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Answer to the Problem of the Week for the week of February 20, 2006 Contributed by Bill Funk |
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| The Pill Problem |
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Bill uses a seven-day pill container to keep track of his daily consumption. On the day after his pill container is empty, he doles out eight days worth of pills, seven days worth to go into his pill dispenser and the eighth day to take with breakfast. Bill and his wife have a housekeeper who comes in every other Tuesday to do some light housework for them.If Bill filled his pill dispenser this Tuesday, February 21, 2006, on the same day that the housekeeper came to work, when will the next date be that she will be here and his pill dispenser will be full? |
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Solution to the Problem: |
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The answer is 56 days from February 21, or on April 18, 2006. Bill fills his pill dispenser every eight days. His housekeeper comes every fourteen days. The next time that she will be there when his dispenser is full is the least common multiple of 8 and 14, which is 56. |
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