# Very tricky logic question

Discussion in 'Odds & Ends' started by Claudius, Feb 26, 2011.

1. ### ClaudiusProfessional

Joined:
Jun 4, 2009
Messages:
1,031
Suppose the manager of a company has 6 letters to send. He gives his secretary 6 letters and 6 envelopes and asks her to put each letter into the correct envelope.

The secretary, being sneaky, puts the letters randomly into the 6 envelopes (assuming 1 letter per envelope).

What is the probability that exactly 5 letters were put into the correct envelopes?

Joined:
Jun 8, 2009
Messages:
2,136
Location:
UK
0,00139 % ?

3. ### DeShaunBanned

Joined:
Aug 22, 2010
Messages:
2,831
The sixth letter (and the only remaining envelope) would be correctly matched, if the other five already were. It would be impossible to match "exactly" five out of six correctly.

Last edited: Feb 26, 2011
4. ### borg number oneLegend

Joined:
Oct 30, 2007
Messages:
7,819
Location:
Houston, Texas
I would think the answer is 1/6 raised to the 6 power, since you have a 1/6 chance with each envelope and you have to get all six envelopes right if you are to get 5 right. How could you get 5 right and not 6? So, my answer would be .166 x .166 x .166 x .166 x .166 x .166= .0000214335.

Last edited: Feb 26, 2011
5. ### ClaudiusProfessional

Joined:
Jun 4, 2009
Messages:
1,031
DeShaun is correct...

6. ### Steady EddyHall of Fame

Joined:
Jul 19, 2007
Messages:
3,283
Location:
Arizona
The probability is 0%.

7. ### GetBettererHall of Fame

Joined:
Apr 19, 2010
Messages:
1,630
Location:
Mesa, AZ
Here's another question: Who killed Hamlet's father, (Old) Hamlet?

8. ### PolarisHall of Fame

Joined:
Mar 28, 2005
Messages:
2,319
Bingo! We have 2 winners.

9. ### SentinelBionic Poster

Joined:
Jan 21, 2008
Messages:
49,515
Location:
Telly, watching AO.
Isn't Hamlet the name of the dog that Hagar's son owns ?

10. ### EndLyRookie

Joined:
Jun 25, 2008
Messages:
249
even though the answer has already been stated, I took a different approach by first taking 1/6 then assuming that is right, then there would be a 1/5 chance to get the next one correct so and the next 1/4 and so on so (1/6)(1/5)(1/4)(1/3)(1/2) = 0.1375% if I'm not mistaken, but obviously if you got the first 5 right, then the last would be correct so you can't get 5 correct. only 4 max... big DUH moment to myself

11. ### fruitytennis1Professional

Joined:
Jul 23, 2009
Messages:
1,090
Location:
I wish i knew
Bob and Rob are going to school.
Bob runs half the time and walks half the time
Rob runs half the distance and walks half the distance
Assuming they both walk and run at the same speed who will reach school first?

12. ### borg number oneLegend

Joined:
Oct 30, 2007
Messages:
7,819
Location:
Houston, Texas
You are right, we are on the same page. Yet, I ran that calculation again. It's not 1/6 raised to the 6th power as I thought (if you're trying to see the probability of getting all 6 right, not 5). It is as you stated, 1/6 x 1/5 x 1/4 x 1/3 x 1/2 (or you could also add the x 1 with the 6th envelope). Yet, when you do the math, I get that the probability of getting all 6 envelopes correct is .001389, so the probability of getting all 6 is much less than 1%. Very interesting. This is tricky, because it is impossible to get exactly five right. Great thread.

Last edited: Feb 27, 2011
13. ### Steady EddyHall of Fame

Joined:
Jul 19, 2007
Messages:
3,283
Location:
Arizona
Bob would get there first.

Bob goes at his higher speed (running) half the time. Does Rob spend half his time running as well? No, he spends less than half his time running. Rob walks half the distance, and runs half the distance. Since walking is slower, he'll spend more time walking to cover the same ground as running. He is then walking over half the time. So Bob makes better time.

14. ### fruitytennis1Professional

Joined:
Jul 23, 2009
Messages:
1,090
Location:
I wish i knew
Yep. There is a more difficult version where you add in bogus variables and something else but I'm too lazy to make that up.

15. ### AndresG.O.A.T.

Joined:
Apr 21, 2005
Messages:
12,527
Location:
Mar del Plata, Argentina
If the company is a big company, the chances of the secretary being fired rises to 89.7%

If the company is not so big, the secretary has a rough 43% chance of keeping her job.

