Mid-week Mindbenders...

Another trip-down-memory lane with this old mind-bender about a few cards, that I’ve posted before and copied verbatim from Futility Closet:

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Given these premises, what can you infer?

1. If there is a king in the hand then there is an ace, or if there isn’t a king in the hand then there is an ace, but not both.
2. There is a king in the hand.

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What is your answer???

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Now, go read the Futility Closet post:

https://www.futilitycloset.com/2016/09/07/a-cognitive-illusion/

As you will see, the post claims that “almost no one sees” the correct answer, and "practically everyone" infers (wrongly, with "cognitive illusion"... "but not both," being the key phrase) instead that “there is an ace in the hand.” I think the correct answer (that you can’t infer anything) may be more obvious to word mavens or to mathematicians (given their familiarity with logic and conditionals), but I don’t know for sure. Again it’s an example of the ambiguity of verbal cues misleading people... language is rarely as precisely interpretable as individuals assume it to be. Indeed, Gödel used to say that it was almost inexplicable that humans could converse effectively with one another at all given how ambiguous most words are.

Reminds me a bit of a lovely old classic math conundrum that throws most people off (if not familiar with it), which in one version (from Wikipedia) runs like this:

"Three people check into a hotel room. The clerk says the bill is $30, so each guest pays $10. Later the clerk realizes the bill should only be $25. To rectify this, he gives the bellhop $5 to return to the guests. On the way to the room, the bellhop realizes that he cannot divide the money equally. As the guests didn't know the total of the revised bill, the bellhop decides to just give each guest $1 and keep $2 as a tip for himself. Each guest got $1 back, so now each guest only paid $9, bringing the total paid to $27. The bellhop has $2. And $27 + $2 = $29 so, if the guests originally handed over $30, what happened to the remaining $1?"