## Magical 111

Submitted by Marianne on February 3, 2011Here's a fact: take the year you were born in (only the last two digits, as in '85), add your age and then (probably) add 1. The answer is ... 111!

This seems to have been making the rounds lately. Some people marvel at the fact that the answer is always 111 no matter how old you are and others think that 2011 is the only year in which a calculation like this will work. Looks like mathematical magic!

But there's a rational explanation. If you take the full year you were born in (as in 1985) and add your age, then it's clear that this takes you (more or less) to the year we're in now. After all your age is exactly the amount of time that's passed since you were born. The only qualification is that if you haven't yet had your 2011 birthday, you need to add an extra 1, because your official age is still the same as it was in 2010.

Here's an example: if you were born in July 1985, then you're 25 years old, and have been since July 2010. Expressing this using numbers gives 1985+25=2010 and therefore 1985+25+1=2011.

Now the difference to the calculation above is just that you leave out the first two digits in the year. This is the same as subtracting 1900 from your birth year and also from the answer 2011. So you get (1985-1900)+25+1=(2011-1900)=111.

So there's no mystery at all. The result just says that if you add your age to the year you were born (and then add 1 if you haven't had your birthday yet), you end up in the current year. That's pretty obvious, so it's surprising how many people seem to be stumped by it. After all we're all used to working out someone's age from their birth year, or vice versa, and we do this by subtracting the age or the birth year from the current year 2011. The calculation above is just the reverse of that. Maybe people find the calculation puzzling because once you reverse it in this way and leave off the first two digits of the year, the numbers lose their meaning as years or ages and just become abstract numbers. Then they also lose their temporal coherence, so there's no reason to suspect that the answer should always be 111.

So what if we were in another year, not 2011? If that year was 2000 or after, then the answer (as long as you were born before 2000) would be 100 plus the last two digits of the current year, as it is for 2011. If it was before 2000, then the answer would simply be the last two digits of the current year. You can work out for yourself what the answer is for someone born after 2000.