entropyembrace wrote:AdamMY wrote:If you are going to discuss math, at least ask interesting questions. Such as stuff relating to what I have been working on, but accessible to lay people who want to think logically.

Assuming between two people they either know each other or they do not. What is the smallest group of people you must assemble such that you either have 3 of them which all know each other, or 3 of them that do not know each other?

I don´t understand how this is possible to answer....if you have any number of people all of them could know each other or none of them could know each other or any number of pairs of people within the group could know each other.

At first I thought the answer was 3...because it´s certainly possible to have a group of 3 that knows each other or a group of 3 that does not know each other but it´s also possible to have a group of 3 in which one person knows both others but they do not know each other or a group of 3 in which two people know each other but neither knows the 3rd person.

If I make the group size 4 then if none of them know each other there are 4 people that do not know each other not 3 people that do not know each other. Any group size greater than 3 has this problem.

A group size less than 3 can´t satisfy the conditions in any case at all since there aren´t 3 people to know or not know each other.

To turn the question slightly on its head, but with an equivalent statement. What is the smallest number of people required such that if you could choose the people very creatively knowing who they know or do not know, you would still satisfy the conditions.

While it could easily happen with three people, but to come up with this number we are looking for the worst case scenario. For example with 3 people you can have 2 of the people not know each other, and the 3rd person know the other two.