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# Diophantus

16 replies to this topic

### #11 Mihir

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Posted 10 February 2008 - 09:07 AM

1/6+1/12=1/7+5+1/2x+4=x 1/6=14,1/12=7,1/7=12,14+7+12+5+4=x-1/2x,14+7+12+5+4+=1/2x,42=1/2x,x=84
he lived to 84

Hmm... thats excactly coorect but lf we would've simply taken the lowst common multiple of 6,7,12 ie. 84 it would become simpler

Edited by Mihir, 10 February 2008 - 09:07 AM.

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### #12 woon

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Posted 13 March 2008 - 12:09 PM

Since his son's life is half of his life

so whatever information given there is equal to the other half of his lifetime

so let L = his whole life

L / 6 + L / 12 + L / 7 + 5 + 4 = L /2

(3/28) L = 9

L = 9 x 28 / 3
= 84

His life = 84 years old
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### #13 lowther

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Posted 17 March 2008 - 08:12 PM

The text of the riddle states,
"Due to one admirer of his, who described his life by the means of an algebraic riddle" so it seems fair to use algebra to solve this puzzle.

My solution follows what others have done. I started by finding a common base for the constraints, which set me up to create two equations. Plugging one into the other . . .

11/28d + 9 = s
2s = d

11/28d + 9 = 1/2d
11/28d + 9 = 14/28d
9 = 3/28d
9X28 = 3d
3X28 = d
d=84

There's probably a hundred ways to prove this one. Kind of fun though.
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### #14 Enigma Time

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Posted 28 March 2008 - 02:59 PM

You would have to consider we are talking about someone who was living around 250 BC and people didn't live as long back then. 2 reasonable ages would be 28 or 42.

Edited by Enigma Time, 28 March 2008 - 03:00 PM.

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### #15 dawgsrule93

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Posted 28 March 2008 - 03:43 PM

Talk about smart people, but he lived to be 84 years old.
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Posted 12 May 2008 - 09:57 PM

I as usual I have not read any previous post, it corrupts your thinking.

I figure the best answer for this is that he lived 1/1 of his life.

Also I notice he had an interesting life, not only did he get married as a youth but he got his first beard half way through his youth . . . this must be the new modern definition of youth, it goes 'til your thirty. Maybe in another ten years it will go 'til we're forty, that way we can stay young forever.
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### #17 hahaha

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Posted 14 September 2008 - 04:30 AM

I solved this quite a different way.. No equations with variables or finding the LCM at all.

Youth=1/6
First beard=1/6+1/12 (1/4)
Married=(1/4)+1/7 (11/28)
Son=(11/28)+5yrs
Son lived=14/28
Son died= 25/28+5 yrs
He died=25/28+9yrs

3/28 of his life=9yrs, so 1/28=3 years, and 28/28=84 years.
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