Tonight the Edinburgh Secret Society will be broadcasting their ‘Lafeyette Seance’ live on the web.  More details here.

So, onto this weeks puzzle…..

On Friday I set this puzzle….
You are shown the four pieces of cardboard shown below.

You are told that each one is either red or green on one side, and that each one has either a circle or a square on the other side.

Which one(s) must you pick up and turn over in order to have sufficient information to answer the question: Does every red one have a square on its other side?

If you have not tried to solve it, have a go now.  For everyone else, the answer is after the break.

Number 2 isn’t important as the question is only concerned with red cards.  If Number 1 has a circle, the answer is no.  If Number 3 is red, the answer is no.  If Number 1 is a square, Number 3 is green, and Number 4 is either red or green, the answer is yes.  Therefore the answer is Number 1 and Number 3.

Did you solve it?  Any other solutions?

If you like the Friday Puzzles, I have produced an ebook containing 101 of the previous Friday Puzzles! It is called PUZZLED and is available for the Kindle (UK here and USA here) and on the iBookstore (UK here in the USA here).  There is also a blog page containing 101 of the puzzles here.

1. Michael says:

Got it. We want to test the implication

red implies square.

In Boolean logic, this is equivalent to

not square implies not red.

We can test both versions of the statement directly by trying cards 1 and 3 as Richard wrote. The other cards are not relevant to the statement.

1. Jerry says:

I like the simple elegance of your explanation.

2. Emlyn says:

This seems obvious to me, not really much of a puzzle.

It can be done without “picking up and turning over” any cards, if you just pick up the cards and look at the other side from underneath without turning them over. 😉

1. Tony says:

>> It can be done without “picking up and turning over” any cards….

Seriously? [Facepalm]

2. OleJ says:

Yes, if the cards are on top of a glass table, you can just go under the table, and see the other side without touching any cards. Easy. Answer is obvious: You do not need to pick up any cards.

3. tort says:

I second that facepalm.

3. Leif says:

Where does it say “oh, by the way the symbol is correlated with the colour”?
Or is it just my understanding of the language that is poor, maybe it’s implied.

1. Berber Anna says:

The question ‘does every red one have a square on its other side’ asks whether the colour red is correlated with the symbol square. That’s what you’re trying to determine. So if you find a red card with a circle on its back, you’ve determined that every red one does NOT have a circle on its back. Ergo, to find the solution to the question, you must find a correlation between the symbol circle and the colour red, which is why you turn over the red and the circle.

2. Berber Anna says:

Uh, does not have a square on its back, I mean.

4. monxas says:

If Number 1 is a square, Number 3 is green, and Number 4 is either red or green, the answer is yes.

can anyone explain me why number 4 could be green?

1. John Hughes says:

The question is does every red card have a square on the other side. It does not follow that every square must be red on the other side.

5. Christian says:

“If Number 1 is a square, Number 3 is green”.

This is faulty logic and does not follow the premise.

1. Alex S says:

I think he means “if no. 1 is a square AND no. 3 is green…”, based on the context?

2. Christian says:

Ah – makes sense. Thanks.

6. Bletherskite says:

I got yay! Avoided the trap.

7. Lazy T says:

I still can’t see a trap, I got the solution coz it’s obvious, but where’s the twistytrap people were warning of?

1. Berber Anna says:

I think the trap is to misread ‘does every red card have a square on its back’ as ‘ does every square have a red back’, and to then turn over the square to check whether its back is red.

2. Lazy T says:

mmmmm…. you’re probably right, people would rather admit to being tricked than to making a mistake

3. Joao Pedro Afonso says:

Or maybe they read “one” instead of “one(s)”. I did that at my first time.

8. Chris Bird says:

Phew, got it instantly. Must have driven past “the trap” because I didn’t see hide nor hair of a trap.

9. misleading … i thought you have to pick only one card … guess the ‘(s)’ must have registered in my attention

10. I’d say something about red/green colorblindness (most common type as far as I know), but I’ll leave it 🙂

I found the answer in a minute or two, didn’t know it was called boolean logic, but I see how it’s relevant.

Not the hardest puzzle, but the topic got me looking up a lot of logic wiki articles, quite amusing 🙂

11. Matt says:

Well, you won’t have to pick up both cards. If you pick up number one and the back is a circle, you can answer ‘no’ without picking up any other cards.

-Matt

12. Let me restate the problem as under:-

There are four people drinking beer or orange juice in a bar. There is a rule that only those over 18 years old can drink beer. Those who are under 18 can only have orange juice.

The four cards in the puzzle represent the above four people in the bar.

The coloured side (either red or green) indicates if they are adults or non adults — red indicates adult and and green, the non-adults.

The side with the shape (circle or square) indicates the drink the person is having — circle for beer square for orange juice.

We can clearly see that the first person (red) is non-adult the second is an adult (green) — but we do not know what they are drinking;. The third person drinks beer (circle), and the fourth has orange juice, but we do not their ages!

Now the puzzle question becomes as under:-

Which person(s) must you check out (on their age or drink) in order to have sufficient information to answer the question: Does every non-adult (green) have orange juice (square)?

We don’t care what the known adult (2nd guy) is drinking. Nor do we care about the age of the fourth guy who we know is having orange juice (square)!

What we do need to check is as to what drink the first person (the child, the red card) is having. We would also need to check the age of the third person (the known beer drinker).

13. So if the question was – Is every card with a square, a red card?
The answer would be different rite?

14. Krishna asked, “So if the question was – Is every card with a square, a red card? The answer would be different rite?”

Indeed so! The answer then would be — 2nd and 4th cards will need to be opened.

15. The other Matt says:

Cant translate “square”…
So, my ultimate Solution: None of them all ! Because each card, red or green, has a square on his backside: The outline !

1. katie k says:

Sorry, that’s technically a rectangle. 😦

16. katie k says:

Yep, I got it! My powers of logic are intact.

17. Charlie says:

The Wason test. I used to work with his son. Used to detect autism I believe, but not sure why, this is pure logic rather than relating to people.

18. YAAAAYYYYY!!!!!

😀

etc

19. Asgeir Rekkavik says:

Got it right, but reckoned I had missed something. It just seemed too easy. Besides: how many cards you have to turn, depends on wheter or not you can answer ‘no’ after turning the first card. If there is a circle on the back of card 1 or a red surface on card 3, you don’t have to turn any more cards.

20. spiderabc1 says:

I just wanted to turn 3 the circle.

21. DJ says:

I would also need to turn over #2 to make sure that it’s not red on the other side.

See, I was *told* that each one is either red or green on one side, and that each one has either a circle or a square on the other side. But I do not believe everything that I am told. So to be completely confident in my answer to the question posed, I would have to flip over cards 1, 2, and 3.