Theorem on Friends and Strangers; Why in Any Party of Six People, Either at Least Three of Them Are Mutual Friends, or at Least Three of Them Are Mutual Strangers
Descrição
Let’s take a look at Alice first. To her, each one of the other five (Bob, Carol, Dave, Ellen, and Frank) is either a friend or a stranger. Suppose Bob, Dave, and Frank are friends to Alice, and…
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Correlation, Causation, and Ramsey Theory
![Theorem on Friends and Strangers; Why in Any Party of Six People, Either at Least Three of Them Are Mutual Friends, or at Least Three of Them Are Mutual Strangers](https://sites.cs.ucsb.edu/~rich/class/cs293-cloud/notes/Ramsey/r33.jpg)
CS290I Lecture notes -- Let's Party
![Theorem on Friends and Strangers; Why in Any Party of Six People, Either at Least Three of Them Are Mutual Friends, or at Least Three of Them Are Mutual Strangers](https://upload.wikimedia.org/wikipedia/commons/e/ef/Friends_strangers_graph.gif)
Theorem on friends and strangers - Wikipedia
![Theorem on Friends and Strangers; Why in Any Party of Six People, Either at Least Three of Them Are Mutual Friends, or at Least Three of Them Are Mutual Strangers](https://miro.medium.com/v2/resize:fit:1200/1*Zi7objuWSKPvJNQaNnXDrw.png)
Theorem on Friends and Strangers; Why in Any Party of Six People, Either at Least Three of Them Are Mutual Friends, or at Least Three of Them Are Mutual Strangers
![Theorem on Friends and Strangers; Why in Any Party of Six People, Either at Least Three of Them Are Mutual Friends, or at Least Three of Them Are Mutual Strangers](https://mediaproxy.salon.com/width/1200/height/1200/%3C?=%20https://media.salon.com/2015/08/a_beautiful_mind1.jpg%20?%3E)
This math puzzle will help you plan your next party
![Theorem on Friends and Strangers; Why in Any Party of Six People, Either at Least Three of Them Are Mutual Friends, or at Least Three of Them Are Mutual Strangers](https://miro.medium.com/v2/resize:fit:416/1*R2NCzU9HfTg5WVmovYxO4w.png)
Theorem on Friends and Strangers. Ramsey Theory and Graham's Number, by Francesco Di Lallo
![Theorem on Friends and Strangers; Why in Any Party of Six People, Either at Least Three of Them Are Mutual Friends, or at Least Three of Them Are Mutual Strangers](https://www.mdpi.com/materials/materials-16-07571/article_deploy/html/images/materials-16-07571-g001.png)
Materials, Free Full-Text
![Theorem on Friends and Strangers; Why in Any Party of Six People, Either at Least Three of Them Are Mutual Friends, or at Least Three of Them Are Mutual Strangers](https://cdn.numerade.com/project-universal/previews/841c35d0-34c4-4ada-8e63-26faee8c3783.jpg)
SOLVED: Prove this theorem: Among any six people, there exists a group of 3 mutual friends or a group of 3 mutual strangers. (Here friends and strangers are considered symmetric relations, i.e.
![Theorem on Friends and Strangers; Why in Any Party of Six People, Either at Least Three of Them Are Mutual Friends, or at Least Three of Them Are Mutual Strangers](https://plus.maths.org/issue16/features/ramsey/images/6rededgesK4.gif)
Friends and strangers
How to prove: at a party of six people either there are three mutual acquaintances or there are three mutual strangers - Quora
![Theorem on Friends and Strangers; Why in Any Party of Six People, Either at Least Three of Them Are Mutual Friends, or at Least Three of Them Are Mutual Strangers](https://miro.medium.com/v2/resize:fit:492/1*_iEChbnDa1iTrZVOS1RgCg.png)
Theorem on Friends and Strangers. Ramsey Theory and Graham's Number, by Francesco Di Lallo
![Theorem on Friends and Strangers; Why in Any Party of Six People, Either at Least Three of Them Are Mutual Friends, or at Least Three of Them Are Mutual Strangers](https://pi.math.cornell.edu/~mec/Winter2009/Thompson/cliques/party1.png)
Friends and Strangers
Solved Counting: product rule, sum rule, inclusion-exclusion
![Theorem on Friends and Strangers; Why in Any Party of Six People, Either at Least Three of Them Are Mutual Friends, or at Least Three of Them Are Mutual Strangers](https://jpmccarthymaths.files.wordpress.com/2018/01/ramsey6.jpg)
Correlation, Causation, and Ramsey Theory
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