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. Raymond says:

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. Surely the answer to 2 is simple logic and implies the answer to 1 given the number of tuples.

2. Michael Sternberg says:

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

2. Justin says:

A few seconds to get a half wrong answer, under a minute to get it completely right.

3. Goliath says:

Where’s the trick? Either it’s super easy or I have missed a vital fact…

1. The trick is you need to know how to calculate probability I expect, not everyone can remember the approach. (For part 1, that is, part 2 seems like pretty straight forward and simple logic.)

2. One Eyed Jack says:

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.

4. Roland says:

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 🙂

5. Michael Sternberg says:

Seconds for (2), and a couple of minutes to count the cases for (1) and muse about subgroups.

6. A little scribble – or scrabble for presents. About 5 mins in all to confirm…

7. Nigel Alexander says:

30 Seconds. Unless I am totally misunderstanding the question.

8. Eddie says:

Must be something about the colour blue.

9. John Loony says:

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

The second part – instantly. The first part needed a minute of scribbling.

11. Ed says:

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. AMWhy says:

There’s always one…

12. Seems too easy if just write down the combinations and marks the correct selections

1. Anonymous says:

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

13. 30 seconds for the first one, 2 seconds for the second. I have used the second puzzle myself a few times.

14. Yat says:

The second one made me lol !

15. Mickey D says:

10 minutes drawin the matrix…

16. This probability puzzle seems to be reasonably unambiguous so I’m confident that my answers will concur with Richard’s on Monday.

17. Andrew says:

Do we assume that Caroline, Joan and Sam are all female?

1. mittfh says:

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

18. AMWhy says:

1: about a minute.
2: not even a second.

19. fgiveme says:

30 seconds draw the matrix for (1)
~5 seconds for (2) 😀

20. Susqueda says:

Today I almost soved my Rubik`s cube: I could fix five faces but the last one did resist!

21. Navneeth says:

Now the important question is: who sprayed the pepper spray?

22. mittfh says:

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 🙂

23. Anonymous says:

more like gcse math rather than a quiz i think..

24. Camel Ali says:

A couple of minutes wasted trying to do it mathematically. Then a minute drawing a matrix, and it all became clear.

25. Lazy T says:

If they all bought identical pairs of socks it’s very easy.

26. Anonymosity says:

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?)

27. ChasTiv says:

1st part: about 20 sec
2nd part: 1 sec.

28. Sometimes I feel smart if I get a question right, today i feel kinda average for getting it right.

29. i would be able to solve this if i took the time to scribble the possibilities down but i wont bother, there is no fun in this puzzle.

30. Matilda says:

The answer is ‘quite’

its ‘quite possible.’

31. dharmaruci@test.com says:

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.

32. Gordon says:

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.

33. 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 ]

34. Kirk says:

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

35. John Loony says:

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.

36. SeleneBlueSky7 says:

I think I have some answers. 🙂 Half a minute.

37. Anders says:

The second part is a classic, and I got it as soon as I read it. The first took about 30 seconds

38. Tan Coul says:

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 🙂

39. Jerry says:

under a minute

40. The second one took me about 1 second. The first one about a minute.

41. 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. The other Matt says:

…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…

2. The other Matt says:

Sorry, i want to link this remark to John Loonys comment.

42. Anonymous says:

What is happening?