On the other hand, if the secretary is the manager's wife, there's a 77% chance all she'll get is a slap on the wrist and a smile. And of course, the manager won't get laid that night.

So that'd be it, give or take

16. ### BobFLHall of Fame

Joined:
Jun 11, 2007
Messages:
3,676
Location:
Orlando
This is the correct answer. It doesn't get any simpler than that:

1/6! = 1/(6x5x4x3x2x1) = 0.001388888888888888888...

17. ### fruitytennis1Professional

Joined:
Jul 23, 2009
Messages:
1,090
Location:
I wish i knew
No. If you get 5/6 envelops right you obviously got the 6th envelop right too. So its not possible to get exactly 5/6 right.

18. ### borg number oneLegend

Joined:
Oct 30, 2007
Messages:
7,819
Location:
Houston, Texas
Thats' the right calculation for getting all six envelopes right though. It's 0.0014 for getting six right (rounded, basically a tenth of 1%). Yet, to get five right is technically impossible, since if you have five right, you must necessarily have six right.

Last edited: Feb 27, 2011
19. ### BobFLHall of Fame

Joined:
Jun 11, 2007
Messages:
3,676
Location:
Orlando
Please...that's irrelevant for this math problem. That was not the question. The question was about probability and they said 5/5 just to add some additional trickiness The answer given in #2 is correct.

20. ### BobFLHall of Fame

Joined:
Jun 11, 2007
Messages:
3,676
Location:
Orlando
What do you mean by "technically impossible"? Everything is possible (think Verdasco winning the slam) and it is all about probability. It can be super-low or very high but it is always a possibility. Some of you guys are focusing on irrelevant part of this question. Of course that if you match 5 you will match 6 but that is not important at all. I mean, it is important to get the right number becasue at least 5 out of 10 people will use 5! instead of 6! and that is the main and only trick about this question. It is 1 divided by 6 factorial. I am 100% sure (probabilty that I am not sure is 0 ).

21. ### borg number oneLegend

Joined:
Oct 30, 2007
Messages:
7,819
Location:
Houston, Texas
What I mean is that if you want to look at it technically, you can't get exactly 5 right. You can get 4 right, or 6 right, but not 5 right. So, the right answer does not leave room for the assumption that yes, to have 5 right, you must necessarily have all six envelopes correct. So, to have exactly five right, and not that sixth one as well is impossible. The probability is 0.0% for 5, which answers the call of the central, question posed by the OP. I am 100% sure and so are you, because we're both saying the same thing lol.

22. ### BobFLHall of Fame

Joined:
Jun 11, 2007
Messages:
3,676
Location:
Orlando
Hahaha, that is 100% true! You are smart guy and you saw that 5 matched = 6 matched hence you saw the main 'trick' about this math-problem

23. ### ClaudiusProfessional

Joined:
Jun 4, 2009
Messages:
1,031
Alright, here's new one.

A man stares at a portrait and says "Brothers and sisters I have none, but this man's father is my father's son.". Who is he staring at?

24. ### Steady EddyHall of Fame

Joined:
Jul 19, 2007
Messages:
3,283
Location:
Arizona
It's his son.

Take the phrase "my father's son", that is the man himself because he has no siblings. Since "my father's son" = "me" replace those three words with the one word. "this man's father is me", then it's clear that the man must be his son.

25. ### GetBettererHall of Fame

Joined:
Apr 19, 2010
Messages:
1,630
Location:
Mesa, AZ
Sentinel:
I'm talking about Shakespeare's play.

26. ### ClaudiusProfessional

Joined:
Jun 4, 2009
Messages:
1,031
Jeebus....
Okay, here's something that may take awhile.

Which of the following words does not belong?

act bone came deified eerie gore later maid no nuclear oodles pot use wary

27. ### Steady EddyHall of Fame

Joined:
Jul 19, 2007
Messages:
3,283
Location:
Arizona
Taking the first letter of each word we have: a b c d e g l m n n o p u w. That's so close to the alphabet that I think I'm on to something. There's two n s in a row, so is the 2nd n the one that doesn't belong? I'll guess it's "nuclear".

28. ### ClaudiusProfessional

Joined:
Jun 4, 2009
Messages:
1,031
^No. Think about the structure of each word.

29. ### GetBettererHall of Fame

Joined:
Apr 19, 2010
Messages:
1,630
Location:
Mesa, AZ
It's bone.

If you switch the first 2 letters of each word, you get another word except for bone.

30. ### PolarisHall of Fame

Joined:
Mar 28, 2005
Messages:
2,319
No, unfortunately, you are wrong here. The question clearly specified that you had to find the probability of getting exactly 5 correct. This means 5 correct and 1 wrong. That combo is impossible.

