### Always Two

Find all the triples of numbers a, b, c such that each one of them plus the product of the other two is always 2.

### Not Continued Fractions

Which rational numbers cannot be written in the form x + 1/(y + 1/z) where x, y and z are integers?

### Surds

Find the exact values of x, y and a satisfying the following system of equations: 1/(a+1) = a - 1 x + y = 2a x = ay

# Thousands of X

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

Solve the equation $(x-2013)(x-2012)-(x-2012)(x-2011)=0.$

This problem is adapted from the World Mathematics Championships

You can find more short problems, arranged by curriculum topic, in our short problems collection.