Brain Teasers
Not So Good Habits
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 14Answer
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 then 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.
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Comments
Excellent teaser, one of the best I've seen. Keep it up.
I dont like math ones. I guessed but it was long so i guess its good. i got it right
gees louis! I would never get that one! well if you look at my other comments I cant get any of them
OMG OMG OMG!!!! i didnt feel like doing any math since i just finished my algebra HW and i guessed the right answer! maybe i'm psychic????
OMG OMG OMG!!!! i didnt feel like doing any math since i just finished my algebra HW and i guessed the right answer! maybe i'm psychic????
Doesn't the explanation of the answer assume that there are always the same number of days between puchasing packets of cigarettes? If, for example, he smoked 3 a day (which is possible according to the teaser question), the gaps between buying cigarettes would be 7,7,6, and not strictly regualr. Show me where I'm wrong!
If he smoked 3 cigarettes a day, after purchasing all 4 items on Flag Day, the next time he would purchase all four items would be on November 15 of the same year.
i hate math!
Statement from question:
"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."
Statement from answer:
"...and the coffee and cream are purchased more often then the pack of cigarettes..."
Am I missing something?
"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."
Statement from answer:
"...and the coffee and cream are purchased more often then the pack of cigarettes..."
Am I missing something?
The answer is correct, the explanation is in error and should state that the coffee and cream is purchased LESS often than the pack of cigarettes.
The hardest part of this was remembering when Flag day is. I knew June, but asked the Mrs. for the exact day. Good teaser!
The hint is definitely necessary to non-US citizens. Other than that a very good teaser.
Thanks for your puzzle. I managed to solve it with scip (a linear, mixed integer and nonlinear programming solver).
The simple model file can be found at
http://pastebin.com/w1R8PpYJ
The simple model file can be found at
http://pastebin.com/w1R8PpYJ
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