A human pyramid is a way of stacking people vertically in a triangle. With the exception of the people in the bottom row, each person splits their weight evenly on the two people below them in the pyramid.

computer science

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A human pyramid is a way of stacking people vertically in a triangle. With the exception of the people in the bottom row, each person splits their weight evenly on the two people below them in the pyramid. Their “weight”, however, includes not only their own body weight but the weight they are supporting above them. For example, in the pyramid above, person A splits her weight across persons B and C, and person H splits his weight—plus the accumulated weight of the people he’s supporting—onto people L and M. In this question, you'll explore just how much weight that is.

For simplicity we will assume that everyone in the pyramid weighs exactly 200 pounds. Person A at the top of the pyramid has no weight on her back. People B and C are each carrying half of person A's weight. That means that each of them is shouldering 100 pounds.

Now, let's look at the people in the third row. Let’s begin by focusing on person E. How much weight is she supporting? Well, she’s directly supporting half the weight of person B (100 pounds) and half the weight of person E (100 pounds), so she’s supporting at least 200 pounds. On top of this, she’s feeling some of the weight that people B and C are carrying. Half of the weight that person B is shouldering (50 pounds) gets transmitted down onto person E and half the weight that person C is shouldering (50 pounds) similarly gets sent down to person E, so person E ends up feeling an extra 100 pounds. That means she’s supporting a net total of 300 pounds.

Not everyone in that third row is feeling the same amount, though. Look at person D for example. The only weight on person D comes from person B. Person D therefore ends up supporting