The St. Patrick's Day Parade : Solution


The number of men when Casey was alive must be a multiple of 2, 3, 4, 5, 6, 7, 8, 9 and 10. We take the least common multiple, 2520, then subtract 1 to get the number of members without Casey. This could be the answer were it not for the catch phrase, "as eleven would not do". Since 2,519 is divisible by 11 we have to go the the next highest multiple, 5040, then subtract 1 to get 5039. Since this is not divisible by 11, and since higher multiples will give answers above 7,000, we conclude that 5039 is the only correct answer.




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