MathDB

21

Part of 2013 Stanford Mathematics Tournament

Problems(1)

2013 General Problem 21

Source:

2/4/2013
How many positive three-digit integers a‾b‾c‾\underline{a}\underline{b}\underline{c} can represent a valid date in 20132013, where either aa corresponds to a month and b‾c‾\underline{b}\underline{c} corresponds to the day in that month, or a‾b‾\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)