Every point in the plane is colored either red, green, or blue. Prove that there exists a rectangle in the plane such that all four of its vertices are the same color.
2006-10-02 09:25:38 · 4 answers · asked by Mr. Cool 1 in Science & Mathematics ➔ Mathematics
Partial solution:
Every horizontal line must have 2 points of the same
color. Why? Use the pigeon-hole principle. There
are infinitely many points on the line and only 3
colors.
Draw a horizontal line and connect 2 points of
the same color.
Call the points A and B.
That's as far as I've got so far.
I'll be back when I get more.
2006-10-02 10:01:55 · answer #1 · answered by steiner1745 7 · 0⤊ 0⤋
A point doesn't have an area on a plane. So it could be said that at any point, there exists multiple points. So all points have red, green and blue points.
2006-10-02 09:35:51 · answer #2 · answered by Take it from Toby 7 · 0⤊ 2⤋
There is insufficient info to solve this problem.
2006-10-02 09:28:52 · answer #3 · answered by Anonymous · 0⤊ 1⤋
do your own homework you lazy git
2006-10-02 09:27:20 · answer #4 · answered by Anonymous · 1⤊ 3⤋