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What would be the controlling factor? That the woman work together? That they live together? Some average of the two?
Strip clubs might provide some useful data. What happens to strippers when they're going through their period? They wait tables at the club. The fact that clubs have both dancers and waitresses throughout the month would indicate that periods do not synchronize. There might be confounding factors such as high turnover, some of the dancers being roommates while others don't associate with co-strippers outside of work. In the name of science, we need a grant so we can do field research and get to the bottom of this.