2012 AMC 10A Problem 12
Problem 12 of 25IntermediateAlgebraNumber Theory
A year is a leap year if and only if the year number is divisible by (such as ) or is divisible by but not (such as ). The th anniversary of the birth of novelist Charles Dickens was celebrated on February a Tuesday. On what day of the week was Dickens born?
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Solution
On a typical year with days, moving one year into the future moves the day of the week forward one since
On a leap year however, the day of the week gets moved forward twice since there is an extra day.
Fifty of the years between and are multiples of but we have to discard which leaves us with leap years.
Therefore, moving back years means we have to go back days, which means we move back days in the week.
This takes us back to Friday, which is the day that corresponds to February
Thus, A is the correct answer.