MathDB
Placing stones on a 1999 x 1999 board

Source: Japanese MO Finals 1999

February 11, 2011
floor functionrotationceiling functioncombinatorics proposedcombinatorics

Problem Statement

One can place a stone on each of the squares of a 1999×19991999\times 1999 board. Find the minimum number of stones that must be placed so that, for any blank square on the board, the total number of stones placed in the corresponding row and column is at least 19991999.