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

So, onto this weeks 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?

As ever, please do NOT post your answers, but do feel free to say if you think you have solved it and how long it took.  Answer on Monday!


  1. About a minute. Had to read the question a few times… but hen again, it’s still before my morning coffee 🙂

  2. Blast it all. Feel like I don’t even understand the puzzle this week. What’s so hard about checking every card?

    Presumably it should be the “one” you pick up, but the “(s)” removes the challenge because if I can pick up more than one, why not all four? I feel dumb… 😦

    1. The puzzle is, in other words: what is the least amount of cards you need to flip, and which ones are that, to answer the question “does every red one have a square on its other side?”

      You should not flip them all.

    2. It’s not the fewest number of cards that is being asked for. That would be one. If you turn over the red and it has a circle then you can answer the question.
      The problem requires the identity (and therefore the number) of the most cards that have to be turned over before the question can be answered but you don’t ever need to turn them all over before you get to that point.

    3. Wintermute: Savant is actually right — the fewest number of cards would be one, assuming that single card disproves the theory. You’re looking for the number of cards that you CAN flip to prove the theory (some cards don’t have anything to do with the statement, so flipping those would be useless).

    4. Berber Anna:

      So your answer to “which one(s) do you have to turn over to see if the theory is right or wrong” is “whichever one it is that proves the theory wrong”?

      That seems like a unsatisfying solution.

    5. This confusion all stems from the words “could” and “must”.

      M’s comment is working with the question “least/fewest you must flip”, which I believe is what’s being asked (along with the position of those cards).

      But Savant misinterprets M’s question to be “least/fewest you could flip”, which is not the same, and is not what is being asked.

      The cards *could* be in a favourable state meaning one flip would do it. But assuming they aren’t, what’s the most you *must* flip to prove the hypothesis right or wrong?

  3. Miggy- the key word is “must”. If you prefer-what is the least number of cards you must turn over to show the hypothesis is true/untrue

  4. And please don’t feel dumb-that’s not a good thing! To those of you Smart As who rushed through cos you know how to do these try to remember how long it took the FIRST time! :0)

  5. The question would be more aptly worded: What is the minimal number of cards one has to flip over to ensure this rule is true? Which cards?

    In any case, while as (some/many) people won’t get this, they will get the equivalent:

    Assuming the drinking law states that a minor (<21) cannot be served alcohol, which of the following patrons at a bar must be checked:
    18yr, 34yr, drinking alcohol, drinking soda.

    1. Nice equivalence but a poor example, since in most areas the 34yo has to be checked, even if he looks 54

    2. @Anderson there are two types of “checking”, (like 2 sides to each card) one for ID and the other for alcohol. the 18 and 34 yr olds have been “checked” for ID, the other two have been “checked” for alcohol.

    3. Noah’s reformulation of this well-known puzzle is also well-known, and has been used as an example to show that many people can more easily solve a puzzle if it is couched in terms of social circumstances than if posed as an abstract puzzle. There is an important lesson for maths teachers there.

  6. As others have said, a poorly worded question (as usual – Richard, is this how you set exams for your students too?) but assuming the question is about the minimal number of cards, I got it more or less as soon as I read it. Fairly trivial

    1. Ooooh no I take it back, it’s more cunning than I thought – after a few more seconds got the answer. Same number of cards as I originally thought but different ones 🙂

    2. I think many people here will have done the same thing as you! It’s a harder question than it looks.

  7. I have an answer but I’m not confident in my logic that got me there, either I just don’t understand the problem, or the problem is not presented very well. Or it is presented well, and I do understand it and I’ve got the right answer. I find that less likely though!

  8. I do not know if this works the same in every language, but I think this puzzle is related to the biased interpretation of conditional sentences as biconditional ones.

  9. I regularly don’t get a lot of these puzzles – because my answer is:
    ” wow – this now moment has fascinating overtones of school tests and assholes who think MENSA membership means they can be great people and attract women and success.”

    So I would want to assure those who don’t get these puzzles on a regular basis – you may be much cooler than those who proudly do.

