Level
pending

The answer is 560.

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To minimize the number of raisins, first minimize the number of days. The best month would thus be February not on a leap year, for $28$ days or $4$ weeks.

Also, the day the bad muffin starts on will be the day he eats on the most, so he should start on Monday. Thus each week he will eat $1+4+9+\cdots+49=\frac{(7)(8)(15)}{6}=140$ raisins; since, there are $4$ weeks, he eats $4\cdot140=\boxed{560}$ raisins as the minimum.