Six Strangers at a Party

The Prompt

Demonstrate the Ramsey-theoretic party problem R(3,3) = 6 with a physical or social exercise. Gather six people (or use six labelled objects) and determine, for each pair, whether they are "friends" or "strangers." Verify that among any six, three mutual friends or three mutual strangers must exist. If you can gather only five, demonstrate a colouring of K_5 that avoids a monochromatic triangle. Record the exercise and the moment the inevitability of the pattern became clear.

Completion Criteria

The number of participants or objects, the pairings, the monochromatic triangle found (or the triangle-free colouring of K_5), and a brief note on the moment of recognition.

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