Last night seven of my friends went to a local restaurant.  They each handed over their coat as they entered.  At the end of the evening the staff returned the coats, but they were totally incompetent and randomly handed out the coats to my friends.  What is the probability that exactly six of my friends received their own coat?

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. Chrs says:

Got it. Took a minute to see it though.

2. I see what you did there! Nice one Richard

1. Navneeth says:

I see what you did there!

Hehe… my thought, exactly.

2. Navneeth says:

Oh, total time: a couple of seconds, maybe.

3. I was trying to overcomplicate the problem, but now I have it.

4. -M- says:

Got it instantly! I did not fall for this one.

5. JCB dumpster says:

Erm, it depends on a variable we clearly don’t have

1. Chris says:

actually, there are several missing variables.

2. -M- says:

I suppose you mean they could have gotten coats from other guests than just these 7 friend I suppose.

I think Richard means just these 7 coats were mixed up.

3. Nick says:

Same thoughts here. I presume “the coats” means ‘the same seven coats that we originally handed in’? Or is there a possibility that the coats we got back were mixed with coats from other guests?

If it is indeed the same seven coats then the answer is easy. If the coats were mixed with those from other guests then we need to know how big the restaurant is!

4. Berhard says:

I am with Nick…
after the time to read through it…
as the riddle says “the coats” and not “seven coats” there is only a single very simple solution..

the time to read the riddle

6. Julie says:

5 seconds. I love these puzzles

7. Ian Morgan says:

Good puzzle – took a few seconds!

To me a puzzle that takes “a few seconds” is a bad puzzle.
It hasn’t challenged me at all and I haven’t learnt anything.

It depends on whether everyone had a coat or not.

1. Bill says:

The question says “They each handed over their coat.” That means they all had a coat.

Thanks for the clarification Bill.
I misread it as “They each handed over their goat”
No wonder I was struggling with it.
TMT

9. SofARMaths says:

A few seconds

Still looking for the puzzle which asks how to draw one line through nine points arranged in the noughts and crosses type of square, 3, 3, 3….
Haven’t solved it in two months…

1. fredb says:

you can draw a line that goes past the final dot in a row…i.e. it extends past the 3×3 grid.

2. -M- says:

The square:
A1 A2 A3
B1 B2 B3
C1 C2 C3

Make it:
A1 A2 A3 A4
B1 B2 B3
C1 C2 C3
D1

4 lines:
A1 – A4
A4 – D1
D1 – A1
A1 – C3

Good luck.

11. Niva says:

Is this even a puzzle? It’s obvious isn’t it? I read it again to see if there’s a trick, but clearly there isn’t.

Technically as Richard does not give us the answer in the question, I suppose it is a puzzle.
Some of the people who have posted and got an answer in a few seconds even think that it is a “good” puzzle – I do not fall into that camp.
What puzzles me is why a look at this drivel week after week……

2. Nanny Mouse says:

Nobody is forcing you Twitty Boy

3. Eddie says:

I am. I demand that the Masked Twit looks at and attempts to solve these puzzles as long as they keep appearing week after week.

4. Nanny Mouse says:

I stand corrected. Lol

12. Anonymous says:

Got it instantly. Nice wording.

13. kroketje says:

ahaaaa, now i see it 🙂 nice!! (took me about 3 minutes)

14. Eddie says:

Sometimes they’re easy, sometimes I don’t touch ’em.

15. Eddie says:

Ne postez pas la solution!

16. Roar says:

A bit more complicated if the party at the next table were leaving at the same time … otherwise; easy.

17. Alex says:

Very quick, same puzzle (with different scenario) was posted here earlier in the year wasn’t it?

1. Alex says:

Hmm, looking back it actually wasn’t this year. Time moves fast on these Friday puzzles.

18. Lazy T says:

You could also ask how many coats will come back….
with curry stains on the arm?
missing a button / scarf / mobile phone?
with a murder weapon planted in a pocket?

1. mittfh says:

…if they bump into Jane Marple or Hercule Poirot on their way out… 😀

19. ElJabba says:

Got this at the as I finished reading the question.

20. ElJabba says:

1. Nanny Mouse says:

Wheesht!

21. saw the answer straight away, this is one of your easier ones

22. Got it in the reading.

Why did they not invite you, Richard? Are you sure they’re your friends?

1. Anonymous says:

Me too, answered it whilst reading and wondered what the puzzle was… then I realised what the question was. Happens to me all the time heh.

Aww… really?

24. 0.5 seconds, if that – but I think I knew this puzzle or it would have been a couple of seconds.

25. Solved that one so long ago I can’t remember how long it took. Back when I first looked at matching protocols like the Natasha Demkina test Richard was involved with.

Remembered the solution in an instant.

26. It’s rather important to make the assumption the staff aren’t so incompetent as to hand more than one coat to any one person (although as they “totally incompetent”, that might not be be a reasonable assumption at all).

It makes a big difference to how difficult the problem is, although only a tiny one to the magnitude of the probability.

