The SCI 301 Puzzler

You are building on an unstable hillside and wish to place the cistern in a location that maximizes the stability of the entire house structure. Consider the two options pictured. In the first case, the cistern is on the uphill side and in the second, it is on the downhill side. In both cases, the center of weight of the house can be taken at the center of the house and the center of weight of the cistern can be taken at the center of the cistern. When full of water, the total weight of the cistern is comparable to that of the house. The house, cistern walls, and support beams opposite the cistern are poured concrete, linked together with steel rebar, so they move as one unit. Here's the puzzle. As the soil beneath the cistern begins to erode, which arrangement pictured offers the greater stability? That is, which one will survive erosion the longest? (Assume the footings for the column supports remain stable.) Be sure to explain your reasoning.

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