Question:
Non-Jew asks to borrow a book from a Jew. The Jew fumbles around in a dark room looking for the book, and the non Jew turns on the light.
The non-Jew did the melacha for the Jew, but really he did it for himself so that the Jew can find the book faster.
Answer:
It would seem that the gentile is actualy doing it for his own benefit, therefore it is permitted.
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