The peanuts and the monkey
Five men checked into a hotel with a bag of peanuts and a monkey. They planned on dividing the peanuts evenly the following morning. However, during the night, one of the men got up, divided the peanuts into five equal parts, took his fifth and had one leftover peanut which he gave to the monkey. He put the other shares of peanuts back into the bag and returned to bed.
A little later, a second man (who did not know that the first man had been up) divided the peanuts five ways and took his fifth. He also had one peanut left over, which he gave to the monkey, and he returned the rest of the peanuts to the bag.
Likewise, during the night the third, fourth and fifth men got up and divided the peanuts, and each had one left over for the monkey. The next morning they divided the remaining peanuts equally five ways. How many peanuts were originally in the bag?
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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...