Problem:
A lucky year is one in which at least one date, when written in the form month/day/year, has the following property: The product of the month times the day equals the last two digits of the year. For example, is a lucky year because it has the date and . Which of the following is NOT a lucky year?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
The last two digits of can only be factored as . All the other choices have at least one date that makes them lucky:
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions