## AK47 CARD PROBLEM - REALLY IMPORTANT

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Skeedish
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### AK47 CARD PROBLEM - REALLY IMPORTANT

There are four cards on a table, each with a symbol on them:

|A| |K| |4| |7|

Theory: If a card has a vowel on one side, then it has an even number on the other side.

How many cards must you flip over to prove this theory?

----------

My philosophy lecturer (Marius Vermaak) told us that the human brain "Is not equipped to solve this problem" so the reward for anyone who solves it before tomorrow morning is a six pack of any drink requested.

Please can anyone help me solve this? Its really important . . .

chickenwire
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### Re: AK47 CARD PROBLEM - REALLY IMPORTANT

Unless the theory refers to all cards, not just the ones on the table...

Spoiler:
Three cards. The one with the vowel (A), and the ones with characters that aren't even numbers (7 and K).

Hi. I'm new here. And I've read the rules.

willport3
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Joined: Wed Apr 16, 2008 10:14 pm UTC

### Re: AK47 CARD PROBLEM - REALLY IMPORTANT

Spoiler:
Only the A and 7. The clause says that any vowel has an even number. You have to flip over the A to make sure the number on back is even, and turn over the 7 to make sure it does not have a vowel on back. The clause does not say that all even numbers have vowels, therefore you do not have to look at the back of the 4.

Cauchy
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### Re: AK47 CARD PROBLEM - REALLY IMPORTANT

Did the "don't do people's homework for them" rule get revoked while I wasn't looking?
(∫|p|2)(∫|q|2) ≥ (∫|pq|)2
Thanks, skeptical scientist, for knowing symbols and giving them to me.

quintopia
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### Re: AK47 CARD PROBLEM - REALLY IMPORTANT

Let's rephrase the problem and see if we can make it easier why don't we?

Theory: If a person is under age 21, then he won't be drinking alcohol.

|16-year-old| |30-year-old| |diet coke| |gin and tonic|

how many people/drinks must you check in order to make sure the theory (that no one is breaking the law) holds?

Cheater Detection is an important evolved skill. This is an exactly equivalent problem, which the brain, for some reason, is equipped to solve. For further discussion of the Wason task, see http://www.rotman.utoronto.ca/~evans/evol/altruis2.htm

Moonbeam
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### Re: AK47 CARD PROBLEM - REALLY IMPORTANT

Bah, beaten to it by quintopia

Something similar has been posted before: viewtopic.php?f=3&t=247 (look at the 3rd post down)

baf
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### Re: AK47 CARD PROBLEM - REALLY IMPORTANT

If the problem as stated is all that you've been told, then the answer he's probably expecting is wrong. He's probably leaving out the implicit premise that every card has a letter on one side and a number on the other. Don't let him get away with that.

Also, saying "the human brain is not equipped to solve this problem" seems a bit strong. Granted, a lot of people get this sort of question wrong the first time they hear it, but then, most people fall down the first time they try to walk. Does this mean that humans aren't equipped for walking?

baf
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### Re: AK47 CARD PROBLEM - REALLY IMPORTANT

To elaborate on that first point, I'm imagining a conversation something like this:

Him: ...So you see, you only have to turn over the A, to see if it has an even number on the other side, and the 7, to see if it has a vowel on the other side!
You: What about the K? Shouldn't you flip that over to see if it has a vowel on the other side?
Him: No, every card has a number on one side and a letter on the other.
You: Ah, that would be a useful lemma! But to prove it, I'd need to flip over all four cards, so I think we're better off without it.

quintopia
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### Re: AK47 CARD PROBLEM - REALLY IMPORTANT

baf wrote:Also, saying "the human brain is not equipped to solve this problem" seems a bit strong. Granted, a lot of people get this sort of question wrong the first time they hear it, but then, most people fall down the first time they try to walk. Does this mean that humans aren't equipped for walking?

It's just a bad way of saying that the brain doesn't have a built-in device for quickly answering these kinds of problems, and our full powers of reason must be turned to it to answer it, whereas the equivalent Cheater Detection problem has a specialized system for solving it without much conscious thought at all. Of course, this is all very theoretical and debatable, but this is probably what the instructor meant.

fyjham
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### Re: AK47 CARD PROBLEM - REALLY IMPORTANT

Spoiler:
Ok, first off I'm going to assume any card can have anything on the other side (And I mean anything, there could be a drawing of a turtle on the other side for all that's told).

Simply looking it looks like you need to check the other side of the A and make sure it's odd would seem valid. But then you have to consider, which cards could break the rule by having a vowel on the other side. The K and the 7 would, because they're not even, so we need to flip those and make sure they don't have a vowel (because if they do it breaks the rule). The 4 it doesn't matter, if it's a vowel it obeys the rule, if it's not a vowel the rule doesn't say it's only with vowels that you get odd numbers so it still satisfies the rule. I suspect your professor expects you to say you need to flip the A.

Skeedish
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### Re: AK47 CARD PROBLEM - REALLY IMPORTANT

- The answer is 2: A and 7

Thanks millions to the people who gave their input to the problem - I won the six pack XD

Puck
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### Re: AK47 CARD PROBLEM - REALLY IMPORTANT

Actually, no.

