Logic test

[Independent voter]

Prove that cards with an even number on one side are blue on the other with the fewest number of moves.

[Deleted]

My cards are sitting on a see through glass table therefore 0 moves.

[Lynarii]

You flip the 8 and the green card.

We don't care what is on the back of the 5, we have no interest in proving anything to do with cards we know have an odd front. Similarly we don't care what is on the front of the blue card. There's nothing saying that all blue cards have even numbers. All we need to know is that the 8 has a blue back, and the green card has an odd front.

[Azadina]

You flip the 8 and the green card.

We don't care what is on the back of the 5, we have no interest in proving anything to do with cards we know have an odd front. Similarly we don't care what is on the front of the blue card. There's nothing saying that all blue cards have even numbers. All we need to know is that the 8 has a blue back, and the green card has an odd front.

Except the statement for it. "if a card shows an even number on one face, then it's opposite face is blue" That means that any even number = blue backside. And to be true, it has to work in reverse too, as in, every blue backside has to have even number on the other side.

Don't have to do anything. We can say that 8 is blue, and the blue is an even number, following the statement. But if one really wants to do something with them, then flip 8 and blue, to see if the statement is correct.

[nextormento]

Don't have to do anything. We can say that 8 is blue, and the blue is an even number, following the statement. But if one really wants to do something with them, then flip 8 and blue, to see if the statement is correct.

OP didn't clarify, but the exercise is generally about figuring if the statement is correct, not assuming that it is.
We don't need to flip blue since the statement is correct either way: if it's even, then it must have a blue backside, if it's odd, it can have any color.
But we do need to test the yellow/green one. If it has an even number, the statement doesn't hold.

[Yxiomel]

Except the statement for it. "if a card shows an even number on one face, then it's opposite face is blue" That means that any even number = blue backside. And to be true, it has to work in reverse too, as in, every blue backside has to have even number on the other side.

Don't have to do anything. We can say that 8 is blue, and the blue is an even number, following the statement. But if one really wants to do something with them, then flip 8 and blue, to see if the statement is correct.

You are wrong; logic does not require the reverse to be true. Consider this: prove that all ketchup is red. Does the existence of other red objects falsify the redness of ketchup?

(A => B) =/=> (B => A)

All that has to be true is the contra-positive
(A =>) B => (not B => not A)

So (even => blue) => (not blue => not even)

[Azadina]

You are wrong; logic does not require the reverse to be true. Consider this: prove that all ketchup is red. Does the existence of other red objects falsify the redness of ketchup?

(A => B) =/=> (B => A)

All that has to be true is the contra-positive
(A =>) B => (not B => not A)

So (even => blue) => (not blue => not even)

We are talking about the cards, not cards + anything imaginable that's also blue. Your analogy doesn't make sense.

[Lynarii]

The statement is "If even, then blue", it says nothing about the reverse. An odd card can have a blue back and everything is fine. All we need to know is that any card that has an even front also has a blue back. The 5 can have either a green back or a blue back and it won't invalidate the statement. The 8 MUST have a blue back for the statement to be correct. The card with the blue back can have either an even or odd front and we're still in the clear. However, the card with the green back can NOT have an even front or the statement is false again.

Ergo, we need to check the 8 and the green card. Two moves.

[apples]

We are talking about the cards, not cards + anything imaginable that's also blue. Your analogy doesn't make sense.

the text very specifically says that if a card has an even numbered face, then its back is blue

this does not imply that all blue backed cards are even faced.

also the answer is this is a dumb question that im pretty sure OP misread

[the game]

The logical thing to do is to get a Vulcan to explain this.

[Azadina]

The statement is "If even, then blue", it says nothing about the reverse. An odd card can have a blue back and everything is fine. All we need to know is that any card that has an even front also has a blue back. The 5 can have either a green back or a blue back and it won't invalidate the statement. The 8 MUST have a blue back for the statement to be correct. The card with the blue back can have either an even or odd front and we're still in the clear. However, the card with the green back can NOT have an even front or the statement is false again.

Ergo, we need to check the 8 and the green card. Two moves.

Oh, I see now, you're right. I should of had my breakfast first D:

[Lynarii]

Easy.

1) Flip the 5 card to make sure there isn't an even number on the opposite face.

2) Flip the 8 card to make sure the opposite face is blue.

3) Flip the green card for the same reason as we did the 5 card.

Actually, this answer is more correct than mine was. I ran under the assumption that each card had a color on one side and a number on the other, but that isn't expressly stated to be the case. If every card has one number and one color than I am correct. If it is possible that a card can have two numbers, then we also do have to check the 5 card.

[Deleted]

Emm... Turn the blue card around and see if it's even or odd? Although then the OP would have to qualify the question a bit more, and say that you have to prove all blue cards are even and that all even cards are blue.

The thing is though, you can't prove squat without definite rules that aren't being given here. It doesn't matter what those cards are, if there are other cards out there, because these four cards can be whatever, and the cards we don't have can be orange and red and black and so on.

Are we talking about just these four cards, or all cards, with all the numbers? Are we talking about just blue and green?

[Cerilis]

only flip the 8. if it's blue, I win. Nothing else matters.