### 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?

# Traffic Tunnel

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

A traffic tunnel is being planned. This diagram shows the cross-section of the tunnel. The shape of the tunnel is the same as the graph of $y=\frac49(9-x^2)$. All distances are in metres.

Which of these vehicles will fit through the tunnel?

a) truck, 2.9 m high, 4 m wide
b) coach, 3.4 m high, 3 m wide
c) lorry, 3.9 m high, 2 m wide

This problem is adapted from the World Mathematics Championships
You can find more short problems, arranged by curriculum topic, in our short problems collection.