2002 AMC 10B Problems/Problem 8
Problem
Suppose July of year has five Mondays. Which of the following must occurs five times in the August of year
? (Note: Both months have
days.)
Solution
If there are five Mondays, there are only three possibilities for their dates: ,
, and
.
In the first case August starts on a Thursday, and there are five Thursdays, five Fridays, and five Saturdays in August.
In the second case August starts on a Wednesday, and there are five Wednesdays, five Thursdays, and five Fridays in August.
In the third case August starts on a Tuesday, and there are five Tuesdays, five Wednesdays, and five Thursdays in August.
The only day of the week that is guaranteed to appear five times is therefore .
See Also
2002 AMC 10B (Problems • Answer Key • Resources) | ||
Preceded by Problem 7 |
Followed by Problem 9 | |
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All AMC 10 Problems and Solutions |