Today I saw Diophantus' Epitaph. For those of you who don't know it and don't feel like googling:
'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.'Stated in prose, the poem says that Diophantus's youth lasts 1/6 of
his life. He grew a beard after 1/12 more of his life. After 1/7 more
of his life, Diophantus married. Five years later, he had a son. The
son lived exactly half as long as his father, and Diophantus died just
four years after his son's death.
From the WolframAlpha blog. Now, when I see this, here's the equation I come up with, where x is Diophantus' lifespan:
$$\dfrac{x}{6} + \dfrac{x}{12} + \dfrac{x}{7} + 5 + \dfrac{x-4}{2} + 4 = x$$
The only part I'm not certain about is $\dfrac{x-4}{2}$. Basically, I reasoned that in order for his son to reach half his age, his age has to double. However, he lives 4 years after his age doubles, so we go with that to avoid doubling the 4 extra years. The problem is, solving this gets me $x=65.333..$. According to the WolframAlpha blog (and a question on here), he was 84 when he died. However, here's the strange part. I haven't worked it out myself the way both WolframAlpha and the question did, but WolframAlpha's blog says
"Solving this simultaneously gives S=42 as the age of the son and D=84 as the age of Diophantus."
Now, I don't claim to be great at math, but I'm pretty sure that doesn't work out. 2 * 42 is definitely 84, and the riddle states that Diophantus waits 4 years after reaching double his son's age to commit suicide. I know the people at WolframAlpha (and on here :)) are much smarter than me, so I assume I both set up my equation wrong and am somehow missing how their approach is solving the problem. Can anyone set me straight?
Best Answer
$$\frac{x}{6}+\frac{x}{12}+\frac{x}{7}+5+\frac{x}{2}+4=x.$$ So $\frac{3}{28}x=9$.