## Friday, February 1, 2013

### Another Simple Logical Puzzle

OK, I got it. We like it simple. Two weeks ago when I posted  A Simple Puzzle over twenty readers dared to answer. I also noticed that when I post logical puzzles more answers are coming from women.  So, let's try something simple and logical.  This puzzle was suggested by our expert puzzle solver - Ilya.  Thank you!

Observe four cards. They all have a number on one side and either red or brown color on another.  Two are turned to the number side and have numbers 3 and 8 and two are turned to the color side and are correspondingly red and brown.

Your friend is saying that among these four cards all the cards with even number on them have a red backside.  Is she right or wrong? What card(s) do you need to flip to confirm or reject her statement? Try flipping as less cards as possible.

Your answers accepted any time until midnight on Sunday on our Family Puzzle Marathon. They will be hidden till then and everyone who submitted something reasonable will get a puzzle point.

Letterpress Help said...

By flipping the red card only you can judge.

Anonymous said...

From Kim via email:

Hi Maria,

Still don't know why I can't seem to submit comments online, but here's my answer this week's puzzle:

You need to flip 2 cards.

You need to flip the 8 to make sure it has a red backside.

You need to flip the brown card to make sure it doesn't have an even number on the other side

You do not need to flip the red card - if the number on the other side is even, great, it matches. But if it's odd, that's OK, too because we didn't say anything about the red cards having to have even numbers on the other side, only that the even numbers have to have a red backside.

As for the three - same thing, you don't need to flip it - it doesn't matter if it's red or not.

-Kim

Dennis (of Dennis and Katrina) said...

Statement to verify: All the cards with an even number on them have a red back.

Flipping the "3" tells us nothing about this statement, as the statement does not say "only" the even cards or anything about the back of odd cards.

Flipping the 8 can have two results: red or brown. If we get red, then the statement remains possible. If we get brown, we have DISPROVED the statement, so we should flip the 8.

Flipping the red has two outcomes: odd or even. If it's odd, we learn nothing, as the statement is silent on the backs of odd cards. If it's even, we only learn that the statement is still possible. So, leave this one alone.

Flipping the brown has two outcomes. A odd number, which tells us nothing or an even number, which DISPROVES the statement. So, flip the brown.

Therefore, flipping the 8 and the brown will either prove or disprove the statement; for the statement, it doesn't matter what backs odd cards have red, brown, or either color backs - just that, for these cards, any EVEN number has a red back.

Answer: Flip the "8" and the brown card.

TyYann said...

The answer is simple: we need to turn the card with an 8 to make sure the back is red. But we also need to turn over the brown one to make sure it's not an even number. Because the logical equivalent of the statement is "All the cards that don't have a red backside are not with an even number"

Anonymous said...

To see if among the four cards shown, all even number cards have red backs, at most you would need to flip two of the cards:
(1) the 8; it's an even number and you need to verify it has a red back. If it does not, you've shown your friend's statement is incorrect. It has a red back, then
(2) you need to flip the brown card, to verify if it is odd or even. If it is even, your friend's statement is incorrect. If it is odd, then your friend's statement if correct for these 4 cards.

You do not need to flip the "3" card (because it is odd) or the red card (because whether it is even or odd, this wouldn't negate your friend's statement that all even cards have red backs).

TracyZ

kj said...

You will have to turn over at most two cards.

You want to prove that "Even implies Red." (Note: You are NOT trying to prove "Red implies Even.")

Even => Red is equivalent to
Not Red (Brown) => Not Even (Odd)

So you first turn over the 8 to see if it is Red or Brown.

If the 8 is Brown, your friend's statement is incorrect, and you are done.

If the 8 is Red, then you turn over the Brown to see if it is Odd. If it is Even, your friend's statement is incorrect. If it is Odd, your friend's statement is True.

It matters not if the 3 has a Red back, or if the Red has an Odd number.

Amy Kemery said...

8 and brown cards

Since you are making no claim about the color of odd numbered cards, it doesn't matter if the three is red, or the red card is odd.

Anonymous said...

I think you need to flip 2 cards over. Either an even number (8) and the brown card or the 3 card and the red card. This way it would most likely confirm or disprove the thesi as the ones being turned over are opposite of what the other is. i.e. brown=odd and red= even.

Gurubandhu

Jerome said...

1. You don't care about the brown ones. They could be either odd or even and you wouldn't care. The statement has to do with red cards.

2. It does you no good to flip the 8. You still are not certain what will happen to the red card. It might be odd or even. Therefore

3. Flip the red card. It will confirm or deny the red/even theorem.

Jerome's wife said...

a matter of just reading it correctly for what it is actually asking. The answer is turn over the red backed card to see if the woman is correct in saying it should be an even number. If it is she is correct, if not, she is incorrect.

Sandy said...

Flip 3 cards. Flip 8 to be sure it is red. Flip red to be sure it is even. Flip brown to be sure it is odd. You don't need to flip the 3. She made no rule for odd numbers.

Maria said...

The truth is that Ilya and I were trying to trick you. The puzzle is simple but as frequently happens with logical puzzles you have to think very clearly and unwrap all the logical knots to solve it right. Concentration, experience, logic - think Carrie from the Homeland series. If you happen to give the "8 and Brown" answer - you are a genius analyst worthy of CIA, Scotland Yard or CSIS.

Most of us, simple mortals, get this puzzle wrong. It is so frustrating that the puzzle even got a name - Wason selection task - after the psychologist who invented it.

Think about it - our statement is "Even is always Red." It doesn't say anything about the Odd-numbered cards that therefore can have either color backing. We are looking for the ways to disprove the "Even -> Red" statement. The only way to disprove is to find an Even card that has Brown backing.

Back to our four cards. How many of them can be "Even-Brown?" Let's check the 8 card and the Brown cards. Here is our answer.

A puzzle point to everyone who dared to answer, correctly or not. You can read more about this puzzle here: Wason selection task Turns out it is much easier to answer in a more concrete context. Thanks again to Ilya for suggestion this. And a puzzle point.

anne-marie said...

Hi Maria,
I sent an answer, I am surprised not to se it posted.
Ane-Marie

anne-marie said...

Hi Maria,
I sent an answer, I am surprised not to se it posted.
Ane-Marie

Maria said...

Anne-marie, I am so sorry but I don't see it anywhere - in the spam or unpublished comments on the Blogger or in my email. This must be some technical error. If you prefer, feel free to email me the answers.

Jerome said...

Hi Maria

Take care

Jerome.

Maria said...

You can just Google "Wason selection task" or go to Wikipedia and find it there. But here is another try: