ASU 075 All Russian MO 1966 arranging soldiers by height
Source:
June 19, 2019
combinatorics
Problem Statement
a) Pupils of the -th form are standing in a row. There is the pupil of the -th form in before each, and he is smaller (in height) than the elder. Prove that if you will sort the pupils in each of rows with respect to their height, every 8-former will still be taller than the -former standing before him. b) An infantry detachment soldiers stand in the rectangle, being arranged in columns with respect to their height. Prove that if you rearrange them with respect to their height in every separate row, they will still be staying with respect to their height in columns.