    1. Spoken just like someone who failed to get into MENSA and is still bitter about it.

    2. What?, you do not try to do the puzzles just because it is fun? In that case, it is an waste of time.

    3. kidding right – you have seen the MENSA crowd? regular Clive Sinclair-alikes who don’t know how to park a bike or find a clitoris…
      of course I take that back if you are a female MENSA member ( still wouldn’t want to be a member)

      (and yes I would qualify, just prefer to be flying, sailing, or solving political problems)

    4. A politician who can sail AND fly? AND park a bike and find a clitoris? Were you privately educated?

      It’s just a bit of fun. There’s no need to insult the people who enjoy puzzles even when they can’t solve them.

  10. Think I’ve got it. Fell into the trap at first but quickly changed my answer, will have to wait to Monday to see if I’m right!

  11. Just reading ‘How we know what isn’t so – Thomas Gilovich’ and saw this problem a few pages back!

  12. “There is also a blog page containing 101 of the puzzles here.”

    Err… not yet there isn’t! As of 10:25am, that link gives me a 404…


    Meanwhile, with the puzzle itself, it could take up to three iterations to prove or disprove the null hypothesis. I’m also reasonably confident of the best order to turn over the cards in the worst case scenario.

  13. About 5 mins to get my answer knowing that Richard has used the same puzzle in a slightly different format before and trying to remember how that one worked. I’m reasonably confident in my answer this time but we’ll see on Monday.

    1. You don’t have to check them all to get the answer though, and the question is ‘which ones MUST you turn over’

  14. I got it straight away because it’s a ‘standard’ that has been doing the rounds for years. A wonderful puzzle when you first encounter it, though.

  15. Contrary to some comments, it is worded right. Here is an equivalent wording: “Which cards, if turned over, would help test the claim, and which (if any) would not?”

    It is basic logic, but it is not intuitive. Whoever has that training that makes it an easy puzzle is very fortunate. Whoever does not … these puzzles are a great primer.

    An excellent puzzle yet again. Thanks Richard.

  16. Is is a competition to see who got it in the shortest time?

    In that case it took me 1.632 seconds.

    Actually it did take a while, probably because I didn’t read the question properly.

    I used to be able to do things like this quickly but have spent the last 6 years working in marketing. As you know working in marketing reduces your IQ by 10 points a year.

    I liked the colours and patterns. They were pretty.

  17. I believe I have it. Took some thinking probably ~ 1 min to get what I believe to be the correct answer. I like this one as it appears straightforward, but you be careful…

  18. This one seems a little too trivial. I’m concerned by my answer’s obviousness.

    To nitpick…the question should’ve said “what is the minimal number you need to turn over”, because “all of them” satisfies the question.

  19. Initially thought the problem was impossible as I read it “which one card” not “which one(s)”
    pretty simple when you are allowed to flip more then one.

  20. I had the answer fast, then I realized I was wrong and got a new answer. Then I realized I was wrong again!

    But I think I have the correct answer now 🙂

  21. I got an answer in about 5 secs, then I read the comments, it doesn’t look like there is a trap/twist so either I’m in it or stepped over it

  22. I didnt understand alle the rules correctly… But then i got a solution while just waching relaxed on the four cards !

  23. I can think of 3 different answers that are arguably correct.

    Not sure how long it took me, I like to ponder on these for some time & find an angle that makes the pedantic interpretation of the question introduce ambiguity.

  24. The puzzle hinges on whether I can trust this given: “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.”

    If I cannot, then I need to turn then all — e.g. the green one may be red on the other side.

  25. I think I have the answer after maybe…a minute of thinking. Pretty quickly, but of course I could be wrong.

  26. Seems perfectly worded to me, got it in a few seconds but feel a bit thick because I can’t see a trap (perhaps because I’m sitting at the bottom of it)

  27. I didn’t see a trap, so maybe my left leg will be held by a steel tap tomorrow. Looks lime a no brainer to me. Read the question and immediately came up with answer. My watch doesn’t time accurately enough to determine actual time taken. So i suspect I have missed something.

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