[Guest]

Hello

This is not too taxing and is my first puzzle, so go easy on me!

There are four cards on the table with faces showing either a letter or a number:

B D 3 7

Given that each card has a letter on one side and a number on the other, which 2 cards would you need to turn over to prove the statement that all cards with a B face have a 3 on the other side?

Maybe not what you first think: You need to turn the B card and the 7 card.

You need to turn the B card to check that there's a number 3 on the other side. The D card proves nothing. It doesn't matter what's on the reverse of the 3 card - the statement only says that a B card has a 3 on the other side NOT that a 3 must have a B on the other side. Turning the 7 card as well as the B card proves the statement one way or the other - if there's a B on the reverse of the 7 card then the statement will be proved to be wrong, otherwise it's true.

[Izzy]

The B and the 7.

I love simple puzzles. Nice one.

[itachi-san]

Hello

This is not too taxing and is my first puzzle, so go easy on me!

There are four cards on the table with faces showing either a letter or a number:

B D 3 7

Given that each card has a letter on one side and a number on the other, which 2 cards would you need to turn over to prove the statement that all cards with a B face have a 3 on the other side?

Maybe not what you first think: You need to turn the B card and the 7 card.

You need to turn the B card to check that there's a number 3 on the other side. The D card proves nothing. It doesn't matter what's on the reverse of the 3 card - the statement only says that a B card has a 3 on the other side NOT that a 3 must have a B on the other side. Turning the 7 card as well as the B card proves the statement one way or the other - if there's a B on the reverse of the 7 card then the statement will be proved to be wrong, otherwise it's true.

I'm not sure about the logic to your answer. You say that all 4 cards are showing their faces. Then you ask: prove that B faces have a 3 on the other side. Since there is only 1 card with a B face, you need only turn that card over. All other cards are irrelevant because they don't have B faces.

[Guest]

I'm not sure about the logic to your answer. You say that all 4 cards are showing their faces. Then you ask: prove that B faces have a 3 on the other side. Since there is only 1 card with a B face, you need only turn that card over. All other cards are irrelevant because they don't have B faces.

As there is a letter or number on either side of each card, each card has two faces. As they are sitting on a table, you can only see one of them. If that's caused you confusion, then I apologise. Does that make sense?

[bonanova]

I'm not sure about the logic to your answer. You say that all 4 cards are showing their faces. Then you ask: prove that B faces have a 3 on the other side. Since there is only 1 card with a B face, you need only turn that card over. All other cards are irrelevant because they don't have B faces.

Suppose there were a B on the back side of the 7 card.

[Izzy]

Suppose there were a B on the back side of the 7 card.

Then you would be proving that the statement is false.

Edited September 30, 2008 by Izzy

[Izzy]

Wait, I've just realized something that would make Skinny's reasoning wrong.

If 3, D, and 7 are all considered to be face cards as well as B, then there is no reason for the 7 to be flipped. 7 would be the same as 3, according to your answer.

So the correct answer is only B.

[itachi-san]

As there is a letter or number on either side of each card, each card has two faces. As they are sitting on a table, you can only see one of them. If that's caused you confusion, then I apologise. Does that make sense?

Well, I got it in the first place. I was just making the point that the opposite side of a card isn't called it's face. It's a petty semantic thing I guess. Nevermind.

[Guest]

Wait, I've just realized something that would make Skinny's reasoning wrong.

If 3, D, and 7 are all considered to be face cards as well as B, then there is no reason for the 7 to be flipped. 7 would be the same as 3, according to your answer.

So the correct answer is only B.

Assuming you have already turned over the B. Turn over 3 and you either have a B or something else. If it is a B, then you haven't discounted that there could also be one on the reverse side of the 7 (which would prove the statement incorrect). If there isn't a B on the reverse side of the 3, you don't disprove the statement (the statement doesn't say that on the other side of 3 there is always a B). So you must turn the 7, which is the only card which will prove or disprove the statement.

I think this had better be my first and last puzzle - I don't think I'm cut out for it!

[itachi-san]

I think this had better be my first and last puzzle - I don't think I'm cut out for it!

Nonsense! Keep em coming!