When is person A and person B's joint 100th birthday?

January 13, 2015 4:23 AM

I have two friends, person A and person B. Person A was born 4 February 1971, so will be 44 soon. Person B was born 29 March 1959 and will be 56 soon. Until 4 February 2016 they will then collectively be 100 years old. But on what date between those two birthdays could they be considered exactly 100?. I want to send a joint 100th birthday card and I think, but I'm not sure, that it's the 2 or 3 March.
posted by dowcrag to Grab Bag (9 answers total)

Best answer: I think, but I'm not sure, that it's the 2 or 3 March.

I think you're right, and you can't really settle it more accurately without knowing the times of day they were born.
posted by jon1270 at 4:38 AM on January 13, 2015

Best answer: Without measuring their age in hours you won't be able to nail down whether it's the 2nd or 3rd. When you round up to whole days the sum of the two ages will always be an even number, and not 36525 days.
posted by nulledge at 4:38 AM on January 13, 2015

Best answer: I think the calculation works a bit like this:

1. Calculate the difference between the two dates. I make this 4330 days. This is the number of days lived by the time the younger person is born.

2. 100 years is 36524 days (to the nearest day.)

3. Subtract 4330 from 36524 to get 32194, which is the number of days remaining to be lived (jointly).

4. Divide 32194 by two (to share the remaining days between the two people). That's 16097 days.

5. 16097 days after 4 Feb 1971 will be Monday, 2 March 2015.

And yes, time of day could be a factor. But you're close enough.
posted by pipeski at 4:39 AM on January 13, 2015

Best answer: There are an odd number of days between the two birthdays, so when you divide them in half, it won't work out quite right. On March 2, they are collectively 100 years minus one day and on March 3 they are collectively 100 years plus one day. I guess you'd have to know times of birth to get any more accurate.
posted by ssg at 4:40 AM on January 13, 2015

Best answer: Your answer's right by me. Here are my results:

2015-3-2: 99.9972621492129
2015-3-3: 100.002737850787

Here's my code:

        static void Main(string[] args)
        {
            var dateOne = new DateTime(1971, 2, 4);
            var dateTwo = new DateTime(1959, 3, 29);

            var potentialDate = DateTime.Today;
            double totalYears;
            do
            {
                var totalDays = (potentialDate - dateOne).TotalDays + (potentialDate - dateTwo).TotalDays;
                totalYears = totalDays/365.25;
                Console.WriteLine("{0}-{1}-{2}: {3}", potentialDate.Year, potentialDate.Month, potentialDate.Day,
                    totalYears);

                potentialDate = potentialDate.AddDays(1);
            } while (totalYears < 100);
        }

Note the fudge factor converting days to years is 365.25 to account for leap years, but that's not 100% precise. There may be a better way to do this, I'm not sure.
posted by Dilligas at 4:47 AM on January 13, 2015

Best answer: 365.25 days is the correct average year duration for all years between 1900 and 2099 inclusive, because the year 2000 was a leap year due to being a multiple of 400.

Be that as it may: if I feed the two birthdays into this online Julian Day calculator, using 12:00:00 as the time because that means I can't be more than 12 hours away from the true birth times, I get this:

29 March 1959 = Julian day 2436657
4 February 1971 = Julian day 2440987
Half way between = Julian day (2436657 + 2440987) / 2 = 2438822 = 2 March 1965

which will be exactly 50 years ago (i.e. 100 years / two lifetimes) on 2 March 2015.
posted by flabdablet at 5:41 AM on January 13, 2015

Best answer: By the way, the ±12 hour uncertainty in each of the assumed birth times gives rise to a ±24 hour uncertainty in the combined lifespan: 2 March could be a day early or a day late. If you can find their exact birth times, redo my calculation above using those instead of 12:00:00.
posted by flabdablet at 6:00 AM on January 13, 2015

Best answer: Actually, scratch that. Properly including the uncertainty terms:

29 March 1959 = Julian day 2436657 ± 0.5
4 February 1971 = Julian day 2440987 ± 0.5
Half way between = Julian day (2436657 ± 0.5 + 2440987 ± 0.5) / 2
= Julian day 2438822 ± 0.5
= 2 March 1965

So it's all good.
posted by flabdablet at 6:08 AM on January 13, 2015

Response by poster: Thanks, everyone!
posted by dowcrag at 6:09 AM on January 13, 2015