[n00b lurker]

Ah haa... I think my error was in assuming that the reverses would be A,K,2,7 with no duplicates. (Sure, the faces we see are thus, but there's no guarantee that the reverses are, also.)

Thanks for your explanation! I think I've got a handle on the contrapositive now.

[e_nygma]

n00b lurker wrote:

No, look, I'm serious. If I turn over the 2 and the reverse is a K, then I know the reverse of the 7 must be A. Therefore the rule is false. If I turn over the 2 and the reverse is A, then I know the reverse of the 7 must be a K, and the rule is true. So why does the answer have to be 7? I've read up a bit on Wason, but I'm still in the dark here. Any insight appreciated, -N

*puts on his pedantic hat* No, different hat than

For a moment, let
p stand for "x is a triangle" and
q stand for "x is a polygon"

I can say "If x is a triangle, then x is a polygon" ("if p, then q"). This is called the statement.

I can also say "If x is NOT a polygon, then x is NOT a triangle." ("if not q, then not p"). This is called the contrapositive.

Note I cannot say "If x is a polygon, then x is a triangle" ("if q, then p" ... AKA the converse) or "If x is not a triangle, then x is not a polygon" ("if not p, then not q ... AKA the inverse). Both of these statements would be false by having x be a square.

Thus, if I have a statement, only its associated the contrapositive is necessarily true. The converse and inverse COULD be true, but they do not necessarily follow.

So what does all of this have to do with your question? Let's look at the card again:

"Each of these cards has a letter (A or K) on one side and a number (2 or 7) on the reverse. If I told you there was a rule stating that a card with A on one side will have a 2 on the reverse, which two cards would you turn over to find out if the rule was true."

Now, let
p stand for "card has an A on one side" and
q stand for "card has a 2 on the reverse."

Obviously, if p then q follows, because Tippy told us that rule exists. So, which of the other three do we have left? The contrapositive is all we know to be true. If not q, then not p. Or "If a card does not have 2 on the reverse, then the card does not an A on one side."

So, why not the 2? Remember, only the contrapositive follows from a statement. If we assume the 2 is the one to flip, we are asserting that "if q, then p" is true (the converse). We've shown that is not the case. Also, we want NOT q (not a 2). So, taking the 2 is out.

So, why not the K? The K would have a number on the other side, but we have been given no information as to what its associated number would be. It could be a 2 or a 7. We don't know because there was no rule given for it. This is the equivalent of saying "if not p, then not q" is true (the inverse), which does not necessarily hold. So, taking the K is out.

Therefore, you pick up the A to satisfy the statement, and the 7 to satisfy the contrapositive.

[n00b lurker]

No, look, I'm serious. If I turn over the 2 and the reverse is a K, then I know the reverse of the 7 must be A. Therefore the rule is false.

If I turn over the 2 and the reverse is A, then I know the reverse of the 7 must be a K, and the rule is true.

So why does the answer have to be 7? I've read up a bit on Wason, but I'm still in the dark here. Any insight appreciated, -N

[chichiri]

That seems to be a kurt card not a tippy, but good prediction.

no da

[Dysper]

Seej wrote:

Next Tippy card: Can you see the dalmatian in the snow?

Do I say something here..?

[Bahamoth]

... yeah, and Tippy is the poker queen after all... I imagine there is significance to that.

I'm quite happy with me right now for getting that right. I really thought about it though, and probably wouldn't have gotten it right had the card not warned that it wasn't as obvious as I would initially think.

Steaming in to logic questions never bodes well.

[cornflake]

Ah, thanks. That kind of helps...

[appleTRON]

cornflake wrote:

I'm wondering if the fact that there are four tiles here with letters and numbers relates to the fact that four thieves were involved in stealing the cube, and they were referred to by letters - "They addressed one another using code – names: Q, C, K and V."

I doubt it, cornflake ... but look at THIS!!!

[cornflake]

I'm wondering if the fact that there are four tiles here with letters and numbers relates to the fact that four thieves were involved in stealing the cube, and they were referred to by letters -

"They addressed one another using code – names: Q, C, K and V."

[Kalt]

It may be solved, but here are some closer shots of Illogical (Green pixel, lower left, #123) from the monitor at E3. This is for personal research and the Perplex City Card Catalog to document. As per usual, I'm trying my best to keep these within the rules of scans and such; I can tinker with the cropping if necessary, and do anything else I can to make this fun for everyone.

It was a lot of fun trying to transcribe from these ;p

I did not have access to the back of the card; this is the same fan of cards shown on the site, at a slightly better (I think) resolution due to the plasma monitors at E3.

So, for categorization purposes, it could either fit in a not-properly-released category, website specific, or an E3 category.

-Kalt


[EDIT: Added to second to last paragraph, added last paragraph.]

[Riiick]

If anyone still has any questions about this, it is an example of The Wason Selection Task. It is quite a famous psycology experiment (as suggested by the card), this site has some information about it. http://coglab.wadsworth.com/experiments/WasonSelection/

So the answer is definitely A + 7.

[Seej]

Leeravitz wrote:

.......We'll expect to be seeing optical illusions and those gestalt experiments about whether you can see the old woman or the young woman on Tippi's cards any time now

Next Tippy card: Can you see the dalmatian in the snow?

[Leeravitz]

Well, damn me for an idiot, but having spent quite a long time speculating on what the Academy Team's specialities are likely to be, I've just clicked. Presumably the 'hostess' depicted on this card is Tippi. So, does that mean her speciality is logic puzzles? Remember, in Tippi's profile, it says something about her revisiting famous puzzles of the past (or words to that effect). We know that this particular card is a version of a famous psychological experiment. So, is that it? We'll expect to be seeing optical illusions and those gestalt experiments about whether you can see the old woman or the young woman on Tippi's cards any time now

[Seej]

Just for the record (seeing as some people still aren't convinced), it's definitely the A and the 7. We had this figured out before we could even see what the 4 cards were.

[tanner]

surely its Perplex City Hold-Em