Let’s play a little game.  Imagine taking 4 playing cards out of a deck.  Two of them are red and the other two are black.  We mix them up and place them face down on the table.  I am going to ask you to turn two of the cards face up.  If they are both the same (as in, if both of them are red cards or both of them are black cards) then you win.  Otherwise, I win.  Is that fair?

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 theKindle (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. Mike says:

Good grief…

2. joshie says:

10 seconds

3. Alison says:

Not fair!

1. Ricksta says:

“As ever, please do NOT post your answers, but do say if you think you have solved the puzzle and how long it took.”

4. Julie says:

totally unfair! You be the one who turns the cards over 😛

1. Ricksta says:

“As ever, please do NOT post your answers, but do say if you think you have solved the puzzle and how long it took…”

5. Astariel says:

Solved after 30 seconds (I think)

6. Roland says:

Depends on how much you pay me when I win and how much I have to pay you when I loose 😉

1. Dave says:

2. -M- says:

Yep!

3. Dave says:

The spelling on the other hand…

4. Ricksta says:

Nice one, Roland. I can see I’d have to get up very early in the morning to get one past you! Respect.

5. Lose is spelled lose, not loose, stop extending this ghastly ignorant misspelling until it enters the dictionary, PLEASE!

Mad G thanks for that…nothing more horrible than spelling ‘lose” as”lo……”….aaaagh! I can’t even write it!

7. Since I teach a class called “Introduction to Counting and Probability”, I was done by the time I had finished reading the question. I’d be really interested to learn what people’s intuition tends to say about this problem, before they do any calculations.

1. Robert says:

I tend to be very cautious with any intuitions on this site. But yes, my stupid brain DID, for just the briefest moment try to convince me of a fair game. We really need an update to patch our outdated frontal lobes. Damn you professor for yet again pointing out that as a species, we really are dumb! 🙂

2. My intuition was that the game couldn’t be fair, but, like Robert, I did wonder for a fraction of a second whether it might be.

8. SofARMaths says:

Unfair on me. A few seconds.
Intuition would probably say fair if it wasn’t for the fact this is a Friday Puzzle.
In any case probability is hard to fathom rationally? e.g. What is the probability that in a room of 30 people that two people share a common birthday?

1. Robert says:

I’ve heard this one before, and it’s somewhere in the regions of 2/3. Evolution is even worse than Microsoft at releasing bugfixes.

2. If you consider the number of *pairs* of people in a room of 30 people, the answer might seem a little more intuitive!

3. -M- says:

Wow, I count 5 !!!SPOILERS!!! up to here!

Come on! spoilers are not fair!

4. Dave's mate says:

Not fair. Only 2 out of 6 possible pairs will be in my favour. (thats 6 spoilers)

9. Anonymous says:

Got it yesterday

10. dave says:

So 6 possible pairs of which 2 are in my favour. Err…. No thanks

1. jumbleguitar says:

Oh my god, DO NOT POST YOUR ANSWERS. It’s literally harder to break this rule than it is to follow it.

2. Dave's mate says:

To be fair dave did not post the answer, just the workings out

11. Martin says:

Inanely simple. 5 seconds.

1. Dave says:

Pride comes before a fall. I suspect you only think you got it.

2. Anonymous says:

Yeah, stop being so smug.

12. Arnaud Gagneux says:

Immediately

1. Dave says:

I got it quicker than that!

14. Anonymous says:

Did everyone just forget this week about the part where he says not to post answers?

1. dharmaruci says:

that is part of the puzzle.why would mr wiseman post an issue he is having difficulty with if he does not want an answer? perhaps it is an ego thing, he does not want to be seen to ask for help.

but the internet is compassionate and wise. people will see through his attitudes and help him anyway.

15. dharmaruci says:

this is how i approached the problem. if the two i turn up are the same (say these are the REDS), then the two that are not turned up are also the same. It is exactly the same win situation if i had tuned up the BLACKS and the REDS remained face down.

that is two 50/50 win situations. so my average must be half of that, so 25% chances of a win.

1. Dave says:

I love how you feel compelled to ignore the request not to post answers and prove how clever you are…

…and then you get it completely wrong. Priceless.

2. Erinia says:

3. Not only do you try to spoil things by completely ignoring the “do not post answer” request, you then go and show a complete and utter ignorance of basic probability theory. You must feel very silly indeed… but there again I doubt your ego will allow it.

4. Niva says:

dh – What an epic fail for an answer. First, ignoring the instructions, then using screwy reasoning to reach a wrong answer.

5. BigBrain says:

Nice trolling Sir!

16. edgar1975 says:

Not fair.

1. -M- says:

6

2. Dave's mate says:

Who do we appreciate

17. Experience-fed intuition patch says not fair. Checked with brute force all-outcomes analysis. 2 min. Not fair.

1. -M- says:

7

18. pdurrant says:

Not fair if we’re betting at even odds. < 10 seconds.

1. -M- says:

8

19. Anonymous says:

Solved after 10 seconds.

20. Anon says:

It depends what you mean by fair…..maybe I like loosing….maybe I feel sorry for Richard and am happy for him to win…

21. mittfh says:

Immediate first thought: fair.

