Problem:
A year is a leap year if and only if the year number is divisible by (such as ) or is divisible by but not by (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?
Answer Choices:
A. Friday
B. Saturday
C. Sunday
D. Monday
E. Tuesday
Solution:
There were non-leap days in the -year time period from February , to February , . One fourth of those years contained a leap day, except for , so there were leap days during that time. Therefore Dickens was born days before a Tuesday. Because the same day of the week occurs every days and , the day of Dickens' birth (February , ) was days before a Tuesday, which was a .
The problems on this page are the property of the MAA's American Mathematics Competitions