THE FOOTBALL PLAYERS.
(
Problems Concerning Games.)
"It is a glorious game!" an enthusiast was heard to exclaim. "At the
close of last season, of the footballers of my acquaintance four had
broken their left arm, five had broken their right arm, two had the
right arm sound, and three had sound left arms." Can you discover from
that statement what is the smallest number of players that the speaker
could be acquainted with?
It does not at all follow that there were as many as fourteen men,
because, for example, two of the men who had broken the left arm might
also be the two who had sound right arms.
Answer:
The smallest possible number of men is seven. They could be accounted
for in three different ways: 1. Two with both arms sound, one with
broken right arm, and four with both arms broken. 2. One with both arms
sound, one with broken left arm, two with broken right arm, and three
with both arms broken. 3. Two with left arm broken, three with right arm
broken, and two with both arms broken. But if every man was injured, the
last case is the only one that would apply.
