Prime numbers

These two group activities use mathematical reasoning - one is numerical, one geometric.

Work out Tom's number from the answers he gives his friend. He will only answer 'yes' or 'no'.

Show that it is rare for a ratio of ratios to be rational.

Use this grid to shade the numbers in the way described. Which numbers do you have left? Do you know what they are called?

A man has 5 coins in his pocket. Given the clues, can you work out what the coins are?

The sum of the cubes of two numbers is 7163. What are these numbers?

Using all ten cards from 0 to 9, rearrange them to make five prime numbers. Can you find any other ways of doing it?

The flow chart requires two numbers, M and N. Select several values for M and try to establish what the flow chart does.

This problem is based on a code using two different prime numbers less than 10. You'll need to multiply them together and shift the alphabet forwards by the result. Can you decipher the code?

How many of the numbers 1 to 20 are not the sum of two primes?