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Four vagabonds - math puzzle of the day

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A very rich lady goes with a bag of coins (not more than 400) to the city. In the city she meets four vagabonds. She gives the first vagabond 4 coins and a quarter of the number of coins which is left in the bag. She applies the same procedure to the second, third and fourth vagabond (so division by 4 worked always). With how many coins did she leave home?

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