27. mittfh says:

Assuming the staff were actually competent enough to find the coats of the seven friends (and not hand anyone A. N. Other’s coat) or the restaurant was so quiet the seven friends were the only diners (in which case they may have left hungry after waiting three hours for a non-existant meal because the waiter was also incompetent and didn’t pass on their order…), then the answer to this problem is very easy, so I’d worked it out by the time I’d finished reading the question.

It helps that Richard asked a very similar question (albeit with a different number of friends and a different scenario) a while ago…

An interesting side exercise would be the probabiltiies of a different proportion of the dining friends getting their coat back…

1. The question states that the seven coats were returned to the friends in question

“They each handed over their coat as they entered. At the end of the evening the staff returned the coats, but they were totally incompetent and randomly handed out the coats to my friends.”

That doesn’t really permit of the possibility that they handed out coats which weren’t from this group, or that any coats from this group were handed to others.

However, what it does not say is that only one coat is given to any particular person. That does make a difference.

28. Justin says:

lol, 20 seconds.

29. Mike Torr says:

Immediately.

30. AMWhy says:

Too easy. Instantly got the answer upon reading the question. A shame as I was preparing myself for some good brain exercise!

31. deepfield says:

Solved upon reading, but, on afterthought, I saw that it was not correctly stated: the seven coats did not mix up with the coats of the rest of the patrons, and it is hard to believe from such incompetent clerks…

32. Wolf Martinus says:

ìnstantly solved

33. Instantly. But I still have to make it through the weekend to be sure I haven’t missed a twist!

34. Bob says:

aww man, too easy.

35. 17 seconds about. Then again I solve things for a living. 😉 Clever!

36. Kyatapii says:

I see what you did here… 🙂

37. Got it. Took about as long as it takes for one to release his bowels 🙂

38. Duncan says:

Got it before finishing the question.

1. Nanny Mouse says:

Got it before reading the question

39. Got it in the reading. But then I thought it was really easy and read it again: I started laughing, I didn’t see it at first.
And then I started laughing again because I was wrong again.
And now I’m laughing because it took me three chances to get it right, and all of them made me think I was right.

ps: sorry for my bad english, I’m still learning

40. Anonymous says:

I remember a very similar puzzle posted not long ago.

41. Jerry says:

A matter of seconds to get an answer, then about a minute of self criticism to check the answer.

42. Martin S Taylor says:

The really interesting (and much harder) puzzle is: what s the probability NO ONE gets the correct coat.

1. Twitty Boy says:

6/7 x 5/6 x 4/5 x 3/4 x 2/3 x 1/2?

43. Depends what you mean by “exactly”. For instance I have five toes, but I also have exactly five other toes.

44. Anonymous says:

Am I getting smarter, or are these getting easier?

45. Richard Dawkins says:

I find this one really hard. I know that God doesn’t exist – that’s easy, but this is like a tripe brainer.

1. Phillip Pullman says:

Yeah, me too. It’s doing my head in. Can anyone give me a clue?

2. Richard Dawkins says:

Sorry chaps, I meant triple brainer, not tripe brainer, but don’t worry about the God thing – i’m 110% certain abut that.

3. spiderabc1 says:

Richard and Phillip Not sure if you guy’s are kidding or not. I have a few numbers but doubting self. Out of 6 not 7. Damn probability.

46. John says:

2 seconds.

47. Nelis says:

Obvious … 5 seconds.

48. Instantaneous. So instantaneous that it took me a further few seconds to realise that there wasn’t a misprint, and that you hadn’t made a mistake.

49. I knew this one already. So it didn’t take me long. I really like it though!

50. Gerard says:

instant correct answer, under the extra assumption that the correct set of 7 coats was returned to the correct set of 7 friends.

51. For the first time in all your puzzles, I got this instantly. Yay!

52. Dharmaruci says:

If there are 30 diners whose coats are mixed up then our seven diners have a 6/30 = 1/5th chance of having all but one right.
But we do not know the size of the total restaurant this this is unanswerable as so often Mr Wiseman’s questions are.

1. Anon says:

….and if the question was “What is the capital of France?” the answer would be Paris…and by the way if there are thirty diners whose coats are “mixed up” the chances of one person getting their own coat back is 1/30. Do you think think there is a higher chance of six people getting their own coat back than one?

2. Nanny Mouse says:

Dharmaruci, you’re having a laugh, right?

3. Dharmaruci says:

Anon….I may not have the ability to explain in mathematical words but i trust my intuition. the more coats there are, the more chances there are to get some of them right, as if i had thirty guesses to say the capital of france then i’d be more likely to get the question right.

and, after a few coats have been returned wrongly the possibility of the remaining coats being right must rise obviously as the number or rights must balance the number of wrongs.

so 1/5th remains my anwer unless you can say otherwise/

4. Anon says:

Dhamaruci, There is a 6/30 chance of getting one coat only right in the example you give (1/30+1/30+1/30+1/30+1/30+1/30) not a 6/30 chance of “having all but one right”. Does tht convince you otherwise?

5. droz says:

You are so far off. Your intuition is not serving you well.

53. Mort says:

Guessed it instantly but went back to reread and check if there was something I missed. No loose ends!