Recent content by proptrader

I got a solution myself. i will try to write it up in the following days.

So what I've been trying to do so far is the following: When a person invites three other students he obviously has to know two of them as the problem demands. There are 10C2 couples of such friends. The thing is for the problem to be satisfied we need the fourth person to know both of the...

Come on guys! Somebody has to have a clue how to approach this

The groups should be made of 4 people as the problem says that one person invites three. In the group of four each person should know at least 2 of the others for the condition to be satisfied.

I think I made a mistake in the attempt of a solution. Inviting three other people does not require that you know all three of them. The problem would ask to know only a couple for the condition to be satisfied. So I guess it comes down to proving such groups of four people can be built? Can...

A school class has 90 students, each of whom has ten friends among the other students. Prove that each student can invite three people at a restaurant so that each of the four people at the table will know at least two of the other three. If this had to be translated to a graph it would...

Homework Statement Prove that for all positive integers n, the equality holds: SUM(nCk)*2^k=(3^n+(-1)^n)/2 Note: The sum goes from k=0 to n. AND k has to be even. Homework Equations Binomial Theorem The Attempt at a Solution I know that if we use the binomial theorem for x=2 and...

As simple as this idea is - it sounds great. I suppose if you could come up with a solution to the following problem this would help solve the current: Our goal is to select two subsets A and B of {1,2,3,4...,n} such that A∩B=Ø. In how many ways is this possible?

I can't see how this procedure would lead me to an answer. Specifically I don't see how to get rid of m. Here is what I've got: I suspect that each person has 3 choices: to talk on the first day, to talk on the second day, or not to talk at all. This implies that there are 3^n ways of...

Homework Statement A teaching event takes two days and involves n people. Some of the people give a talk on day 1, some others give a talk on day 2. Everybody gives at most 1 talk, and there can be some teachers who do not give a talk in either of the two days. At the end of the event, a...