You are at a meeting with ten other colleagues. Each of the ten colleagues shakes hands with you. Furthermore, some of the colleagues also shakes hands with each other. Can you say with certainty that there are at least two people in the room that shook hands with exactly the same number of people?

There are 11 people in the room, 10 colleagues plus you. Each of them shook hands with between 1 and 10 people (included). Does this sound familiar to you? We have 11 people and 10 possible numbers of handshakes. By the Pigeon Hole principle, we know with certainty that at least two people shook hands with exactly the same amount of people!

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