway? If everyone liked at least one, how many only liked Indian?

Problem 1 was solved by 70% of the pupils. Problem 2 was solved by 60% of them. Can you work out how many pupils took the exam?

Can you work out how many children answered all the questions correctly?

What is the probability that all three monkeys left the cafe wearing the wrong hats?

How many students are in the maths club and the science club?

Can you design a die which rolls 'fairly' against mine?

Can you work out how many kangaroos Rachel draws in one colour?

Consider a 10-digit number which contains only the numbers 1, 2 or 3. How many such numbers can you write so that every pair of adjacent digits differs by 1?

Can you work out the smallest number of socks Rachel needs to take out of the box to be guaranteed a pair?