Red/Blue Dominated Columns
Source: 2014 CMO #2
May 11, 2014
floor functioncombinatorics proposedcombinatoricsCMO
Problem Statement
Let and be odd positive integers. Each square of an by board is coloured red or blue. A row is said to be red-dominated if there are more red squares than blue squares in the row. A column is said to be blue-dominated if there are more blue squares than red squares in the column. Determine the maximum possible value of the number of red-dominated rows plus the number of blue-dominated columns. Express your answer in terms of and .