The Dark and Stormy Night

Jan 11, 2020

RAY: It was a dark and stormy night. The dozen inhabitants of a small three-story apartment building began to worry. The rain got heavier and soon the roof began to leak.

The people living in the top floor apartment sought refuge in the apartment one floor below, i.e., the second floor. When they did, the second floor people said, "We can't admit all of you, we can just accept the same number of people that we already have living here." So some people moved from the top floor to the middle floor and the rest stayed behind.

Soon the rain got heavier. Those on the second floor began to get wet and sought refuge on the first floor. They were told the same thing: “We can only accept the same number of people that we have already.” And so some moved, and some stayed behind.

The next morning, when the rescue workers arrived, an equal number of people emerged from each of the three apartments.

The question is: How many people started out on each floor?



RAY: We know the first floor must have started with two, because it wound up with four people. Remember, it accepted the same number it had, making for four.

Since there are twelve people total, we had to start off on the top floor with seven, and three on the second floor. Remember, we know the first floor had two people. The top floor gave up three, ending with the requisite four. So, it had to start with seven.

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