Doc
Doc
  • Threads: 46
  • Posts: 7287
Joined: Feb 27, 2010
October 29th, 2015 at 1:49:16 PM permalink
Hope the thread title isn't too morbid.

A little factoid I recently came across intrigued me, and I thought I would express it in the form of a puzzle. No, it’s not nearly so clever as the Wizard’s recent puzzle on poisoned wine, and it’s not particularly math-oriented, though this seemed like a reasonable sub-forum in which to post it.

So here’s the problem:

A person dies after having reached just 18 birthdays. What is the extreme range (minimum and maximum) of the possible number of days that he could have been alive until the time that he died? (Let’s treat it as if birth and death both occur at noon and not worry about fractional days.)

Extra Credit (since my students always liked that): Name the famous person, well-known for music he wrote, who inspired this puzzle and tell how many days old he was when he died.


Note: I suppose I need to clarify a definition, just because some of us nerdy folks on this site might like to point out the implications of a different interpretation. I don’t consider the day that I emerged from the womb a “birthday,” in the sense of this puzzle. To me, my first birthday was the day that I turned one year old, 365 days later.


If you care to hide answers behind spoilers, that's fine, but many others are likely to peek. Maybe in this case I could suggest that bare answers and/or guesses may be posted in the open, with explanations, calculations, and Extra Credit answers posted behind spoilers, so that others who get different answers aren't immediately aware of whether you screwed up or figured out something they overlooked.
waasnoday
waasnoday
  • Threads: 3
  • Posts: 162
Joined: Jan 13, 2015
October 29th, 2015 at 2:05:19 PM permalink
Will take a shot at the extra credit. Ritchie Valens and 6,476 days.

Edit: Doh! he did not make it to a full 18 years. In my best Emily Litella voice: never mind.
Joeman
Joeman
  • Threads: 36
  • Posts: 2410
Joined: Feb 21, 2014
October 29th, 2015 at 2:30:53 PM permalink
I dunno, Doc, I think just giving my answers in this case might be a hint in and of itself. How about if I put my answers under one tag, and my explanation in a separate one? Peekers gonna peek anyway. :)

6,573 / 27,758

The min is 18 x 365 plus 3 for leap days = 6,573. E.g. born Jan 1 1897, died Jan 1, 1915. There are leap years in 1904, 1908, and 1912. There is not a leap year in 1900 because it is divisible by 100, but not 400.

The max assumes the person was born on Feb 29 and only gets a birthday every 4 years. So, let's say he was born on Feb 29, 1904. His 18th birthday is on Feb 29, 1976. He would have his 19th birthday on Feb 29, 1980, so if he dies on Feb 28, 1980, he still has seen only 18 birthdays. So 76 years - 1 day = 76 x 365.25 - 1 = 27,758

Nope. Don't know that one.
"Dealer has 'rock'... Pay 'paper!'"
beachbumbabs
beachbumbabs
  • Threads: 100
  • Posts: 14260
Joined: May 21, 2013
October 29th, 2015 at 2:33:10 PM permalink
Quote: waasnoday

Will take a shot at the extra credit. Ritchie Valens and 6,476 days.

Edit: Doh! he did not make it to a full 18 years. In my best Emily Litella voice: never mind.



Actually, I would guess that your answer is correct on the EC. It seems well within the spirit of the question, anyway. :)
If the House lost every hand, they wouldn't deal the game.
Doc
Doc
  • Threads: 46
  • Posts: 7287
Joined: Feb 27, 2010
October 29th, 2015 at 3:31:29 PM permalink
Joeman: I'll give you 1 out of 2 on min/max. Nice start.

Quote: beachbumbabs

Quote: waasnoday

Ritchie Valens and 6,476 days.

Actually, I would guess that your answer is correct on the EC. It seems well within the spirit of the question, anyway. :)



I have to go with waasnoday's edit. Ritchie Valens only had 17 birthdays, if you follow the definition I called out. Yes, his premature death could have been an inspiration, but I really got the thought based on another music writer who lived closer to the max answer instead of a bit shy of the minimum.
waasnoday
waasnoday
  • Threads: 3
  • Posts: 162
Joined: Jan 13, 2015
October 29th, 2015 at 3:59:21 PM permalink
I think I know who it is, but I missed my shot. It is not Otis but there were several others around the right age that also died with Otis when their plane went down. Now I have "The Dock of the Bay" playing in my head.
Ayecarumba
Ayecarumba
  • Threads: 236
  • Posts: 6763
Joined: Nov 17, 2009
October 29th, 2015 at 4:21:11 PM permalink
I recall the calendar was "reset" at some point in history. Could this affect the min/max?
Simplicity is the ultimate sophistication - Leonardo da Vinci
Mosca
Mosca
  • Threads: 191
  • Posts: 4140
Joined: Dec 14, 2009
October 29th, 2015 at 4:34:45 PM permalink
King Tut died at age 18. Born in Arizona, moved to Babylonia, King Tut. Delighted generations with that one, don't you think?
A falling knife has no handle.
teliot
teliot
  • Threads: 43
  • Posts: 2871
Joined: Oct 19, 2009
October 29th, 2015 at 4:41:58 PM permalink


If you were born on February 30, 1712, then you have a long life ahead of you.

http://www.timeanddate.com/calendar/?year=1712&country=21

Climate Casino: https://climatecasino.net/climate-casino/
1BB
1BB
  • Threads: 18
  • Posts: 5339
Joined: Oct 10, 2011
October 29th, 2015 at 4:42:02 PM permalink
Quote: waasnoday

I think I know who it is, but I missed my shot. It is not Otis but there were several others around the right age that also died with Otis when their plane went down. Now I have "The Dock of the Bay" playing in my head.



Don't feel too badly. I've got La Bamba in my head.

