A man smokes and drinks coffee lightened with cream. He is absolutely consistent in his habits. Every day, except every four years when he abstains on Leap Day, he smokes the same number of cigarettes, brews the same amount of coffee grinds, and uses the same amount of cream in his coffee. Every day, he buys the daily newspaper, which he purchases more often than a pack of 20 cigarettes. The pack of cigarettes is purchased more often than a half-pint of cream, which in turn is purchased more often than a one-pound can of coffee. On Flag Day (USA), he purchased all four items. The next time, he purchased all four items on the same day was the fourth of July of the following year. How many cigarettes does he smoke each day?
Hint
Flag Day (USA) is June 14
Answer
4 cigarettes a day.
The purchases are made according to 4 different cycles. There are 385 days from Flag Day until July fourth of the following year excluding Leap Day. These purchasing cycles intersect every 385 days and are thus in the set of factors for 385 (1, 5, 7, 11, and 385). Since the newspaper is purchased every day, and the coffee and cream are purchased more often than the pack of cigarettes, then the pack is purchased either every 5 days or every 7 days. The pack contains 20 cigarettes which only has the factor 5 in common with the possible cycle for the cigarettes. Therefore a pack of 20 is purchased every 5 days.