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And Which War Would This Be?


A certain captain being asked how many soldiers he had in his company, replied: one half of them are in camp, one third in the trenches, one eighth in the hospital, and four in prison. Of how many men did his company consist?



Solution: Solution suggested by Kim K. (in my calculus class):

Let n = # men in company

Frac--Place--# men
1/2--camp--?
1/3--trench--?
1/8--hospital--?
x--prison--4

And, 1/2 + 1/3 + 1/8 + x = 1 implies x = 1/24.

Then, 4/n = 1/24 implies n = 96 men.

Source: Selected Amusements in Philosophy and Mathematics Proper for Agreeable Exercising of the Minds of Youth, 1801, p. 160