- #1

- 166

- 2

## Homework Statement

If the 2-subsets of a 9-set are colored red and blue, there is either a red 3-set or a blue 4-set.

## Homework Equations

None

## The Attempt at a Solution

My book first proved for 10 points, the proof given is:

Consider first for 10 points. Consider the nine edges joining one point x to the others. By the Pigeonhole Principle, either there are four red edges or six blue edges.

Here is where I got confused, why is it that "there are four red edges or six blue edges"? Also, when it says the 2-subsets are colored red and blue does that mean for a 9-set X where X = {1,2,3,4,5,6,7,8,9} then all two subsets that consist of this set X are colored blue and red, e.g. for a 2-subset {1,2} then 1 is colored blue and 2 is colored red?