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(431) 1

Part of 1994 Tournament Of Towns

Problems(1)

TOT 431 1994 Autumn O S1 boys and girls dancing a waltz, senior version

Source:

6/12/2024
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 either a more handsome or more clever boy than for the previous dance, and that each time at least 80%80\% of the girls get 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)
algebracombinatorics