Let's denote the day of the month a person was born as dd e.g. 03 or 24. Let's denote the month by mm e.g. 04 or 11. Create a number dd0mm e.g. a birthdate of 19th June would generate 19006. Let this number represent the age of the person reckoned in days (counting the day the person is born as day 0 which is consistent with the way age is reckoned). The range of numbers possible then lies between 01001 and 31012, corresponding to ages between 2 and 84. Without the intervening zero, the age range would be far more restricted which is not what I want.
The question is when will such a number fall on a person's birthday? I stumbled upon one such number which I'm happy to share. I discovered it quite by accident. It's 23011 or the 23rd November. It doesn't always work. For example, it works for this year (2016) and 23rd November 1953 but not last year (2015) and 23rd November 1952 (the person is only 23010 days old on the birthday). So I've partially answered my question but I'm wondering if that's the only date that sometimes works. Are there any others? My research so far suggests that it is unique but I'm not certain. I looked for possible candidates by solving abs(x-n*365.242199)<1 for n ranging from 2 to 84 but didn't find anything. To refine my question further then, am I correct in stating that 23rd November (23011) is the only birthdate that sometimes satisfies the condition that dd0mm falls on a birthday?