Prime numbers

problem
Stars

Age

11 to 14

Challenge level

Can you work out what step size to take to ensure you visit all the dots on the circle?
problem
Can it be?

Age

16 to 18

Challenge level

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

Age

16 to 18

Challenge level

How many divisors does factorial n (n!) have?
problem
A conversation piece

Age

7 to 11

Challenge level

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?
problem
Fac-finding

Age

14 to 16

Challenge level

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.
problem
Just repeat

Age

11 to 14

Challenge level

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?
problem
Code breaker

Age

7 to 11

Challenge level

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?
problem
Penta primes

Age

7 to 11

Challenge level

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

Age

7 to 11

Challenge level

Can you make square numbers by adding two prime numbers together?
problem
Factor lines

Age

7 to 14

Challenge level

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