Help me in hurry,PLZ!!!?

Question

If every point in the x-y plane is painted either blue,red or yellow prove that there must exist 2 points EXACTLY 1 unit apart that are the same colour(in fact there are infinitely many such points).

Can you explain the question and answer clearly since I even misunderstand the question.Thank you1

Answer 1

we choose two color for example (blue and yellow)
if we call the points painted on blue Nb(Xb;Yb)
and
points painted on yellow Ny(Xy;Yy) so
Nb =/= Ny means that
if Xb=Xy => Yb=/=Yy
and if
Yb=Yy => Xb=/=Xy
in this case:
there is only one point in witch satisfy that
Xb=Xy and Yb=Yy => o(0;0)
it means Nb fall exactly on Yb (or the inverse)and where:
the mixture of blue and yellow gives one green point
so this point is Nby or Nyb (0;0)

Answer 2

Imagine you have three different colors of poker chips. You are going to lay them down on a table, and jam them all together so that they form sort of a grid. Once you've done this, you will find that there are lots of places where two chips of the same color are adjacent. And if your table was infinitely large, there would be an infinite number of such occurances.

As for the proof, unfortunately I've got nothin'.

Answer 3

they are saying that when you pick 2 points that is right next to each other like 1,2 and 1,3 that is 1 unit apart. so they said that there must be 2 points in the same colour plane

just image the colour planes in area