General
How Many Guests Guarantee 3 Friends or 3 Strangers?
What is the Ramsey number R(3,3), the minimum number of people at a party that guarantees either 3 mutual acquaintances or 3 mutual strangers?
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What is the answer to the 3 friends or 3 strangers party riddle?
The answer is 6. Among any 6 people, you are guaranteed to find either 3 who all know each other or 3 who are mutual strangers. This is the Ramsey number R(3,3) = 6.
Why isn't 5 people enough?
With 5 people you can arrange the acquaintances so that no group of 3 are all friends and no group of 3 are all strangers, so 5 does not guarantee it. Once you reach 6, it becomes unavoidable.
What is the Ramsey number R(3,3)?
R(3,3) equals 6. It is the smallest number of people that forces a trio who all know each other or a trio who are all strangers, no matter how the friendships are arranged.