two sequences of coins in infinite chessboard , a_n in n row, b_n in n column
Source: 1993 ITAMO p3
January 31, 2020
combinatoricsinfinite chessboardSequences
Problem Statement
Consider an infinite chessboard whose rows and columns are indexed by positive integers. At most one coin can be put on any cell of the chessboard. Let be given two arbitrary sequences () and () of positive integers (). Assuming that infinitely many coins are available, prove that they can be arranged on the chessboard so that there are coins in the -th row and coins in the -th column for all .