Comments on: puzzles are fun http://omgzombies.org/2007/10/18/puzzles-are-fun seeking brains for many long years, no luck so far Sun, 11 Oct 2009 12:15:27 -0700 http://wordpress.org/?v=2.8.4 hourly 1 By: Nigel James http://omgzombies.org/2007/10/18/puzzles-are-fun/comment-page-1#comment-1211 Nigel James Wed, 21 Nov 2007 09:12:15 +0000 http://worsethanhitler.org/2007/10/18/puzzles-are-fun#comment-1211 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 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

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