Sum Days
A sum-day is a date in which the day and month add up to the year. For example, January 1, 2002 is the first sum-day of the new century, since the date is 01/01/02 in standard notation, and .
How many sum-days are there in the century?
The answer is 365.
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1 solution
Given any day-month, there is at most a unique year, namely the year of day+month, that satisfies the conditions of a sum-day. For example, November 26 is a sum-day only for the year 2037, because 11+26=37.
In general, this works for any day-month that isn't a leap day, since each year has 365 days. However, for the leap day of February 29, we have to consider the year 2+29 = 31. Since 2031 is not a leap year, hence February 29, 2031 is not a valid sum-day.
As such, there are exactly 365 sum-days in the 21st century.