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?

Coffee

To make 11 kilograms of this blend of coffee costs £15 per kilogram. The blend uses more Brazilian, Kenyan and Mocha coffee... How many kilograms of each type of coffee are used?

Algebraic Differences

Age 14 to 16 Short Challenge Level:

If $6x - y = 21$ and $6y - x = 14$, what is the value of $x - y$?

This problem is taken from the UKMT Mathematical Challenges.
You can find more short problems, arranged by curriculum topic, in our short problems collection.