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My New Year’s resolution is to paint the long fence that goes all the way around Tran Towers. In January I will paint 1/12 of the fence. In February I’ll paint 2/12 of the length of fence remaining. In March I’ll paint 3/12 of the remaining portion of the fence and so on throughout the year. When during the year will I require the most paint?

(Extension for rocket scientists: what if there were x months in a year instead of 12?)
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