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Problem of the Day #185: Not Paying Attention in AP Chinese Class September 20, 2011

Posted by Seungln in : potd , trackback

Andrew Tao and David Guo decide to not pay attention during ┬áMs. X’s AP Chinese class. Because they are sitting directly next to each other, however, they decide that at least one of the two have to be paying attention at any given time in order to avoid grabbing the attention of Ms. X, who would undoubtedly give both of them a bad grade. Andrew, however, has a short attention span and can only pay attention for $n$ minutes at a time, where $n$ is a positive integer between $5$ and $20$, before he has to take a $3$ minute break from paying attention. If the class is $90$ minutes and David decides to go in a cycle of $14$ minutes of attention and $4$ minutes of not paying attention, what is the sum of the values of $n$ that will allow the two of them to get away with their lack of attention, regardless of where in their cycle each of them start?

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