A nice simple one this week.  As ever, please do NOT post your answers, but do say if you think you have solved the puzzle and how long it took. Solution on Monday.

From a full deck of 52 playing cards, how many cards do you need to draw to ensure that you have four of a kind in your hand?

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). You can try 101 of the puzzles for free here.

70 comments

    1. 0.238921961696395381535549104701266481251516152361839 seconds. If you are seriosuly lucky then the first 4 cards drawn could meet the desired criteria. On the other hand,if you are unlucky and the first 39 cards drawn are either say hearts, diamonds or spades, then you need to draw a 40th card

    2. Probably not, but it IS possible for you to NOT read the comments until you worked out your answer thereby eliminating the ‘spoiler’ effect.

    3. Of course it’s possible to ban people by IP adress, blogs do it all the time. Does Dave’s Neighbor do this often? It’s rather rude when one has been expressly asked not to post the answer.

    1. It doesn’t matter if the deck is shuffled or comes as-is from the manufacturer. The answer will still be the same.

    1. A fair question, but “four-of-a-kind always means “of the same number” in the context of cards.

    1. It won’t be obvious to everyone. There is a wrong answer that a good number of people will jump to first.

    1. Wait for monday….,its not so a “nice simple one”, i think. Or did you know suddenly what means “four of a kind” ?

  1. I agree with Dave’s Neighbor. The worst case scenario is that you have to wait for the 40th card to ensure 100% success

    1. Do you agree that it’s okay to specifically ignore the instructions regarding posting your answer prematurely? Do you simply not care, or are you cognitively defective, or are you just such a firebrand rebel you can’t help your anti-authoritarian impulses? You and Dave’s Neighbor should start a bad-ass street gang. You could travel town-to-town on souped-up Segways, breaking hearts, scoffing at the law, tearing off mattress tags, and tagging spoilers on Movie Marquis posters with indelible marking pens.

    2. The best way to piss off an attention seeker is to ignore them. Sorry Mervulon, but after your post, I think that Dave/Dave’s neighbour/Anonymous will be back for more on Monday.

    3. That’s okay… just so long as they’re not rolling through my ‘hood on those Segways… we sure don’t need that kind of trouble….

  2. four cards of the same deck require me to draw ___ cards. why is that blank so diffikult for some people?

    now if multiple decks are sorted together that would be harder

    1. No Martha
      No matter how many packs there are the answer is the same
      PS Unless we are we playing to Lemmy’s
      rules when the answer would be four more

    2. yes m. le twit that does seem to be the case.
      a more interesting puzz to me is “how many cards you would have to draw and perhaps discard to guarenty you have four different cards (eg not of same type)”

    3. Actually, with two decks, the answer remains the same. The limiting factor is still how may cards you can draw without making 4 of a kind. Adding another deck doesn’t change that.

    4. Dharmaruci
      The answer to your question is the same as that for Richard’s question – different cards though.

  3. I can draw cards until doomsday, but none of them will ever mysteriously materialise in my hand, as if by magic, no matter how long I carry on drawing. I fear that I would run out of pencils first. I think it’s a trick question.

  4. I’m not sure if my answer is correct but it took me 32.4 seconds to arrive at it. My thought process was that I always had a one-in-four chance of drawing the same suit of card in a deal (of four cards). I extrapolated this out until I was certtain of having three of a kind in three deals. The last deal might get me the forth four-of-a-kind card on the first card dealt, the second, or the third, but I figured that there would be no doubt that I would have four of a kind by the fourth card. My head hurt by this time, so I had to go lie down.

  5. I see people here make jokes about how easy this puzzle is, but I remember spending a significant amount of time at university doing pigeon hole principle (the basis of this puzzle), and people not getting it and asking many many questions on it during revision sessions. I always found it incredibly easy but apparently it is worthy of being varsity level…

  6. ~20 seconds, easy answer, but:
    It depends on what you mean by “ensure”; I take it to mean “be certain”.
    Are the cards in fact face-down?
    Four of WHAT kind? The kind with that particular pattern on the back?

    THEN I read some of the comments. Gee, folks, this is becoming just another collection of ad hominem ripostes. Boring.

  7. Obviously too straightforward a question for attention seeking pedantics to benefit from. However, as for attention seeking trolls…….

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