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?

(In reply to re(3): Solution by Dustin)

If you turned over the 7, there might very well be an E on the other side. But, that's not the hypothesis that the problem proposes. The hypothesis only states that if there is an E in the front, there is a 4 in the back. It states this and nothing else. Therefore, you can't assume anything else.

"So, if you have a number that isn't a 4, an E cannot be on the back, and you must look under the 7 to make sure."

It doesn't say anywhere that a certain number/letter can only have a certain letter/number on the back, so you can't assume that that's the case. For all you know, looking under B could get you a 4, too. You have to work with what you're given.

It might help if I substituted the letters for real objects:

If there is an E in the front, there is a 4 in the back, right?

Okay.

Let say that if there is a treasure box, there is treasure inside.

What would be the only true way to prove or disprove this?

It would be looking in the treasure box. Not looking in the cardboard box or in the garbage can or in cookie jar or anything else. If you look in a cardboard box and find treasure, that doesn't mean you wouldn't find treasure if you also looked in the treasure box. It just means that you found treasure in a cardboard box. I didn't say treasure will only be found in a treasure box (in which case, yes, looking in the cardboard box and finding it would've disproved it). I just said treasure will be found in it. But, how do you know that for sure? You don't. That's why you look in it.

I hope I made myself clear.  = \

Posted by Sean on 2005-03-07 00:37:42