October 12, 2009

The Statue of Pallas Athene

According to a puzzle book published in the Middle Ages, the statue of the goddess Pallas Athene was inscribed with the following information:

“I, Pallas, am made from the purest gold, donated by five generous poets. Kariseus gave half; Thespian an eighth. Solon gave one-tenth; Themison gave one-twentieth. And the remaining nine talents’ worth of gold was provided by the good Aristodokos.”

How much did the statue cost in total? [A talent is a unit of weight, roughly one kilogram.]

8 comments by 4 or more people

1. Steven Jones

It was a donation, so didn’t cost anything to anyone other than poets. But it was made from about 40 talents of gold, which I’ve no idea how much that was worth in the middle ages. Also a talent is not roughly one kilogram according to my [wiki] sources.

12 Oct 2009, 12:33

2. Peter Dunn

Ah pedantry so useful for generating blog posts but not for solving the intended fun maths problem

If you do actually want to solve the maths problem though just assume the good Professor said “How much did the statue cost in total in terms total number of talents of gold donated at that time”.

Peter Dunn

12 Oct 2009, 12:42

3. Steven Jones

Ah okay, cost to the poets. Fair enough.

Pedantry! He is a mathematician, he should expect pedantry!

12 Oct 2009, 12:46

4. Iain Wallace

Agree with Steven, 40 talents but the question doesn’t seem to make sense. Wolfram Alpha reckons it would be worth £25.73M though http://www.wolframalpha.com/input/?i=40+talents+of+gold

Also, the ?hideComments option doesn’t do anything to the page if you forbid javascript by default :/

12 Oct 2009, 12:46

5. Mathew Mannion

Also, the ?hideComments option doesn’t do anything to the page if you forbid javascript by default :/

Well, it’s just a bit of Javascript to complement the existing system, which doesn’t actually have the capability to hide comments when linking to an individual entry. Progressive enhancement :)

The pedantry of the comments on this blog never ceases to amuse me…

12 Oct 2009, 18:23

6. Iain Wallace

Pedant mathematicians? Surely not!

12 Oct 2009, 20:02

7. Alison Kakoura

40 talents

13 Oct 2009, 14:14

8. Eleanor Lovell

Thanks for all the comments… even the pedants ; ) As a few of you calculated, the statue contained 40 talents of gold.

The four fractions add up to give
$\frac{1}{2} + \frac{1}{8} + \frac{1}{10} + \frac{1}{20} = \frac{20+5+4+2}{40} = \frac{31}{40}$

so what’s left is $\frac{9}{40}$

Since this requires 9 talents, the total must have been 40 talents.

13 Oct 2009, 14:35

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