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How many guests need to come to a party, to guarantee that either at least five of them all know each other or at least five are mutual strangers? This question turns out to be surprisingly hard to solve, and has led to the creation of some maths that feels more like a newspaper puzzle than real work. We'll explore connections ranging from friendship, through marriage, to the spread of infectious diseases.

Colva's research is mostly in finite group theory, with a few excursions into theoretical computer science. More recently she has been dipping her toe in the infinite as well. There is information on group theory in Colva's article for Plus magazine available at She has written another article for Plus magazine on Chaos, Chance and Money: She has taken part in numerous radio broadcasts about mathematical subjects such as Carl Friedrich Gauss, the history of probability, Indian mathematics and Maths in the Islamic world.
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