Prime numbers

When if ever do you get the right answer if you add two fractions by adding the numerators and adding the denominators?

How many divisors does factorial n (n!) have?

Take the number 6 469 693 230 and divide it by the first ten prime numbers and you'll find the most beautiful, most magic of all numbers. What is it?

Lyndon chose this as one of his favourite problems. It is accessible but needs some careful analysis of what is included and what is not. A systematic approach is really helpful.

Think of any three-digit number. Repeat the digits. The 6-digit number that you end up with is divisible by 91. Is this a coincidence?

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?

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

Can you make square numbers by adding two prime numbers together?

Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.

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