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Which cards do you minimally need to turn around?
None 0%  0%  [ 0 ]
1 4%  4%  [ 1 ]
2 0%  0%  [ 0 ]
3 4%  4%  [ 1 ]
4 0%  0%  [ 0 ]
1, 2 0%  0%  [ 0 ]
1, 3 4%  4%  [ 1 ]
1, 4 0%  0%  [ 0 ]
2, 3 63%  63%  [ 15 ]
2, 4 4%  4%  [ 1 ]
3, 4 4%  4%  [ 1 ]
1, 2, 3 4%  4%  [ 1 ]
1, 2, 4 0%  0%  [ 0 ]
1, 3, 4 0%  0%  [ 0 ]
2, 3, 4 8%  8%  [ 2 ]
1, 2, 3, 4 4%  4%  [ 1 ]
Total votes : 24
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 Post subject: 4 cards problem
PostPosted: Mon Jan 23, 2012 11:04 am 
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Joined: Fri Feb 08, 2008 1:47 am
Location: near Utrecht, Netherlands
This is quite funny problem I found, also known as the Wason Selection Task. You are shown these four cards, which one one side have a number and have a colored back:
Attachment:
File comment: The first card has a three on it, the second card has a red back, the third has an eight on it and the fourth and final card has a blue back.
cards.png
cards.png [ 10.13 KiB | Viewed 913 times ]

You want to verify the following theorem: "If the number on a card is even, then the back is blue."
What cards do you (minimally) need to turn over to verify the theorem?

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 Post subject: Re: 4 cards problem
PostPosted: Mon Jan 23, 2012 11:49 am 
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This is a very interesting problem indeed!

I gathered the right answer (checked wikipedia if I was correct), but I got there by "proof by exhaustion" do you know of any other/more elegant way to arrive at the correct solution?

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 Post subject: Re: 4 cards problem
PostPosted: Mon Jan 23, 2012 1:19 pm 
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Joined: Mon Aug 18, 2008 10:16 pm
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Here's what I came up with (spoilers):

We don't need to check the first card because it doesn't have an even number on it, and we don't need to check the last card because, since it's blue, if it has an odd number we don't care. We do need to check the second and 3rd cards because either one of them could disprove the theorem.


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 Post subject: Re: 4 cards problem
PostPosted: Mon Jan 23, 2012 4:39 pm 
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Joined: Thu Jun 03, 2010 2:25 pm
Location: Farmington, NM
Oh! I just got it. Nice puzzle! I'll have to share this!

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 Post subject: Re: 4 cards problem
PostPosted: Mon Jan 23, 2012 7:18 pm 
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I throw this on the board as a warmup in an intro-level math class, didn't know it had a name though, so that's pretty neat. It's not so much a puzzle, though, it's more just "do you understand the meaning of the word IF?"


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