Critical Thinking is important!

*Sigh* In an otherwise FANTASTIC book (The Tipping Point by Malcolm Gladwell) there was a brainteaser to show that people are not naturally good at logic, critical thinking, and all that.

Unfortunately, I think that his answer is flawed! Of all things, in an example to show that peopel don’t know logic, to mess it up yourself is embarassing. In my debates and arguments with everyone, Christians, non-Christians, I always try to be logically sound in my reasoning. 

Here’s the teaser, I’ll post my answer and reasoning after I get at least a few trys.

Consider the following brain teaser. Suppose I give you 4 cards labeled with the letters A and D and the numerals 3 and 6.  The rule of the game is that a card with a vowel on it always has an even number on the other side. Which of the cards would you have to turn over to prove this rule to be true?

what do you say the answer is?  and why?  Leave you answer before reading on…

***************EDIT**************

All right, so the guy in the book writes the answer as: A and 3.  He says, usually people say, just A or A and 6.

My answer is that you have to check A, D and 3.

The form of the brainteaser is as follows:

If P, then Q.

Where, P = Card has a vowel on one side, and Q = Card has an even number on the other.

The two cases that you need to check are then, the case when P is true, and the case when Q is false.

This is because the ONLY thing that shows that this rule is false is when the set-up is exactly:

P ^ ~Q   ( "P" and "not Q" ).  Since this is the only case, it does not matter if you have either a ~P or a Q at all, that doesn’t tell us anything about the rule.

"P" is true if any vowel is on the one side, and "not Q" is true if there is NOT an even number on the other side.  Not an even number means that anything counts – a picture of a cow, or the letter D is "not Q."

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Hmm, I’m trying to think about it, but it’s 2 am..hmm. If you turn over the obvious (A) then you can’t prove that it was the A that you turned over because all you’d see is the 6 and then D. I’d go with the opposite, turn over the D and then see the three, hold it so you can see both at the same time and then, poof you have you’d have the proof. wow, sorry if that made no sense…LOL HAGD!

June 5, 2005

whoa there, you have 4 cards, and you can see each one is labeled with one of the following “A” “D” “3” “6” – and you cannot see the other side of those 4 cards. Which do you turn over to prove the rule true?

Oh, duh, I’m retarded. Ugh, need sleep, good one, though, I’ll think about it, harder…lol… Dumb me, now I feel stupid, ha ha.

June 5, 2005

Of those four cards and given that you can only turn one over, the A is the only one that speaks to the rule. Constenents aren’t proihibited from having even numbers. Seeing how it’s not a stated rule that you can only turn one over, though, turn them all over and the rest of the cards in the deck.

June 5, 2005

We can’t prove it, you only gave me two cards. If you gave me forty cards, maybe we could figure it out. I dont think the real problem is which to turn over, I think the problem is that I dont have enough evidence. Aaaand… like an aobve noter, it’s two in the morning.

June 5, 2005

If four cards is all there is to the deck, you’d have to turn over the A and the three. And I disagree with the above noter. In a game such as chess or spades the rules apply only to the context of the game, for instance you can’t not play spades because 52 cards don’t give you enough evidence, nor can you play pinnocle with a spades deck. In the context of the game all the evidence you need

June 5, 2005

Is available. If the question is asking is the rule universally true for every card available it’s not really a game so much as a set up. e.g. the rules of twister state that you need to do what the spinner says while playing the game, you aren’t expected to do what it says outside the confines of the game.

June 5, 2005

haredawg’s right as far as the confines of the game. 1. You are allowed to turn over more than one card. 2. The point is which cards to flip that are necessary to prove the rule? 3. You are considering only these 4 cards that are in front of you, don’t worry about any other cards.

June 5, 2005

Sorry, here’s the why to adding the three into the proof. If there is a vowel on the other side the rule is wrong. It doesn’t matter whats on the other side of the D and Six, because, again, constenents aren’t prohibited from having even numbers nor even limited to numbers, they can, by the singular rule, have pictures of cows or the number six on them.

June 6, 2005

ahh…confirmation bias.

June 6, 2005

Turn over the A, D, and 3. If there’s a vowel on the other side of either the D or 3, the rule is wrong. If there’s not an odd number on the other side of the A, the rule is wrong. Who cares what’s on the other side of the 6, it wouldn’t disprove the rule either way, if it’s a vowel the rule is supported, if it’s not a vowel, it doesn’t relate to the rule.

June 6, 2005

^– Should be “if there’s not an *even* number on the other side of the A…”

June 6, 2005

I thought about adding D but I also thought about the assumption inherent in the question and the same assumption I believe the author made, that all cards had a letter on one side and a number on the other. I mentioned a picture of a cow to suggest the assumption is necessaryily made. But, like a test in school, one anticipates the authors assumptions and discusses the fallacys after the test.

June 6, 2005

^^^ That should be tghe assumption is not neccessarily made.

June 6, 2005

Jesus my keyboard is possessed. Too many ashes and scotch.

June 6, 2005

“I also thought about the assumption inherent in the question and the same assumption I believe the author made, that all cards had a letter on one side and a number on the other.” It’s ok to assume something, I think, but you have to state your assumptions, which the author didn’t do. Otherwise, you could assume so many things that the answer is completely different.

You’re right. I didn’t get it until I read. My thinking was off. Apparently, I’m not as logical as I’d like to think some days. 😉

June 6, 2005

“the same assumption I believe the author made, that all cards had a letter on one side and a number on the other.” I think that the author may have even had that stipulation written in, but it may have been edited out.

June 6, 2005

With that stipulation then there is no need to flip the D.

June 6, 2005

Without that stipulation, given anything including nothing be on the back of that D, the probablity of it being a vowel is incredibly low, lower than it being a sign of the zodiac, a poem by Dylan Thomas, a picture from Audobons book. But seeing how there isn’t a stipulation on how many cards you can flip over it’s not really much of a problem — flip everything including the unecessary 6.

June 6, 2005

My answer of the A and 3 given you can flip more than one card is an indictment of the public school system which teaches you how to test and not imagine cows or vowels where numbers should be.

June 6, 2005

I posted a similar puzzle 04/19/2001: http://www.opendiary.com/entryview.asp?authorcode=A219369&entry=10122&mode=date His answer would be correct given the additional condition that you know for a fact that there’s always a letter on one side and a number on the other. In other words, if it’s not possible for D to have a vowel on the other side then D does not need to be checked.

June 6, 2005

That was given as a condition in the puzzle I posted – it makes me wonder whether or not the author meant to include it as well.

June 7, 2005

On a related topic, I read The Tipping Point at Seminary. I’m not sure how you feel about the book being employed that way, but I enjoyed it.

June 7, 2005

“I read The Tipping Point at Seminary. I’m not sure how you feel about the book being employed that way, but I enjoyed it.” I understand how and why it would be a tempting book to use in seminary.

June 7, 2005

If the assumption is that each card has a letter on one side and a number on the other flipping D does absolutely nothing.

June 7, 2005

oh oops.. already been said multiple times.