Monday Madness

A famous mathematician has the following inscription on his headstone:

Here lies Diophantus,' the wonder behold.
Through art algebraic, the stone tells how old:
God gave him his boyhood one-sixth of his life,
One twelfth more as youth while whiskers grew rife;
And then yet one-seventh ere marriage begun;
In five years there came a bouncing new son.
Alas, the dear child of master and sage
After attaining half the measure of his father's life chill fate took him.
After consoling his fate by the science of numbers for four years, he ended his life.

How old was he?

25yrs old when married 30yrs old when son born 60yrs old when son died 64 yrs old when he died. would of been neater(whole numbers only) if he had mourned for 8 years then the answer would of been 84.

Anybody else have a response?

i'm wrong.. ok will try again but this time using months instead of whole years.. be back soon with an edit of my new answer. ok, i haven't been able to work it out to any whole numbers the way the puzzle is, so will stick with my 64years but add the 3.4285714284 months to it..

Diophantus lived to be about 84 years old.

correction 784 months old. or 65.3333333 yrs old.

Let's see the math for each of your answers.

lmao you think i never worked it out?? 784/6=130.666666667 add to calculater memory 784/12=65.3333333333 add to cal. mem. 784/7=112 add to cal. mem. recall cal mem = 308 now add 60 for 5 years =368x2 for when son died(half his age) =736 now add 48 months mourning. = total lived of 784 months divide by 12 to get years= 65.3333333333

your question + google = answer (sometimes) d/6+d/12+d/7+5+d/2+4=d multiply both sides by 84(7*12)lcd 14d+7d+12d+5*84+42d+4*84=84d combine 75d+9*84=84d subtract 75d from both sides 9*84=9d divide by 9 84=d

something not quite right with your math Jkc73 been to long since i did any algebra but i just can't see how you went from d/6+d/12+d/7+5+d/2+4=d(looks right) to 14d+7d+12d+5*84+42d+4*84=84d(doesn't look right).. no idea what you did wrong tho..

so come on then Tomk put us out of our misery is Jkc73 or my answer the one you have?

the more i look at the algebra the more i think it should look like this jkc (d/6+d/12+d/7+5)+((d-4)/2)=d

Jkc73 "cheated" but has the correct answer. (I think he found it on google instead of working it out for himself.) His solution is a little hard to track… but correct none the less. If d =Diophantus's age at death….. the equation would, in fact, be: d/6+d/12+d/7+5+d/2+4=d which can be shown as d(1/6+1/12+1/7+1/2)+9=d Combining the fractions into a least common denominator gives :. d(14/84+7/84+12/84+42/84)+9 = d(75/84)+9=d Seeing as how the first part of the equation is 9 parts short of one… and we are adding 9 to it… it is fairly obvious that d must = 84. if you really wanted to work it out you would get 75d/84=d-9 => 75d=84d-9(84) => 9(84)=9d => d=84 Congrats Jkc73 @terry1966, I think where you went wrong is that people don't often count by months to get to the date of their marriage or birth of child, but certainly not their age at death.

your question + google = answer

something not quite right with your math Jkc73

Not my math

Though assuming it was correct, it found me the correct answer.

childhood: d/6
adolescence: d/12
bachelorhood: d/7
childless marriage: 5
age of child at death: d/2
life after child's death: 4

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

Edit: How did you slide that post above mine Tomk. your a magician
I did state I used Google.

Diophantus lived to be 84 years old.
You can check the answer if you like, by plugging "84" into the original problem. If he lived to be 84, then one-sixth of his life is 14 years, one-twelfth of his life is 7 years (so he'd be 21, and he certainly should have a beard by this age), one-seventh of his life is 12 years (so he didn't marry until he was 33 years old), his child was born when he was 38, the boy died at 42 (when Diophantus was 80), and then Diophantus died four years later.

if you see in my first post i couldn't get 84 to work out correctly with him only mourning 4 years, yes 84 is the common denominator for 6,7,12 but when i did the math it never worked out right. 84/6=14 84/12=7 84/7=12 so that's 33 plus the 5 years till his son was born that's 38 multiply by 2 for when his son dies that's 76(his son lived to only half his age at the time of his death is how i read the puzzle) plus 4 years mourning that's only 80 not the original 84.