Divisibility

Use properties of numbers to work out whether you can satisfy all these statements at the same time.

Can you guarantee that, for any three numbers you choose, the product of their differences will always be an even number?

Sequences of multiples keep cropping up...

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

Three people chose this as a favourite problem. It is the sort of problem that needs thinking time - but once the connection is made it gives access to many similar ideas.

Ben, Jack and Emma passed counters to each other and ended with the same number of counters. How many did they start with?

What is the largest number which, when divided into these five numbers in turn, leaves the same remainder each time?

Take any prime number greater than 3 , square it and subtract one. Working on the building blocks will help you to explain what is special about your results.

Can you create a Latin Square from multiples of a six digit number?

Here is a Sudoku with a difference! Use information about lowest common multiples to help you solve it.