## Theorem of Friends and Strangers

The statement of the Theorem is: "In any party of six people either at least three of them are (pairwise) mutual strangers or at least three of them are (pairwise) mutual acquaintances." In 1930, in a paper entitled 'On a Problem in Formal Logic,' Frank P. Ramsey proved a very general theorem of which this theorem is a simple case. This theorem of Ramsey forms the foundation of the area known as Ramsey theory in combinatorics. If time permits we will also see an application of colouring argument used in proving this Theorem to other problems.

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