### 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?

# In the Hundreds

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

For how many positive values of $n$ are both $\frac{1}{2}n$ and $2n$ three-digit whole numbers?

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