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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?


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

Traffic Tunnel

Age 14 to 16 Short Challenge Level:

A traffic tunnel is being planned. The 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.