April’s Math Olympiad Question was a particularly tough one, only four people in the world solved it! One from Japan, one from Slovakia, one from Ankara, and one from Singapore!

The question starts off seemingly simple enough:

In a party attended by 2015 guests among any 7 guests at most 12 handshakes had been

exchanged. Determine the maximal possible total number of handshakes.

However, when one starts trying out the questions, one quickly realizes the number of handshakes is very large, possibly even up to millions. This question definitely can’t be solved by trial and error!

This question is ideally modeled by a graph, and has connections to the idea of a Turán graph.

The official solution can be accessed here: http://www.fen.bilkent.edu.tr/~cvmath/Problem/1504a.pdf

The Turán graph T(13,4)

To read more about Math Olympiad books, you may check out my earlier post on Recommended Math Olympiad books for self-learning.

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I’m glad that my solution was correct lol. That problem was quite hard for an olympiad level question IMO.

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Yeah, it was a tricky one. Thanks for commenting!

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Reblogged this on Problemas e Teoremas and commented:

Pela blogosfera: uma questão difícil das Olimpíadas de Matemática

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