15.Two Thirds Off the Bus
★★★puzzlesJane Street
A bus starts with some number of passengers. At each of three consecutive stops, two thirds of those on board get off and then 7 new passengers board. The number aboard is a whole number at every moment. What is the smallest number of passengers the bus could have started with?
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The count entering each stop must be divisible by 3. Push that requirement backwards through all three stops.
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