Para bailar la bamba

Para bailar la bamba .....
Many people, especially ignorant people, want to punish you for speaking the truth. - Mahatma Ghandi
Doc
Doc
  • Threads: 46
  • Posts: 7287
Joined: Feb 27, 2010
October 29th, 2015 at 6:16:19 PM permalink
Quote: Ayecarumba

I recall the calendar was "reset" at some point in history. Could this affect the min/max?


Quote: teliot



If you were born on February 30, 1712, then you have a long life ahead of you.

http://www.timeanddate.com/calendar/?year=1712&country=21


In response to Ayecarumba's and teliot's posts:

Yes, in the conversion from the Julian calendar to the Gregorian calendar, some days had to be eliminated. Countries adopted the new calendar at different times from 1582 to 1923, and the number of days that had to be eliminated depended upon how long a country delayed in adoption. In all cases that I was aware of, the days were eliminated in a single block, though gradual elimination had been proposed.


I confess that:

(1) I had not considered this factor when I came up with the puzzle, and I suppose it would give a different answer for the minimum number of days, if the person were alive at just the right time.

(2) I had never heard of the extreme issue shown in teliot's spoiler. Is that really how they did things there? Was it done anywhere else? BTW, I don't see how that can be the result of the same factor, since it goes in the opposite direction.


Edit: I found this info to explain #2 above.
MathExtremist
MathExtremist
  • Threads: 88
  • Posts: 6526
Joined: Aug 31, 2010
October 29th, 2015 at 6:44:23 PM permalink
If you were born on PSR J1719-1438 b, you'd be about 39 hours old on your 18th birthday.

http://www.reuters.com/article/2011/08/26/us-planet-diamond-idUSTRE77O69A20110826
https://en.wikipedia.org/wiki/PSR_J1719-1438_b
"In my own case, when it seemed to me after a long illness that death was close at hand, I found no little solace in playing constantly at dice." -- Girolamo Cardano, 1563
Doc
Doc
  • Threads: 46
  • Posts: 7287
Joined: Feb 27, 2010
October 29th, 2015 at 6:49:49 PM permalink
Nope. Don't think I've ever met anyone from there.


Guess I neglected to go far enough to nail down all the definitions.

:-)
Joeman
Joeman
  • Threads: 36
  • Posts: 2410
Joined: Feb 21, 2014
October 30th, 2015 at 3:39:59 AM permalink
= 29,218 days

For some reason, I remembered to use the fact that some "divisible by 4 years" are not non-leap years in my Min calculation, but completely forgot this nugget when making my Max calculation.

So, if the Max person's lifetime were to span a turn-of-the-century year not divisible by 400, he would completely miss his birthday during that "cycle." Thus, you can add another 365 x 4 or 1460 days to my previous answer of 27,758 to get 29,218 days.
"Dealer has 'rock'... Pay 'paper!'"
Doc
Doc
  • Threads: 46
  • Posts: 7287
Joined: Feb 27, 2010
October 30th, 2015 at 5:52:26 AM permalink
Joeman:
That's what I got, not considering the special case that Ayecarumba alluded to and I described above. Very well done! Want to give the answer to that special case, too?

I'm posting from my phone now. When I get to my computer, I'll post the Extra Credit answers.
Dieter
Administrator
Dieter
  • Threads: 16
  • Posts: 5479
Joined: Jul 23, 2014
October 30th, 2015 at 6:33:21 AM permalink
Quote: Doc

I don’t consider the day that I emerged from the womb a “birthday,” in the sense of this puzzle. To me, my first birthday was the day that I turned one year old, 365 days later.



Yes, but... that's not your birthday. If you were born once, the day it happened is your birthday. The celebrations usually fall on the anniversary of that event.

(I am surely not above being "That Guy". Anyway, back to the common usage of the term...)


Supposing a person were born on 29 February. This is an "intercalary day", which only occurs ever 4 years (usually). The next time the date of their birth came around, in general, they would be 1481 days old.

However, what if they were born on 29 February, 1896? The peculiarities of leap years mean that century aligned years only are leap years if they are evenly divisible by both 100 and 400. By the time our person has his first birthday, people who were born the day before him have had eight. At this point, he is 2921 days old. Every 1461 days going forward, the date is the same as the day he was born.

So, I get 2921+(17*1461)+1460=29218 days as the maximum. (By the common reckoning, that's about 80 years old.)

The nice girl next door who born on 1 March, 1896 would have celebrated the 18 anniversaries of the date of her birth when she met her untimely death on 1 March, 1914 - having aged just 6573 days.


Years can be adjusted, but I think if you include a year where the intercalary day would ordinarily fall but doesn't (yes 1900, but not 2000), you can add or subtract an extra day.




Not going for extra credit, since I think that would involve leap seconds, and my brain just isn't there this morning.


Edit: no, I didn't peek.
May the cards fall in your favor.
Doc
Doc
  • Threads: 46
  • Posts: 7287
Joined: Feb 27, 2010
October 30th, 2015 at 12:16:06 PM permalink
As promised, here are my answers. These do not consider "really" special situations, where normally-expected days are deleted from the calendar (as first noted by Ayecarumba and later expanded upon by me), or "extremely" special situations (oddities), where there was a month/day combination that will perhaps never appear again (as first noted by teliot and later expanded upon by a link I provided.)

6,573
See explanation from either Joeman or Dieter.


29,218
See explanation from either Joeman or Dieter.


Gioachino Antonio Rossini, Feb. 29, 1792 - Nov. 13, 1868
(Think "William Tell Overture", if you're not familiar with other works.)
18 birthdays (birth date anniversaries) experienced
76 years, 258 days old at death.

Total days = 28,016

He would have needed to live 3 years, 3 months, and 15 days longer to reach the "maximum".
  • Jump to: