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

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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

Tennis Training

Age 14 to 16 Short
Challenge Level


After tennis training, Andy collected twice as many balls as Roger, and five more than Maria. If they collected $35$ balls in total, how many did Andy collect?


If you liked this problem, here is an NRICH task that challenges you to use similar mathematical ideas.

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