Mathematicians and Light Bulbs

1. None. It's left to the reader as an exercise.
2. In earlier work, Wiener has shown that one mathematician can change a light bulb. If K mathematicians can change a light bulb, and if one more simply watches, then k+1 mathematicians will have changed the light bulb. Therefore, by inductions, for all n in the positive integers, n mathematicians can change a light bulb.

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