If the questioner had asked for the probability of getting at least 5 correct, then your answer would be fine.

31. ### borg number oneLegend

Joined:
Oct 30, 2007
Messages:
7,819
Location:
Houston, Texas
Good catch there. That must be it.

32. ### dlkHall of Fame

Joined:
Nov 26, 2009
Messages:
4,448
Location:
Indy
I'm a simpleton, so my basic logic tells me the two words that don't have a vowel as the second letter. Therefore: Act & Use

33. ### BobFLHall of Fame

Joined:
Jun 11, 2007
Messages:
3,676
Location:
Orlando
What is the correct answer then?

34. ### PolarisHall of Fame

Joined:
Mar 28, 2005
Messages:
2,319
Correct answer is what DeShaun and Eddy gave. The probability of getting exactly 5 correct is zero.

35. ### ClaudiusProfessional

Joined:
Jun 4, 2009
Messages:
1,031
GetBetterer got it.

Now this:

ample crib dress gender grate here may mute pound peach tract vex

36. ### GetBettererHall of Fame

Joined:
Apr 19, 2010
Messages:
1,630
Location:
Mesa, AZ
That one's easier than the first.

It's crib.

All the other words can get some sort of prefix and still make another letter (adhere, immute, impound, impeach, intract etcetera).

37. ### fruitytennis1Professional

Joined:
Jul 23, 2009
Messages:
1,090
Location:
I wish i knew
Genius!

Here is a well known riddleish thingy
A farmer was going to town with a fox, a goose and a sack of corn. When he came to a stream, he had to cross in a tiny boat, and could only take across one thing at a time. However, if he left the fox alone with the goose, the fox would eat the goose, and if he left the goose alone with the corn, the goose would eat the corn. How does he get them all safely over the stream?

38. ### dlkHall of Fame

Joined:
Nov 26, 2009
Messages:
4,448
Location:
Indy
Won't answer cause I know the answer, but these guys will tear this one up.

39. ### RoddickAceHall of Fame

Joined:
Jul 2, 2007
Messages:
2,636
Tell the goose to fly/swim over while he brought the corn over, go back and tell the goose to fly/swim back, then bring the fox, and tell the goose to fly/swim to the other side again?

We'd need a pretty obedient goose though lol.

edit: WAIT got it, he can carry the goose over and get back to get the corn over, but on his way back, bring the goose back, and bring the fox over, then go back and get the goose over.

Last edited: Feb 27, 2011
40. ### fruitytennis1Professional

Joined:
Jul 23, 2009
Messages:
1,090
Location:
I wish i knew
Actually really close...
The goose cant fly/swim though.

41. ### dlkHall of Fame

Joined:
Nov 26, 2009
Messages:
4,448
Location:
Indy
Yeah, 4 trips.

42. ### ClaudiusProfessional

Joined:
Jun 4, 2009
Messages:
1,031
How about this:

Take the goose over, comeback and take the corn over, take the goose back, bring the fox over, and then come back to bring the goose..

43. ### ClaudiusProfessional

Joined:
Jun 4, 2009
Messages:
1,031
There are 20 people in an empty, square room. Each person has full sight of the entire room and everyone in it without turning his head or body, or moving in any way (other than the eyes). Where can you place an apple so that all but one person can see it?

44. ### dlkHall of Fame

Joined:
Nov 26, 2009
Messages:
4,448
Location:
Indy
On top of one person's head?

Joined:
Jun 4, 2009
Messages:
1,031
Yes 10char

46. ### dlkHall of Fame

Joined:
Nov 26, 2009
Messages:
4,448
Location:
Indy
Yeah, I'm okay with the visual ones, it's the code breaker one's that I'm too simple for.

47. ### BobFLHall of Fame

Joined:
Jun 11, 2007
Messages:
3,676
Location:
Orlando
Yeah, the same thing as putting the label on one person's forehead. Everyone can read it but the person with the label

48. ### fruitytennis1Professional

Joined:
Jul 23, 2009
Messages:
1,090
Location:
I wish i knew
"This statement is false"

49. ### fireiceNew User

Joined:
Feb 19, 2010
Messages:
93
Let's try one more. This probably won't take you that long, BUT...

A man was born before his father, killed his mother, married his sister, and was considered perfectly normal by everyone he knew. Why?

50. ### fruitytennis1Professional

Joined:
Jul 23, 2009
Messages:
1,090
Location:
I wish i knew
Everyone he knew didn't know this?