Challenge Level

Caroline and James pick sets of five numbers. Charlie chooses three of them that add together to make a multiple of three. Can they stop him?

Challenge Level

Can you produce convincing arguments that a selection of statements about numbers are true?

Challenge Level

Show that if you add 1 to the product of four consecutive numbers the answer is ALWAYS a perfect square.

Challenge Level

Can you find out what numbers divide these expressions? Can you prove that they are always divisors?

Challenge Level

A polite number can be written as the sum of two or more consecutive positive integers, for example 8+9+10=27 is a polite number. Can you find some more polite, and impolite, numbers?

Challenge Level

Can you find a three digit number which is equal to the sum of the hundreds digit, the square of the tens digit and the cube of the units digit?

Challenge Level

Here are two games you can play. Which offers the better chance of winning?

Challenge Level

This problem challenges you to sketch curves with different properties.

Challenge Level

This problem challenges you to find cubic equations which satisfy different conditions.

Challenge Level

Quadratic graphs are very familiar, but what patterns can you explore with cubics?

Challenge Level

This problem asks you to use your curve sketching knowledge to find all the solutions to an equation.