Thu 18 Oct 2007
At work, the following was passed to the email list with a $5 starbucks card as prize for the first person to get it right. Finally a chance for me to use my finely-tuned puzzle solving skills to use besides in job interviews.
> Diophantus was an algebraist who lived in Alexandria in the third
> century AD. Most of what is known about his life comes from an
> epigram about him (which has been slightly simplified.)
>
> His boyhood lasted a sixth of his life.
> His beard grew after another twelfth.
> He married after a seventh more and his son was born nine years later.
> When he died, he had been a father for half of his life.
> How long did he live?
Answer follows:
You need a number that is divisible by 7,6,and 12. 12*8=84 which happens to be divisible by 6, so that was my first try.
14 years childhood
beard grew 7 years, until he was 21
married after 12 years, when he was 33
son born when he was 42
42*2=84
Bing. Five bucks worth of coffee!!!!



November 21st, 2007 at 2:12am
Ahh you have a slight error in your solution. Good thinking but you have:
“12*8=84 which happens to be divisible by 6, so that was my first try.”
What I think you mean is “12* 7 =84 which happens to be divisible by 6, so that was my first try.”
The algebraic solution that Diophantus would have used would have run something like this…
(just for completeness)
Let s = Diophantus’s livespan
We have s/6 + s/7 + s/7 + 9 = s/2
=> 14s/84 + 12s/84 + 7s/84 + 9 = 42s/84
=> 33s/84 + 9 = 42s/84
=> (subtracting from both sides)
9 = 9s/84
=> (solving for s)
s = 9/9 * 84
Therefore Diophantus’s livespan was 84 years.
Thanks for the puzzle and I hope you enjoyed the coffee,
regards
Nigel