Portia of Belmont has inherited a huge amount of gold from her father. Being unmarried, young, and fair, she is suddenly surrounded by suitors. Being a crafty and artful woman, she decides to perform a test to choose her husband, against the will of her deceased father.

She made two caskets of gold and silver, and put her own portrait in one of them, and fixed a note on each of the caskets.

Gold Casket
This casket does not contain a portrait.

Silver Casket
Of the two statements on these caskets, only one is true.

Which casket should a suitor choose, to gain Portia's hand in marriage? If there isn't a portrait inside when he opens the casket, he doesn't get to marry her. He can only make a single choice.

Please provide a complete solution when answering, please. Partial points will not be awarded.

If nobody comes up with the correct answer within 24 hours, I'll explain the answer. If you've solved this before, or if you are certain what the answer is, please refrain from posting.

If nobody at Hydrogenaudio can answer correctly, I'll be mightily disappointed.

edit: 24 hours, not 24 days. Doh.

I don't know if I understood it correctly. Anyways, I think that if he chooses the gold casket, she can see that the man is actually after the money.

There's no distracting lead casket here. That silver casket would be worth a lot of money too.

I don't know if I understood it correctly too.

To reveal the conjunction of both statements, the first one has to be false and the potrait has to be in the gold casket. Otherwise the first and the second statement is true, which will lead to a paradoxon.

Possible solution (I hope), so don't read on if you still want to think about it.

I think he should open the Gold Casket. Reasoning as follows:

If the statement on the Silver Casket is true then the statement on the Gold Casket must be false, for if it were true then either two statements would be true, leading to a contradiction, or only the statement on the Gold Casket would be true, also leading to a contradiction. So if the statement on the Silver Casket is true the portrait must be in the Gold Casket.

If the statement on the Silver Casket is false then either both statements or true or both statements are false. If both statements are true that would result in a contradiction, so that can't be the case. If both statements are false the statement on the Gold Casket is false and the portrait must therefor be in the Gold Casket.

Sorry, no partial points. Those solutions would be incomplete ones, I'm afraid.

where did she get the silver casket from? she only inherited gold...

so as she cant have created a silver casket (at least not from the heritage) and hence there is none, the gold casket would be the only logical choice... or am i missing the point?

She could have bought the silver with a part of the gold.

Which casket to open... I guess the gold one.
There are two statements, which means four possibilities...
1. Both false. To make the first statement false, the picture can't be in the silver casket, so it must be in the gold one. To make the second statement false, both must be true or false at the same time (assuming "only one is true" means "exactly one is true"), which is the case this time.
2. Both true. Impossible, because it'd make the second statement false, which is a paradoxon.
3. Only the first statement is true. Impossible again, because if only one statement is true, the second one becomes true -> paradoxon.
4. Only the second one is true. Only the second one being true means the second one being true, so this combination works. To make the first statement false, the picture has to be in the gold casket.
2 and 3 are both impossible, 1 and 4 have the same result, so the bottom line is: the gold casket.

...I guess my solution is practically the same as Jasper's. I thought it was different when I started writing it. I guess I'm no good as a logician.

Actually, I'd say you're closer to the answer than Jasper is, but there's still something missing: something crucial.

Let's see...I suppose the portrait is in the silver casket:
If only one of the statements is true, then the Gold casket's statement ("This casket does not contain a portrait") must be true, as the Silver casket's ("Of the two statements on these caskets, only one is true.") points to the Gold casket's statement.
That is, there is no "second statement", as they both act as one.

Jasper and Ruby are right, assuming that she actually puts the portrait in the casket the notes point to. However, she can really put the portrait wherever the hell she wants to; if it weren't explicitly stated in the riddle that she put the portrait in a casket, I'd say she taped it to the underside of a table or something. Since it isn't too hard to deduce the gold one from the clues and since she probably wouldn't want to just take the first guy who came in, I'm going to say she put the portrait in the silver casket to trip everyone up.

Sorry if I'm going beyond the bounds of the riddle here .

[edit]: Just noticed that it never says she has to marry the person who picks the right casket. There goes my argument :/

bleh: nope, your argument is sound, regardless of whether she actually will marry anyone. I only asked "what should the suitor do?"

.. and "she can really put the portrait wherever the hell she wants to" is the answer that I was waiting for. (In other words, this riddle can't be solved by logic, because not enough assumptions were given.)

Congratulations!

Logic is a way of ariving at conclusions, where the conclusion can't be wrong if all the assumptions are true. I posted this riddle to emphasize how important a little skepticism or a leave-no-stones-unturned attitude can be.

edit: I'm suffering from sleep-deprivation right now, so this post might not make sense.