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Imagine a chess tournament in which every contestant is supposed to play exactly one game against every other contestant. But two people pull out – player A stops after 10 games and player B plays just one game. A total of 55 games were played. Did A and B play each other?

The charity UK Maths Trust uses questions like this to select four aspiring mathematicians to compete in the European Girls Maths Olympiad.

Dr Vicky Neale, Whitehead Lecturer in Mathematics at the University of Oxford, explains how to work it out.

Question Credit: UK Maths Trust