The answer to the problem as you stated it in your original post is 3, since you didn't pose the restriction that all cards have a number on one side and a letter on the other side. Therefore, you would have to check to see if the K card has an A on the other side, which would disprove the statement. Just like baf said.
22/7 wrote:If I could have an alternate horn that would yell "If you use your turn signal, I'll let you in" loud enough to hear inside another car, I would pay nearly any amount of money for it.

chickenwire
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### Re: AK47 CARD PROBLEM - REALLY IMPORTANT

So, in conclusion, three cards, like I originally said.

Poorly worded questions make me think of first grade.
My teacher quizzed us on "fact vs. opinion".
If on the quiz, like me, you were asked to categorize these statements as 'fact' or 'opinion', what would you say?

"Sally's favorite color is pink."
"Trees are tall."

I would get mad and answer the way the teacher intended them to be answered, just so I wouldn't flunk... as opinion and fact, respectively. Which is just outright WRONG.

Puck
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### Re: AK47 CARD PROBLEM - REALLY IMPORTANT

chickenwire wrote:So, in conclusion, three cards, like I originally said.

Poorly worded questions make me think of first grade.
My teacher quizzed us on "fact vs. opinion".
If on the quiz, like me, you were asked to categorize these statements as 'fact' or 'opinion', what would you say?

"Sally's favorite color is pink."
"Trees are tall."

I would get mad and answer the way the teacher intended them to be answered, just so I wouldn't flunk... as opinion and fact, respectively. Which is just outright WRONG.

Wow. That's just horrible.
22/7 wrote:If I could have an alternate horn that would yell "If you use your turn signal, I'll let you in" loud enough to hear inside another car, I would pay nearly any amount of money for it.

quintopia
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### Re: AK47 CARD PROBLEM - REALLY IMPORTANT

In first grade, I totally would have answered the other way around. I failed some sort of IQ test in kindergarten because the questions were so easy I answered them wrong just to be funny. . .i thought it was just a silly, unimportant game.

DYRE
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### Re: AK47 CARD PROBLEM - REALLY IMPORTANT

Yeah, the answer to that is definately fact, then opinion.
I really hate questions of that sort.

Kaiyas
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### Re: AK47 CARD PROBLEM - REALLY IMPORTANT

Oh god. I did F/O in sixth grade. Which is how I learned how history is not a good class to bring up philosophical arguments.
clintonius wrote:This place is like mental masturbation

AvalonXQ
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### Re: AK47 CARD PROBLEM - REALLY IMPORTANT

My favorite wrong-answer question from school was:
"True or False: Everything is made of matter."

4=5
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### Re: AK47 CARD PROBLEM - REALLY IMPORTANT

(watch saint seya then you'll understand)

AvalonXQ
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### Re: AK47 CARD PROBLEM - REALLY IMPORTANT

I wrote "false", and got it backed marked wrong.
I took it to the teacher. She asked, "Okay, name something that's NOT made of atoms".
I responded, "Light, heat, sound. Basically, things made of energy" (not technically correct, but okay for a sixth grader).
She said, "Did you read the chapter of the book the test was based on?"
"No," I replied honestly.
She smiled. "Let's look at it, shall we?"
On the first page of the assigned reading, it said: "Everything is made of matter".
She had said the test was based on that chapter of the science book.
I took my reduced score and learned my first lesson about standardized education: It's about what you're taught, not about what's actually true.

quintopia
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### Re: AK47 CARD PROBLEM - REALLY IMPORTANT

a better answer would have been "your name" or "oliver twist" or "the fifth symphony"

M.qrius
Rainbow Brite
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### Re: AK47 CARD PROBLEM - REALLY IMPORTANT

AvalonXQ wrote:I wrote "false", and got it backed marked wrong.
I took it to the teacher. She asked, "Okay, name something that's NOT made of atoms".
I responded, "Light, heat, sound. Basically, things made of energy" (not technically correct, but okay for a sixth grader).
She said, "Did you read the chapter of the book the test was based on?"
"No," I replied honestly.
She smiled. "Let's look at it, shall we?"
On the first page of the assigned reading, it said: "Everything is made of matter".
She had said the test was based on that chapter of the science book.
I took my reduced score and learned my first lesson about standardized education: It's about what you're taught, not about what's actually true.

I so would have made a huge point of this. Screw the book. Screw the chapter. The answer to the question was right.

AvalonXQ
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### Re: AK47 CARD PROBLEM - REALLY IMPORTANT

M.qrius wrote:I so would have made a huge point of this. Screw the book. Screw the chapter. The answer to the question was right.

I'm not sure I honestly agree. I mean, that's getting into really philosophical issues about objective right and wrong, the meaning of words, and all sorts of things.
It seems to me (more now than then, actually), that it's quite reasonable to say, "Here's a chapter in a book. At the end of the week, I'm going to test you on the material in the chapter." Then, when tested, you're expected to give answers which match the chapter the test is on.

M.qrius
Rainbow Brite
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### Re: AK47 CARD PROBLEM - REALLY IMPORTANT

AvalonXQ wrote:
M.qrius wrote:I so would have made a huge point of this. Screw the book. Screw the chapter. The answer to the question was right.

