(puzzle by Henry Dudeney):

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.

1/3 have not lost an eye, 1/4 have not lost an arm, and 1/5 have not lost a leg.  At least 1 - 1/3 - 1/4 - 1/5 = 13/60 must have lost all three.  26 divided by 13/60 = 120, which is the number of men in the hospital.

Posted by Steve Herman on 2023-05-03 13:40:47