Commentary for Avodah Zarah 42:3
אבל לכותי מאי שרי כותי אימר עביד ביה מלאכה בחולו של מועד בחולו של מועד אנן נמי עבדינן
But to a Samaritan is it permitted? Say that he might do work on the intermediate days of the festival. On the intermediate days we too do such work.
Daf Shevui to Avodah Zarah
By implication, renting a bath-house to a Samaritan should be permitted. But while Samaritans observe the Sabbath and do not work on it, they do work on intermediate days of the festival. The assumption here is that Jews do not work on these days and thus people might think that he is working on behalf of the Jew.
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Daf Shevui to Avodah Zarah
The answer is that Jews also are allowed to work in a bath-house on hol hamoed by heating up the water.
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