I'm not sure I honestly agree. I mean, that's getting into really philosophical issues about objective right and wrong, the meaning of words, and all sorts of things.
It seems to me (more now than then, actually), that it's quite reasonable to say, "Here's a chapter in a book. At the end of the week, I'm going to test you on the material in the chapter." Then, when tested, you're expected to give answers which match the chapter the test is on.

I think it's more important to know what information is in the book than to literally be able to copy every sentence. Of course, this is hard to test with a written standardized test, and in the example the person hadn't actually read the chapter... so my argument isn't that strong.

BeetlesBane
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### Re: AK47 CARD PROBLEM - REALLY IMPORTANT

From the OP
My philosophy lecturer (Marius Vermaak) told us that the human brain "Is not equipped to solve this problem"...

The lecturer was probably rephrasing this "Wason and Johnson-Laird gave this test to 128 University-educated adults. The most common answer given was "A and 4," by 59 students (46%), with "A" being a close second (42, or 33%). Only 5% gave the proper answer," from the Wason's Four-card link.

4=5
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### Re: AK47 CARD PROBLEM - REALLY IMPORTANT

wow that was amazing, with this one I had to logic it out, with the bar one the answer instantly popped right into my head.

Patashu
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### Re: AK47 CARD PROBLEM - REALLY IMPORTANT

Spoiler:
We are trying to prove that 'If a card has a vowel on one side, then it has an even number on the other side.'

A:
If on the back of A there is not an even number then the theorem is disproven, therefore we must check.
K:
If on the back of K there is an even number then the theorem is disproven, therefore we must check.
4:
This is the pincher.You do not need to check on the back of 4; if it is a vowel then the theorem holds, if it is anything else then the theorem still holds since the theorem asserts that vowel -> even not vice versa, that is even -> vowel.
7: If on the back of 7 there is a vowel then the theorem is disproven, therefore we must check.

So, 3 cards must be flipped to prove this theorem: A, K, 7

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### Re: AK47 CARD PROBLEM - REALLY IMPORTANT

Patashu wrote:
Spoiler:
We are trying to prove that 'If a card has a vowel on one side, then it has an even number on the other side.'

A:
If on the back of A there is not an even number then the theorem is disproven, therefore we must check.
K:
If on the back of K there is an even number then the theorem is disproven, therefore we must check.
4:
This is the pincher.You do not need to check on the back of 4; if it is a vowel then the theorem holds, if it is anything else then the theorem still holds since the theorem asserts that vowel -> even not vice versa, that is even -> vowel.
7: If on the back of 7 there is a vowel then the theorem is disproven, therefore we must check.

So, 3 cards must be flipped to prove this theorem: A, K, 7

Spoiler:
Actually there wouldn't be a problem if K had an even number on the reverse. The problem would be if there was a vowel on the other side.

We're proving two statements:
1. If a card has a vowel on one side, then it has an even number on the reverse.
2. If a card does not have an even number, then it does not have a vowel on the reverse.
since the two are equivalent.

• A -- Since A is a vowel, we have to check it to ensure that the reverse has an even number.
• K -- Since K is not a vowel, we don't have to worry about statement 1. However, K is not an even number, so we have to check it for the validity of statement 2.
• 4 -- 4 is not a vowel and 4 is not not (ie is) an even number, so both antecedents are false, and hence the implications are true. No need to check.
• 7 -- 7 is not a vowel, but is not an even number so, 7 must be checked against statement 2.

Patashu
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### Re: AK47 CARD PROBLEM - REALLY IMPORTANT

Patashu wrote:
Spoiler:
We are trying to prove that 'If a card has a vowel on one side, then it has an even number on the other side.'

A:
If on the back of A there is not an even number then the theorem is disproven, therefore we must check.
K:
If on the back of K there is an even number then the theorem is disproven, therefore we must check.
4:
This is the pincher.You do not need to check on the back of 4; if it is a vowel then the theorem holds, if it is anything else then the theorem still holds since the theorem asserts that vowel -> even not vice versa, that is even -> vowel.
7: If on the back of 7 there is a vowel then the theorem is disproven, therefore we must check.

So, 3 cards must be flipped to prove this theorem: A, K, 7

Spoiler:
Actually there wouldn't be a problem if K had an even number on the reverse. The problem would be if there was a vowel on the other side.

We're proving two statements:
1. If a card has a vowel on one side, then it has an even number on the reverse.
2. If a card does not have an even number, then it does not have a vowel on the reverse.
since the two are equivalent.

• A -- Since A is a vowel, we have to check it to ensure that the reverse has an even number.
• K -- Since K is not a vowel, we don't have to worry about statement 1. However, K is not an even number, so we have to check it for the validity of statement 2.
• 4 -- 4 is not a vowel and 4 is not not (ie is) an even number, so both antecedents are false, and hence the implications are true. No need to check.
• 7 -- 7 is not a vowel, but is not an even number so, 7 must be checked against statement 2.

That's what I meant, sorry.

And thanks, whoever spoilered my post.