MathDB

8

Part of 1986 Austrian-Polish Competition

Problems(1)

rearranging reals in a m x n array

Source: Austrian Polish 1986 APMC

4/30/2020
Pairwise distinct real numbers are arranged into an m×nm \times n rectangular array. In each row the entries are arranged increasingly from left to right. Each column is then rearranged in decreasing order from top to bottom. Prove that in the reorganized array, the rows remain arranged increasingly.
combinatoricstable