Puzzles to puzzle you

Ashutosh · 03-12-2010, 01:16 AM

Geometric puzzles:

(1) Suppose that every point in plane is coloured red, blue or green. Show that there are two point of same colour which are at a unit distance from each other.

(2) Suppose that every point in plane is coloured red or blue. Show that there is a colour such that there are points of this colour at all possible distances.

(3) Show that you cannot cover the plane by any collection of pairwise non-intersecting circles (i.e., boundaries of circles) of positive radii.

(4) Show that the space can be covered with such circles.

03-12-2010, 01:16 AM	#21
Ashutosh Member Join Date: Feb 2010 Location: Madison Posts: 12 Rep Power: 0	Re: Puzzles to puzzle you Geometric puzzles: (1) Suppose that every point in plane is coloured red, blue or green. Show that there are two point of same colour which are at a unit distance from each other. (2) Suppose that every point in plane is coloured red or blue. Show that there is a colour such that there are points of this colour at all possible distances. (3) Show that you cannot cover the plane by any collection of pairwise non-intersecting circles (i.e., boundaries of circles) of positive radii. (4) Show that the space can be covered with such circles.