🚀 go-pugleaf

In article <1993Jan8.193314.3289@zip.eecs.umich.edu>, kanad@quip.eecs.umich.edu (Kanad Chakraborty) writes:
|> Here's a very *easy*, and nice, puzzle.  This puzzle is a close
|> relative of the one I posted on New Years' eve.  No flames, please,
|> for posting something so simple. Simple things can be interesting 
|> sometimes, as some of you would undoubtedly agree.
|> 
|> Suppose you are given 3 colors and asked to assign a color
|> to each point in a plane such that (a) you *must* use more than one
|> color for the entire plane; (b) *every* pair of points 1 inch apart
|> are colored alike.  Can you make such an assignment ? The plane is
|> a continuum of points, it is not a grid.
|> 
|> Kanad


Obviously if two points X and Y are N inches apart (N = integer) they must
have the same color.
So, let A and B be two points with different colors.
Construct a triangle ABC, so that AC and BC have integer lengths (if measured
in inches!). Such a triangle can always be constructed, e.g. you can choose
AB = BC = ceiling(AB)
Then A has the same color as C, B has the same color as C, therefore A has
the same color as B, so......... no, you can not color the points of a
plane the way you described.

Nice little puzzle indeed!

Spyros Potamianos
potamian@hpl.hp.com