A Tombstone
On a tombstone:
One sixth of his life was spent in childhood
One twelfth as a teenager
One seventh of his life passed from becoming an adult 'til marriage
A son was born in five years
His son died four years before him
He lived twice as many years as his son
At what age did he die?
One sixth of his life was spent in childhood
One twelfth as a teenager
One seventh of his life passed from becoming an adult 'til marriage
A son was born in five years
His son died four years before him
He lived twice as many years as his son
At what age did he die?
posted by Zaux at
10:18 PM
11 Comments:
He is 84
14 years as a child, age 14
7 years as a teenager, age 21
12 years as adult to marriage, age 33
5 years later son is born, age 38
42 years with a son, age 80
Dies four years later, age 84
son is half his age 42.
Cam
S=1/2A
A=S+4+5+(1/6+1/7+1/12)*A
A=S+9+11/28*A
17/28*A-9=S
A=must be n*28 for s to be integer
for n=1 S is -v
for n=2 A=56 S=34-9=25. But 25!=0.5*56
for n=3 A=84 S=51-9=42. 42=0.5*84
Thus A=84 s=42
Cam
Eesh, missed something obvious before
S=1/2A
A=S+4+5+(1/6+1/7+1/12)*A
A=S+9+11/28*A
17/28*A-9=S
17/28*A-9=1/2*A
3/28*A=9
A=9*28/3
A=84
Cam
I see to have approached this from the wrong angle, and come up with the right answer...?
I just assumed that teenage years were from 13-19 - 7yrs in total - 1/12th of his life = 84yrs, and then the rest slotted in.
Surely, if he lives 1/12 of his life as a teenager, there are only 7 teenage years so 7 x 12 =84
regards, Curtis
I noticed that(1/12*A=7 A=12*7=84) before, but decided to check using the method I detailed above in case 18+19 were exclude as they may have been excluded for being part of the adult years.
The troubling thing is it yields:
14 years as a child, age 14
7 years as a teenager, 14+7=21
14 to 21 as teenage years doesn't quite seem right, yet the solution it yields is the same. Possibly fortuitous. If it yielded different solutions I was going to post both, but as it yield only one I posted the one(s) I did above.
Cam
And the name on the tombstone was Diophantus.
Interesting.....
I misread/remembered the 1st line as 1/7
I took each line as a clue, not as part of a sum.
with assumptions that ages may be different "accross the pond"
I considered that childhood was 1-12 (1/7)
teenage years 13-19 (1/12)
and that adulthood started at 21
perhaps I assume too much, lol
regards, Curtis
obviously 84 is the correct age ... Karl, you did it very cleverly with only a single clue
sorry Curtis .. I missed that you also solve it it with one clue.
but the most incredible thing is that Chris determined the name on the tombstone from the arithmetic clues ... :D
The original wording used "youth", not "teenager".
I knew it was Diophantus, because I'd seen the riddle a few weeks ago.
Diophantus is the chap whose lent his name to Diophantine equations - equations that are in the domain of the integers only. He is somtimes referred to as "the father of algebra". So now you know who to blame for all tha that math you have to do at school.
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