Tuesday, March 17, 2015

The Age Old Problem

Here we have two completely random people: Anna en Ben. Anna's birthday is in February, while Ben's birthday is in April.

Today (15 March 2015) I take Anna's age, Ben's age, Anna's year of birth, and Ben's year of birth, and add all of 'em together.

This results in one number. What is it?

That doesn't seem a lot to go on, does it? Still, the answer is pretty straightforward. Ask yourself this: what does my age represent?

Your age is simply the difference between the year of your birth and the year of your last birthday. In the same way, adding someone's age to his or her year of birth gives the year of his or her last birthday. So that could either be the current year or last year, depending on whether they already had their birthday this year. Since the birthday months are given in this riddle, you know which one it is.
In this case: 2015 + 2014 = 4029 ← (click to spoil)

Details: A more algebraic approach would be the following. Here you'll see that by rewriting the age terms, you can cancel out the birthyear terms, leaving only the simple addition of two years.
Let A be the age and Y the year of birth.

N = Aanna + Yanna + Aben + Yben

N = (2015 − Yanna) + Yanna + (2014 − Yben) + Yben

N = 2015 + 2014 = 4029

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