2004 queens on a 2004 x 2004 chess table
Source: Romanian IMO TST 2005 - day 5, problem 1
April 24, 2005
geometryrectanglemodular arithmeticcombinatorics proposedcombinatorics
Problem Statement
On a chess table there are 2004 queens such that no two are attacking each other\footnote[1]{two queens attack each other if they lie on the same row, column or direction parallel with on of the main diagonals of the table}.
Prove that there exist two queens such that in the rectangle in which the center of the squares on which the queens lie are two opposite corners, has a semiperimeter of 2004.