330.Three Quarters Off the Bus
★★★puzzlesJane Street
A bus sets out with some number of passengers. At each of three consecutive stops, exactly three quarters of the passengers on board get off and then 7 new passengers get on. The number of people on the bus is a whole number at every moment. What is the smallest number of passengers the bus could have started with?
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Work forwards with the divisibility requirement: the count entering each stop has to be a multiple of 4. Chase that condition back to the start.
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