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Mathematics

Ramsey Theory and Unavoidable Patterns in Large Structures

Quick fact

The famous 'party problem' asks: how many people must be at a party to guarantee that either at least three all know each other or at least three all are strangers? The answer is 6, and the number 6 is called the Ramsey number R(3,3).

Why this is interesting

Imagine you throw any large group of people into a room. Can you guarantee that among them there are three mutual strangers? Or three mutual friends? The surprising answer is yes—if the group is big enough.

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Ramsey Theory and Unavoidable Patterns in Large Structures

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