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
Por um escritor misterioso
Last updated 06 julho 2024
![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:1400/1*5LJcp4pk7Y_XsTLx-KvvUw.png)
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…
![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://mediaproxy.salon.com/width/1200/height/675/%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://jpmccarthymaths.files.wordpress.com/2017/11/ramsey2.jpg?w=584)
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://mediaproxy.salon.com/width/1200/https://media.salon.com/2015/08/a_beautiful_mind1.jpg)
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:1400/1*vR65axJce24009HPwQM-Aw.png)
Theorem on Friends and Strangers. Ramsey Theory and Graham's Number, by Francesco Di Lallo
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: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://miro.medium.com/v2/resize:fit:1400/1*RrHqj9z7d0iPU0_paW40Sg.png)
Can Math Prove You'll Always Be the Odd One Out At Parties?, by Mary Paskhaver, Geek Culture
![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://i.ytimg.com/vi/8GvO5wej5pA/maxresdefault.jpg)
Proof by cases example: Three mutual friends/enemies theorem
![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://media.cheggcdn.com/media/51c/51ccffc0-0660-4669-9a89-6a351d40f2f5/image.png)
Solved 1. Show that in any group of 6 people, there is
![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/tree.gif)
Friends and strangers
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