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Daily Brain Teaser / Puzzle
October 23, 2006
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A certain division in an army was composed of a little over twenty thousand men, made up of five brigades. It was known that one-third of the first brigade, two-sevenths of the second brigade, seven-twelfths of the third, nine­thirteenths of the fouth, and fifteen-twenty-seconds of the fifth brigade happened in every case to be the same number of men Can you discover how many men there were in every brigade?

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THE SOLUTION

The five brigades contained respectively 5,670; 6,615; 3,240; 2,730; and 2,772 men. Represent all the fractions with the common denominator 12,012, and the numerators will be 4,004; 3,432; 7,007; 8,316; and 8,190. Combining all the different factors contained in these numbers, we get 7,567,560, which, divided by each number in turn, gives us 1,890; 2,205; 1,080; 910; and 924. To fulfill the condition that the division contained a little over 20,000 men, we multiply these by 3 and have the correct total--21,027.