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| − | == Problem==
| + | #redirect [[2010 AMC 12B Problems/Problem 4]] |
| − | A month with <math>31</math> days has the same number of Mondays and Wednesdays. How many of the seven days of the week could be the first day of this month?
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| − | <math>\textbf{(A)}\ 2 \qquad \textbf{(B)}\ 3 \qquad \textbf{(C)}\ 4 \qquad \textbf{(D)}\ 5 \qquad \textbf{(E)}\ 6</math>
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| − | ==Solution==
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| − | In this month there are four weeks and three remaining days. Any 7 days must have exactly one Monday and one Wednesday, so it works if the last <math>31 - 4\cdot 7 = 3</math> days have the same number of Mondays and Wednesdays. We have three choices: Monday, Tuesday, Wednesday; Thursday, Friday, Saturday; Friday, Saturday, Sunday. The number of days the month can start on are Monday, Thursday, and Friday, for a final answer of <math>\boxed{\textbf{(B)}\ 3}.</math>
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| − | ==See Also==
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| − | {{AMC10 box|year=2010|ab=B|num-b=4|num-a=6}}
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| − | {{MAA Notice}}
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