Somebody was commenting here that they thought the sun would rise from the Boston (south) side of the river in the morning, but in fact it rises from the Cambridge (north) side these days. A little more than ten years ago, sitting in my northern-latitude abode watching the sun set into the northwest, I wondered the same confused thing: why does the sun appear to venture into the northern part of the sky? (For reference, the sun’s direct projection on the earth never crosses north of the tropic of cancer, and that is south of here.)
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Well, the original problem was X-rated, so let me recast it.

Three surgeons (A, B, C) participate in an operation involving three patients (a, b, c). For simplicity, each surgeon operates with just one hand, and operates just once on each patient. There are a bunch of sterile surgical gloves that stop contamination from one side to the other. What’s the minimum number of gloves needed to ensure that no body part ever comes into contact with another, even indirectly? Note, surgeons do not want to contaminate each other either.

Clearly, the upper bound is 9, for the 9 pairings. The lower bound is 3, for the 3 patients, or alternatively the 3 surgeons. Is the answer something in between?
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