TOT 420 1994 Autumn O J1 boys and girls dancing waltz at a ball
Source:
June 12, 2024
combinatorics
Problem Statement
Several boys and girls are dancing a waltz at a ball. Is it possible that each girl can always get to dance the next dance with a boy who is either more handsome or more clever than for the previous dance, and that each time one of the girls gets to dance the next dance with a boy who is more handsome and more clever? (The numbers of boys and girls are equal and all are dancing.)(AY Belov)