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Formal Reasoning (Posted on 2004-12-15) Difficulty: 2 of 5
I present to you a deck of 4 cards. Each card has on one side a letter of the alphabet, and on the other side a single digit from 0-9.

I propose a hypothesis that may apply to this deck:
If the letter is 'E', then the number on the other side is '4'.

I then drop the 4 cards on the table, and you see: 'B', '7', 'E', '4' (on the respective cards).

Which of the 4 cards must you turn over to verify or disprove my hypothesis?

See The Solution Submitted by SilverKnight    
Rating: 3.0000 (22 votes)

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re(5): Solution | Comment 51 of 60 |
(In reply to re(4): Solution by Sean)

Suppose you had a bunch of stuff in the attic, some of it was treasure and some was junk.  Suppose also that some of the stuff is in treasure boxes, and some is in cardboard boxes.

If you go up into the attic and see the boxes sorted, (treasure boxes on one side, other boxes on the other,) all you would have to do would be to look in the treasure boxes to make sure there was treasure in it.
But suppose you couldn't tell treasure boxes from cardboard boxes, and there was a label inside saying what kind of box it was.  Suppose also there is a label on the outside of each saying what is contained: treasure or junk.  In this case, you would need to check all the boxes saying junk, to make sure none of them are treasure boxes.
Why?

Because if you found a box that contained junk, and it turned out to be a treasure box, then the statement that all treasure boxes contain treasure is disproven.

The B is like a cardboard box.  It doesn't matter what it has, so you don't need to flip it over.

The E is like a treasure box.  You need to flip it over to make certain that the treasure (the number 4) is on the other side.

The 4 is like the treasure.  It doesn't matter what kind of box it's in, so you don't need to flip it over.

The 7 is like the junk.  You don't know what kind of box it's in, so you have to flip it over to make sure it isn't a treasure box (letter E), because if an E was on the other side of the 7, then 'Every E has a 4' is wrong.

I hope I made myself clear.  = \


  Posted by Dustin on 2005-03-07 01:20:18
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