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Start with Monday as the first day, and count. This will give the maximum number of Mondays possible. The answer turns out to be 7, with a couple of days of wiggle-room. I just now realized that I mis-read the question. You are not asking for the maximum number, but in fact the smallest: the greatest number that can appear in any 45 day period. So the answer is actually 6, not 7. There can be no fewer than 6 Mondays in any interval of 45 days.

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Q: How do you find the greatest number of mondays that may occur in any 45-day interval?
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