The local recycling plant had a contract requiring anyone who obtained recycled bottles for storage from them, to bring them back to be recycled again. The plant could make one new bottle from every seven bottles returned. One week, on Monday, they got 343 bottles to recycle. Assuming that everybody brought back all the empties, how many could they eventually remake from the 343?
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Fifty-seven. The forty-nine recycled from the original batch could be recycled themselves, and so on.
The engineering department was arranging for a rather expensive catered lunch to bid farewell to their retiring colleague. They calculated that it would cost each person $30. One good mathematician remarked, "It's lucky that there aren't five fewer of us to split the...