As we approach the holiday season, I thought that it would be good to have a Christmas-related puzzle.  So….

Caroline, Joan and Sam all go shopping.  They all buy a present, and all of the presents are the same size and wrapped in the same paper.  At the check-out the parcels get mixed up.  What is the probability that……

1) At least one of the three women gets the present she bought?
2) Only one woman gets a wrong present?

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.

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.


  1. I assume you want the probability of 1 and the probability of 2.
    One of them to me seconds while the other took a minute with scribbling.

    1. Damocles, (2) helps for (1), but not by much, unless I’m missing something. You’d still have to enumerate the cases.

    1. It’s not a trick. It’s simple probability. Not what I generally consider a brain teaser. A brain teaser should make you think outside the box. None of that here.

  2. The first one, about 30 seconds, the second one, had it before the second one in about 1 second 🙂

    Now wait about 259,000 seconds to know if I’m right 🙂

  3. The “obvious” answer is of course very quick and easy, but I think I might have guessed what the trick is in this puzzle.

  4. For question 2, what’s a “wrong present”? The present you bought, or a present that wasn’t intended for you? I get a different answer either way.

    1. Sometimes the easy answer is the right one
      one thing I have learnt from these puzzles is it is always best to read the question and then work through it systematically

    1. We don’t need to assume – question one quite clearly states “the three women” – so Sam is definitely a Samantha and not a Samuel.

  5. Righteo, draw up a table of permutations (6, unless I’ve screwed up!)…

    Question 1:

    1 – p(nobody gets the correct present)

    Question 2:

    Hang on a minute… ooh, crafty 🙂

  6. Too easy, unless I’m missing something. Now, show Sam that one of the other presents isn’t hers…. should she switch?

    (old Chestnuts are appropriate for the season, correct?)

  7. Unless they were drunk, they will not make these mistakes.

    So we need to know their level of endrunkeness.

    Without that knowledge we can only make culturally-specific statistical guesses.

  8. Oops. I misread the problem and did it for four women. Took several minutes to work that one out. After that, re-figuring for three women was a snap.

  9. The second part I figured out in a few seconds. The first part took a couple of minutes, because I made the mistake of interpreting “at least one” to mean “exactly one”: [ draw matrix, get incorrect answer, feel smug for half a moment, realize I made a mistake, get correct answer ]

  10. Are we assuming that Caroline, Joan, and Sam are all women? What if Sam were a man? That changes the scope of the question.

  11. If there is a trick (and there may not be one) I think it is that we are supposed to assume, or it is implied, that the three named women are also the recipients of the three presents as well as the purchasers, and we are supposed to exclude the possibility that they may be intending to give the presents to other people. Also, it is assumed that the presents they “get” will not be extraneous ones from people outside the confines of the defined puzzle group.

  12. Just got home from work’s Christmas do very drunk and
    both parts seem remarkably easy – hope it’s still as easy when I sober up 🙂

  13. Two I knew instantly, one I had an inclining of but wanted to take a minute to check. Although I do need to ask, since the three women all purchased the presents and it is not stated that they bought them for each other, considering that the random mix-up seems to occur at the front counter, wouldn’t it just make sense to open and re-wrap them? Possibly away from the dunderhead who mixed them up to begin with? Just asking…

    1. …me too. But im not sure its needly to think so far. Some facts will make another sense if the puzzle is embedded in a story.
      There so many other ways, they also can weight and shake the parcels…

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