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.

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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.

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

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

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

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

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.)

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.

Job done. Simple.

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 🙂

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

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

30 Seconds. Unless I am totally misunderstanding the question.

Must be something about the colour blue.

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.

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.

There’s always one…

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

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

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

The second one made me lol !

10 minutes drawin the matrix…

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

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

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

1: about a minute.

2: not even a second.

30 seconds draw the matrix for (1)

~5 seconds for (2) 😀

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

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

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 🙂

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

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

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

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?)

1st part: about 20 sec

2nd part: 1 sec.

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

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.

The answer is ‘quite’

its ‘quite possible.’

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.

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.

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 ]

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

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.

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

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

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 🙂

under a minute

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

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…

…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…

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

1

What is happening?