Henry Ernest Dudeney/Modern Puzzles/91 - Counting the Wounded

Modern Puzzles by Henry Ernest Dudeney: $91$

Counting the Wounded

When visiting with a friend one of our hospitals for wounded soldiers, I was informed that

exactly two-thirds of the men had lost an eye,

three-fourths had lost an arm,

and four-fifths had lost a leg.

"Then," I remarked to my friend, "it follows that at least twenty-six of the men must have lost all three -- an eye, an arm, and a leg."

That being so, can you say exactly how many men were in the hospital?

It is a very simple calculation, but I have no doubt it will perplex a good many readers.

Sources

• 1926: Henry Ernest Dudeney: Modern Puzzles ... (previous) ... (next): Arithmetical and Algebraical Problems: Various Arithmetical and Algebraical Problems: $91$. -- Counting the Wounded
• 1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Arithmetical and Algebraical Problems: Miscellaneous Puzzles: $174$. Counting the Wounded