### Upsetting Pitagoras

Find the smallest integer solution to the equation 1/x^2 + 1/y^2 = 1/z^2

### Rudolff's Problem

A group of 20 people pay a total of £20 to see an exhibition. The admission price is £3 for men, £2 for women and 50p for children. How many men, women and children are there in the group?

### Euler's Squares

Euler found four whole numbers such that the sum of any two of the numbers is a perfect square...

# Never Prime

##### Age 14 to 16 Challenge Level:

Take any two digit number, reverse its digits, and subtract the smaller number from the larger. For example $$42-24=18$$ I've tried this a few times and I never seem to end up with a prime number. Try some examples of your own. Do you ever end up with a prime number?

Can you prove that you will never end up with a prime?

What happens when I do the same with a three digit number?

What about a four digit number?

What about a five, six, seven, ... $n$ digit number?