MathDB
2013 General Problem 21

Source:

February 4, 2013

Problem Statement

How many positive three-digit integers abc\underline{a}\underline{b}\underline{c} can represent a valid date in 20132013, where either aa corresponds to a month and bc\underline{b}\underline{c} corresponds to the day in that month, or ab\underline{a}\underline{b} corresponds to a month and cc corresponds to the day? For example, 202 is a valid representation for February 2nd, and 121 could represent either January 21st or December 1st.
(Note: During the actual test they had to write the number of days in each month so don't feel bad if you have to google that :P)