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A sewer or rotten egg type odor when you run a faucet is usually caused by an interaction between the stock magnesium anode in the water heater and a harmless bacteria. It doesn't matter which faucet it comes from since this odor will take the path of least resistance. The fix is to replace the anode with an aluminum/zinc anode.
Like I said before there is no predicting where the odor will show up. It takes the path of least resistance. If you had the odor at every faucet then your would probably be the source of the odor.