Problem:
In year , the day of the year is a Tuesday. In year , the day is also a Tuesday. On what day of the week did the day of year occur?
Answer Choices:
A. Thursday
B. Friday
C. Saturday
D. Sunday
E. Monday
Solution:
Note that, if a Tuesday is days after a Tuesday, then is a multiple of . Next, we need to consider whether any of the years , is a leap year. If is not a leap year, the day of year is days after a Tuesday, and thus is a Monday, since if larger than a multiple of . Thus, year is a leap year and the day of year is another Tuesday (as given), being days after a Tuesday. It follows that year is not a leap year. Therefore, the day of year precedes the given Tuesday in year by days, and therefore is a Thursday, since is larger than a multiple of .
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions