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Solution

(related to Problem: The Football Players)

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 a broken right arm, and four with both arms broken.
2. One with both arms sound, one with a broken left arm, two with a broken right arm, and three with both arms broken.
3. Two with a left arm broken, three with a 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.

Thank you to the contributors under CC BY-SA 4.0!

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References

Project Gutenberg

1. Dudeney, H. E.: "Amusements in Mathematics", The Authors' Club, 1917

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