Adding up ages may lead to surprises
- So, yesterday was your birthday?!
- It makes no sense denying it.
- And you were 56?
- I was 19 for the third time.
- That is interesting.
- Why do you say that?
- You have four sons, right?
- Four sons, no daughters.
- And they are currently 27, 25, 3, and 1 years old.
- More or less.
- What do you get when you add them?
- I try not to. To me they are unique individuals.
- OK, I respect that. What I meant was, what is the sum of their ages?
- 56. Well actually a bit more since they did not all have a birthday yesterday as I did.
- So maybe their age is 57, just like yours?!
- I see what you mean. What day was their total age equal to my age?
- What are their birthdays?
- 11.06.1981, 01.07.1983, 17.11.2005, and 20.07.2007.
- At what time of the day were they born?
- Let’s say they were born at noon, just like me.
- OK.
- I wonder, when they will be twice as old as me?
- That’s a good question.
- Will they ever be ten times as old as me?
- Who knows!
March 30th, 2009 at 12:31 am
Let your date of birth be a, and your children’s be b, c, d, e.
a is 29 Mar 1953 (taking “today” as the date of this article, 30 Mar 2009, so “yesterday” is 29 Mar 2009, and taking “56″ as your age on his birthday that day)
Then your children’s ages will sum to your age at day x where
x-b + x-c + x-d + x-e = x-a
=> 3x = b+c+d+e-a
=> x = 17 May 2008, when you were 20138 days old, and your children were 9837, 9087, 912 ad 302 days old.
Then your children’s ages will sum to twice your age at day x where
x-b + x-c + x-d + x-e = 2(x-a)
=> 2x = b+c+d+e-2a
=> x = 11 Dec 2035, when you will be 30207 days old, and your children will be 19906, 19156, 10981 and 10371 days old.
March 30th, 2009 at 3:13 pm
a was meant to be 29.03.1952.
My spreadsheet tells me that at 16.09.2008 we were equally old (20,625 days) and that 10,312.5 days later (11.12.2036) they will be twice as old. They will be three times as old 2 x 20,625 days after 16.09.2008, but can only dream of being four times as old.