A bad muffin III

Level pending

A bad muffin eats raisins. Every Monday, he eats 1 raisin, every Tuesday, he eats 4 raisins, every Wednesday he eats 9 raisins, every Thursday he eats 16 raisins, ... and every Sunday he eats 49 raisins. What is the minimum number of raisins he eats in a month?


The answer is 560.

Vincent Huang by Vincent Huang , 30, USA

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1 solution

Sean Elliott
Jan 22, 2014

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 28 days or 4 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 + ⋯ + 49 = ( 7 ) ( 8 ) ( 15 ) 6 = 140 1+4+9+\cdots+49=\frac{(7)(8)(15)}{6}=140 raisins; since, there are 4 4 weeks, he eats 4 ⋅ 140 = 560 4\cdot140=\boxed{560} raisins as the minimum.

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