TOT 058 1984 Spring J-A2 15+15 boys and girls, ballroom, heights
Source:
August 19, 2019
combinatorics
Problem Statement
In a ballroom dance class boys and girls are lined up in parallel rows so that couples are formed. It so happens that the difference in height between the boy and the girl in each couple is not more than cm. Prove that if the boys and the girls were placed in each line in order of decreasing height, then the difference in height in each of the newly formed couples would still be at most cm. (AG Pechkovskiy, Moscow)