MathDB
Vietnam NMO 2002_3

Source:

October 26, 2008
combinatorics unsolvedcombinatorics

Problem Statement

Let be given two positive integers m m, n n with m<2001 m < 2001, n<2002 n < 2002. Let distinct real numbers be written in the cells of a 2001×2002 2001 \times 2002 board (with 2001 2001 rows and 2002 2002 columns). A cell of the board is called bad if the corresponding number is smaller than at least m m numbers in the same column and at least n n numbers in the same row. Let s s denote the total number of bad cells. Find the least possible value of s s.
Back to ProblemsView on AoPS