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The curiosity of the easy riddle of Portia’s three urns, posed final week, lies in the truth that it’s a type of issues which are solved instantly if we belief within the assertion. If the portrait have been within the silver urn, all three statements (which are literally two) could be false, and if it have been within the lead urn, all three could be true, so we will conclude, by elimination, that the portrait is within the golden urn, with out bothering to verify whether or not the situations of the issue are met in that case. But we should keep in mind that, when reasoning on this means, we don’t contemplate the likelihood that the assertion is incoherent (which is extraordinarily unlikely in a ebook by Raymond Smullyan, however not so unlikely in different circumstances).

The most placing instance that I do know of the sort of downside is the next, a traditional analyzed on the time by Martin Gardner and which, if I keep in mind accurately, already appeared years in the past in one other installment of The Science Game:

The cylindrical gap of a spherical gold bead (the well-known little tube that perforates it diametrically to have the ability to string it) measures 6 millimeters in size. How a lot does the bead weigh? (Well no, there isn’t a lacking information, except you do not know that the density of gold is nineteen.3).

As for the quadruple downside of the inexperienced ball, nobody has but proposed an answer, and Bretos Bursó feedback that ChatGPT has not been capable of remedy it. The problem stays, due to this fact, pending, each for pure and synthetic intelligences.

The mocked suitor

Returning to the urns of Portia, here’s a final (within the sense that it might be thought of definitive) riddle, apparently quite simple, however which hides a depraved entice:

Portia subjected her final suitor to a check that appeared simpler than the earlier ones: there have been solely two urns, considered one of gold and the opposite of silver, and he or she advised him that in considered one of them was his portrait. On the gold urn there was an indication that mentioned: “The portrait is not here,” and on the signal on the silver urn it mentioned: “One and only one of these two statements is true.”

The suitor (and maybe you too, naive reader) reasoned as follows: “If the assertion in regards to the silver urn is true, and because it says that solely one of many statements is true, the assertion in regards to the gold urn has of being false. And if the assertion on the silver urn is fake, the gold urn should even be false, in any other case there could be one true and one false. So, whether or not the assertion in regards to the silver urn is true or false, the assertion in regards to the gold urn have to be false, and because it says that the portrait isn’t there, it have to be there.

The suitor opened the golden urn very glad and noticed that it was empty.

―You have fooled me, there isn’t a portrait within the urns! -he exclaimed indignantly.

And by the use of reply, Portia laughingly opened the silver urn, and there was her portrait.

Where is the fault within the apparently impeccable reasoning of the mocked suitor?