IMO Shortlist 2007 problem C5
Kvaliteta:
Avg: 0,0Težina:
Avg: 8,0 In the Cartesian coordinate plane define the strips , and color each strip black or white. Prove that any rectangle which is not a square can be placed in the plane so that its vertices have the same color.
IMO Shortlist 2007 Problem C5 as it appears in the official booklet:In the Cartesian coordinate plane define the strips for every integer Assume each strip is colored either red or blue, and let and be two distinct positive integers. Prove that there exists a rectangle with side length and such that its vertices have the same color.
Edited by Orlando Döhring
Author: Radu Gologan and Dan Schwarz, Romania
IMO Shortlist 2007 Problem C5 as it appears in the official booklet:In the Cartesian coordinate plane define the strips for every integer Assume each strip is colored either red or blue, and let and be two distinct positive integers. Prove that there exists a rectangle with side length and such that its vertices have the same color.
Edited by Orlando Döhring
Author: Radu Gologan and Dan Schwarz, Romania
Izvor: Međunarodna matematička olimpijada, shortlist 2007