20210806, 05:44  #1 
"Matthew Anderson"
Dec 2010
Oregon, USA
2×5×89 Posts 
Exercise for 'Daryll's' age
Hi again,
Many of you will know how to solve this sort of problem. Determine how old Daryll was when he died. His boyhood lasted one sixth of his life, he married after one seventh more, his beard grew after one twelfth more, and his son was born five years later, the son lived to half his father’s age, and the father died four years after the son. I found this famous exercise in a (free to me) online book called An Introduction to Diophantine Equations by Andresscu, Andrica and Cucurezeanu. My answer Daryll lived 84 years, and his son lived 42 years Regards, Matt 
20210806, 06:49  #2 
Sep 2017
3^{2}·13 Posts 
You don't have to multiply any large numbers:
x/6 + x/7 + x/12 + 5 + x/2 + 4 = x (14+12+7+42)*x/84 + 9 = x 75*x/84 + 9 = x 9 = 9*x/84 x = 84 In this particular case, you may also use the clues to guess the answer: the answer is most likely divisible by 12 and 7, hence by 84. Unless he lived 168 years or more, the first plausible candidate is 84. 
20210806, 07:24  #3 
"Matthew Anderson"
Dec 2010
Oregon, USA
2·5·89 Posts 
Well done SmartMersenne. I'm glad you worked that out.

20210806, 11:50  #4 
Feb 2017
Nowhere
2×13×191 Posts 
Looks remarkably like (Spoiler alert!) Diophantus's Riddle...

20210806, 23:16  #5 
Sep 2017
3^{2}·13 Posts 
Not just "like", but "exactly"!

20210807, 11:02  #6 
Romulan Interpreter
Jun 2011
Thailand
10011000110000_{2} Posts 
To get admitted into high school (9th grade) we had to solve the following problem (beside of doing other stupid things), which we still remember: "Good morning one hundred geese". "We are not a hundred, if we would be once more we are, and a half more, and a quarter more, we would be a hundred together with you". Something like that, excuse the translation which sounds crappy in English. We found out how many geese were, of course.
Last fiddled with by LaurV on 20210807 at 11:02 
20210807, 11:55  #7  
Feb 2017
Nowhere
2·13·191 Posts 
Quote:
First possibility: "Once more we are" means "twice as many": 2*x + x/2 + x/4 + 1 = 100 11*x/4 = 99 x = 4*9 = 36 Second possibility: "Once more we are" means "one more than": x + 1 + x/2 + x/4 + 1 = 100 7*x/4 = 98 x = 4*14 = 56 

20210808, 07:00  #8 
Romulan Interpreter
Jun 2011
Thailand
2^{4}·13·47 Posts 
Yep, that was correct. My English translation skill sucks. My excuse is that in English it sounds bad either way , in Romanian there was no doubt which possibility it was, Romanian is a lot more flexible/poetic. And that exam was to test math skills not language skills.
Last fiddled with by LaurV on 20210808 at 07:04 
20210808, 14:20  #9  
"Robert Gerbicz"
Oct 2005
Hungary
1,493 Posts 
Quote:
Then solve this: His boyhood lasted one sixth of his life, he married after one ninth more, his beard grew after one eighteenth more, and his son was born five years later, the son lived to half his father’s age, and the father died six years after the son. And you get that the answer is not divisible by 18 or 9. 

20210808, 17:44  #10  
"Viliam Furík"
Jul 2018
Martin, Slovakia
2·3·113 Posts 
Quote:
He was born in Carpathian Ruthenia/Zakarpattia, now part of west Ukraine  this may be the reason why LaurV also knows this riddle, it's a region neighbouring today Romania. I don't quite know, how my grandfather knows it, because he was born in 1935, only a few years before WWII, so he didn't have many opportunities to study, even if he had the money for it. As far as I know, he used to be a car mechanic and electrician. I am not sure what education he had, but I know he didn't go to university (nor college, because I think those are considered different things in some countries), neither did my grandmother. My father did. 

20210808, 22:49  #11  
Undefined
"The unspeakable one"
Jun 2006
My evil lair
3·7·13·23 Posts 
Quote:
Smart people (the real meaning of smart, not the fake "smart" devices) can find a way to excel, if they are willing to try. 

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