# Combinatorics Dates question

This is the problem:

A usual way of writing dates is the ‘YY/MM/DD’ method of expressing a date as a six-digit number. For instance, 7th March 2004 is denoted as 04/03/07. Since 04 + 03 = 07, we say that this is a ‘good day’. In general, a day is said to be a ‘good day’ if, among the three two-digit numbers representing ‘year’, ‘month’ and ‘day’ in the above representation, one of them is equal to the sum of the other two. How many ‘good days’ are there in the 21st century (from 1st January 2001 to 31st December 2100)?

This was from an invitational mathematics competition held in 2004, and it was recently discussed in a course I had. The link to it is here: (http://www.pca.edu.hk/pcimc/3rd/questionandanswer/3rdIndividualS3.pdf), in question number 9.

Do you have any tips I have to solve this question? I missed listening to a part of the solution, so it would be great if anyone reading this would be able to help.

Note by Toby M
11 months ago

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