On fields of n×n chessboard n2 different integers have been arranged, one in each field. In each column, field with biggest number was colored in red. Set of n fields of chessboard name admissible, if no two of that fields aren't in the same row and aren't in the same column. From all admissible sets, set with biggest sum of numbers in it's fields has been chosen. Prove that red field is in this set. combinatoricsChessboardgraph theoryPolandcombinatorics unsolved