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  "body": "\n## Statement\n\nColour each edge of the [[complete graph|03WKB2H474]] $K_6$ red or blue.\nThen there are three vertices such that the three edges between them have the same colour.\n\n## Remarks\n\nProof: a vertex $v$ has $5$ edges, so at least $3$ of them have one colour, say blue, by the [[pigeonhole principle|0HGVCWQGY3]]. If an edge between their ends is blue, it closes a blue triangle with $v$. Otherwise these three ends form a red triangle.\nThe number $6$ is the least possible: $K_5$ has a colouring with no triangle of one colour.\nThus the [[Ramsey number|01DSVCRF6X]] $R(3, 3)$ is $6$.\n\n## Explanations\n\n### L1 human\n\nAt any party of six people, there are three people who all know each other, or three who are all strangers to each other.\nWith five people this can fail.\n",
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