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- 2012-11-26
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Description: How far can you make a stack of cards overhang a table? If you have one card, you can create a maximum overhang of half a card length. (We re assuming that the cards must be perpendicular to the table.) With two cards you can make the top card overhang the bottom one by half a card length, and the bottom one overhang the table by a third of a card length, for a total maximum overhang of 1/2+ 1/3 = 5/6 card lengths. In general you can make n cards overhang by 1/2+ 1/3+ 1/4+ ...+ 1/(n+ 1) card lengths, where the top card overhangs the second by 1/2, the second overhangs tha third by 1/3, the third overhangs the fourth by 1/4, etc., and the bottom card overhangs the table by 1/(n+ 1). This is illustrated in the figure below.
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