Very closely followed by: hang on, this is a Friday puzzle. The nature of Friday puzzles is such that what initially sounds fair is bound to be unfair and advantagous to him.

Shortly after: scribbling out combinations to confirm my hypothesis.

I think in this particular case, what Richard would probably expect us to refrain from is not so much stating fair / unfair, but why in mathematical terms, rather than “Past performance indicates Richard will never set a fair test in a Friday puzzle”.

22. NickC says:

If the deck is ‘marked’ I would play

23. -M- says:

First I thought: too easy.
So I thought: let’s check.
Then I thoought: Well that’s an unexpected answer!

Checking took me about a minute

1. Dave says:

Yes. I suspect a lot of the smug “I got it before I was born” folks posting above never got to that second stage, and thus have an incorrect answer.

2. Ricksta says:

@Dave – I suspected that much quicker than you did.

3. Nanny Mouse says:

I suspected that before I was born

4. Dave's mate says:

I’m just about to be born. Give me a couple of moments for the umbilical cord to be cut and then I’ll answer the question

5. pretty sure my mom and dad were suspecting it as i was being conceived.

24. Terry Hornsby says:

not fair at all! It took me 30 secs to work this one out

25. Lazy T says:

If roulette and the tote are fair this game fair.
I got it before Dave (and Dave his wife)

I did not have any intuition or preconceived ideas at all. Maybe that’s why it took me an excessively long two minutes to get an answer and check it.

26. Hilary says:

Took about a second and seems so obvious I am probably wrong.

27. jumbleguitar says:

Perhaps Richard should move the “do not post your answers” thing to the top of the puzzles instead of the bottom. I can only assume people are skipping past it. There cannot be this number of idiots reading this blog.

28. Duncan says:

Only took a few seconds to check my intuitive guess was right.

29. JazerNorth says:

30. Mike Torr says:

Lose (verb, transitive and intransitive): to fail to win.
Loose (verb, transitive): to shoot an arrow.

Thank you, and goodnight.

1. Anonymous says:

I love a good non-sequitur

31. pigomatic says:

Monte, are you listening?

32. bombast says:

Guessed the answer immediately. I wasn’t sure of my answer so I took a few minutes to carefully reason it out, and convinced myself I was right.

33. Rodney says:

I think it’s unfair that people are posting their answers when they were asked not to.

34. spiderabc1 says:

It’s worth visiting this site just for the comments. Shall be thinking the puzzle over later. (With a deck of cards and dunce hat.)

35. spiderabc1 says:

I came by a similar one in DB’s TOTM book. Can’t see the logic in it but maths is not a strong point of mine. Shall revise.

36. Mickey D says:

15 secs

37. Farhk Yoo says:

If Richard wanted to find the answer to this question, why doesn’T he Google it like any normal person?

38. Are we allowed to cross the river or take a short-cut across the corner of the field, or do we have to count the number of steps on the way before we get there? I think the answer is 47, but only if you’re allowed to use a mirror.

39. John says:

Like most commenters I saw the answer in seconds but took a minute or two to check the odds. Unlike many commenters I can read and follow instructions as well as doIng Maths so won’t be giving my answer here!

40. FirstTimeCaller says:

I spent about a minute working out all possible outcomes.

41. but you didn’t tell us what suits the cards are. how can we possibly figure it out?

42. Gail Hatton says:

Like it, but easy

43. Anonymous says:

after gathering my thoughts it took me about 10 seconds to calculate the odds. But I quite agree with Roland, it depends on how much I have to pay to play and on how much I win if anything ^^

1. Jerry says:

The puzzle does not ask whether you would play or not, only whether the game is fair, i.e. whether he has the same probability of winning as you do.

44. Took me about 10 seconds to calculate the odds, though I quite agree with Robert 😉

45. Nigel says:

Less than 8 seconds

46. It doesn’t matter what the odds are, the House Always Wins.

47. Jerry says:

under a minute

48. Of course it’s fair – you’ve told us how it works up front. Now will you win more than I do, that’s a different question…

49. Rachel Day says:

Less than a minute.

50. Only had to wake up for a split second to see the game is FAIR since there are equal chances for win or lose, of COURSE. How could anyone even think otherwise is a mystery. However since this is a site full of smartypants Mad Hatters no doubt they will say this is too obvious blah blah blah the answer is otherwise blah blah blah.

I am but a Dormouse so who am I to argue.

Someone drank my tea AGAIN.

51. bentnine says:

cue blond joke

52. Ian says:

Cheers, Richard 🙂 Well, this one looks remarkably simple and I got the answer immediately; which leads me to wonder if I’ve actually missed something and it’s cleverer than I’ve realised….

1. I’ll try this…

54. Eddie says:

O I see. You can leave a response, or trackback from your own site.

55. Simple simon says:

Normally I not too quick getting the answer. This time it was a mere few seconds, so maybe I am missing something…..

56. Dormouse says:

OK I found my tea, got my mind back and used a pencil and paper and laboriously drew every option. Unfair!! very unfair!! Time including pencil point licking, three minutes.

57. Remind me what was the question?

1. Lazy T says:

2 B or not 2 B (ie 2 Red) that was the question.
The question now is do I fancy a glass of red with my lunch?

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