Brain Teasers and Riddles

[Coach A]

Just some good brainteasers and logic problems. You don't have to answer them all. But lets see if we together can all get them eventually. Some are really easy. Others are kind of hard.


1. You drive to work at an average speed of 32 miles/hour. The trip back your average speed was 44 miles/hour.

Is it possible to determine what was your average speed for the whole trip? If so, what was it?


2. A train leaves for Chicago from Detroit. It is traveling 80km/hr. Half an hour later, a train leaves from Detroit to Chicago, it is traveling 60km/hour. Which train will be close to New York when they meet?


3.

Five friends are in a game room. There is a video game which 2 at a time can play. Is it possible to determine who is playing if the following is known? Either Kelly or Henry, or both, are playing. Either Ron or Victor, but not both, are playing. If Amy is playing, so is Ron. Victor or Kelly are either both playing or neither is. If Henry is playing, then so are Amy and Kelly. If it's possible to know for sure, which 2 are playing?

4. In an island there are 2 type of people, knaves and knights. Knaves always lie, and knights always tell the truth.
You encounter 2 people. Person A and Person B.

A: "I'm a knave or B is a knight".
B doesn't say anything.

Determine what A is and what B is (Knight or Knave). If not possible to determine, say so.


5. You are given 3 boxes. 1 box contains a million dollars, the others is empty. If you pick correctly which box has the million dollars, you win the million dollars.

Suppose you pick Box 1. The host then opens Box 3 to show you it's empty, then he asks you if you want to change your choice to Box 2. From a probability aspect, would it matter if you changed your choice or not?


6. You are in a classroom full of 20 students. Everyone has a paper. The teacher says exchange papers with everyone that is shorter than you. How many total exchanges will there be?


7.. You have 2 ropes and a box of matches. You want to measure 60 minutes exactly using only the ropes and the box of matches. Here is what you know:

a) Each rope takes exactly 80 minutes to burn end to end.
b) The rope itself is made out of different material throughout the rope. So, it's rate of burning is not constant throughout the rope.

Can you measure exactly 60 minutes? If so, how?


8.. A King tests 3 logicians. He has 8 hats. 4 Black and 4 White. He asks the logicians to close their eyes. While that is being done, he hides 2 of the hats behind him, and puts 2 hats on each logician. When the logicians open their eyes, they can only see the hats of the other 2 logicians, but can't see their own hats nor the hats the king hid.

The king then starts asking them if they can tell which hate they have on:

Logician A: "No Idea"
Logician B: "Don't know"
Logician C: "Not sure"
The King gets mad, and asks around 1 more time
Logician A: "I still don't know"
Logician B: "I've figured it out"

And he gets it correct. What hats was B wearing and why?

[sixerfan82]

5. You are given 3 boxes. 1 box contains a million dollars, the others is empty. If you pick correctly which box has the million dollars, you win the million dollars.

Suppose you pick Box 1. The host then opens Box 3 to show you it's empty, then he asks you if you want to change your choice to Box 2. From a probability aspect, would it matter if you changed your choice or not?


From a probability standpoint yes.

By the host eliminating 1 choice, you can choose between 2 that it might be and 1 that it isn't, therefore you get an extra 33.3 percent chance,



6. You are in a classroom full of 20 students. Everyone has a paper. The teacher says exchange papers with everyone that is shorter than you. How many total exchanges will there be?

My guess is 0. Both people can't be shorter than another, and if you're the same height there is no exchange.

[GatorKid117]

I always liked this one when I was younger: Connect all of the dots using 4 straight lines w/o lifting your pencil.


o o o


o o o


o o o



My guess is 0. Both people can't be shorter than another, and if you're the same height there is no exchange.

That's what I was thinking. I'll look over them more when I get the time.

Edit: Lame, the dots aren't spaced out. If you want to try it, it's much easier if you space em out in a square.

[AirGauge23]

1. 38mph, no?

[Coach A]

1. 38mph, no?
No



From a probability standpoint yes.

By the host eliminating 1 choice, you can choose between 2 that it might be and 1 that it isn't, therefore you get an extra 33.3 percent chance,

Correct





My guess is 0. Both people can't be shorter than another, and if you're the same height there is no exchange.

Correct

[GatorKid117]

In an island there are 2 type of people, knaves and knights. Knaves always lie, and knights always tell the truth.
You encounter 2 people. Person A and Person B.

A: "I'm a knave or B is a knight".
B doesn't say anything.

Determine what A is and what B is (Knight or Knave). If not possible to determine, say so.

Well, if I understand this correctly, no one can say they are a knave. Knaves would have to say they are knights while knights would have to say they are knights as well b/c they always tell the truth. Thus, A is a knave. The or is kinda throwing me off though. I guess I would say B is a knave too because he would be lying about B as well.

[Mikaiel]

1. You drive to work at an average speed of 32 miles/hour. The trip back your average speed was 44 miles/hour.

Is it possible to determine what was your average speed for the whole trip? If so, what was it?

37.05

[Coach A]

Well, if I understand this correctly, no one can say they are a knave. Knaves would have to say they are knights while knights would have to say they are knights as well b/c they always tell the truth. Thus, A is a knave. The or is kinda throwing me off though. I guess I would say B is a knave too because he would be lying about B as well.

No



37.05


Correct

[Doomsday Dallas]

37.05


explain.

[Mikaiel]

explain.

You can't do (32+44) / 2 because that would mean you were going at 32 for the exact same time that you were at 44. Let's say you have to drive for 40 miles and you drive the 1st 20 miles at 5 miles/hour and the other 20 miles at 195 miles/hour. Your average speed is gonna be A LOT smaller than 100 miles/hour.

d = distance home-work
t1 = Time between home-work going at 32 miles/hour
t2 = Time between work-home going at 44 miles/hour

speed = distance / time

So :

32 = d / t1
t1 = d / 32

44 = d / t2
t2 = d / 44

x = average speed

x = 2d / (t1 + t2)

x = 2d / (d/32 + d/44)

x = 2d / [d (1/32 + 1/44)]

x = 2 / (1/32 + 1/44)

x = 37.05

[WADE MONEY]

In an island there are 2 type of people, knaves and knights. Knaves always lie, and knights always tell the truth.
You encounter 2 people. Person A and Person B.

A: "I'm a knave or B is a knight".
B doesn't say anything.

Determine what A is and what B is (Knight or Knave). If not possible to determine, say so.

There are only four cases.

Case 1: Suppose both A and B are knaves. Then one part of A's statement is true, even though B is not a knight. Since his statement has an "or", only one part needs to be true for A to be telling the truth. Hence A is telling the truth. But this contradicts the fact that he's a knave and is supposed to lie. Hence case 1 is impossible.

Case 2: Suppose A is a knave and B is a knight. Then again, A's statement would be a true statement, which contradicts his job, as a knave, to lie. Hence case 2 is impossible.

Case 3: A is a knight, B is a knave. Now both parts of A's statement is false; i.e. A is not a knave and B is not knight. Hence A is lying, and this contradicts the fact that he is a knight. Hence case 3 is impossible.

Case 4: A is a knight, B is a knight. Now A's statement is correct, since B is a knight. This makes sense because A should be telling the truth. Hence both A and B are knights, and this case is the only possibility.

[Coach A]

Case 4: A is a knight, B is a knight. Now A's statement is correct, since B is a knight. This makes sense because A should be telling the truth. Hence both A and B are knights, and this case is the only possibility.

bingo!

[iamgine]

7.. You have 2 ropes and a box of matches. You want to measure 60 minutes exactly using only the ropes and the box of matches. Here is what you know:

a) Each rope takes exactly 80 minutes to burn end to end.
b) The rope itself is made out of different material throughout the rope. So, it's rate of burning is not constant throughout the rope.

Can you measure exactly 60 minutes? If so, how?

We know you can measure 40 minutes by lighting both ends of the rope. So first you light one rope at two ends and the other rope on one end. Then when the first rope burn out, you'll know 40 minutes has passed and the second rope only has 40 more minutes to burn out. If you immediately light the second rope at the other end, that will measure half of 40 minutes which is 20 minutes. That way 40 minutes + 20 minutes = 60 minutes.

[EroticVanilla]

From a probability standpoint yes.

By the host eliminating 1 choice, you can choose between 2 that it might be and 1 that it isn't, therefore you get an extra 33.3 percent chance.
I've never bought that though process, I don't understand why just because C has been eliminated as an option it would have any effect on A or B. It seems that after you have eliminated C the choice between A or B would be an independent event from C.

Someone who is good in math could probably explain this, but really from what I can tell it should have no effect.

[InspiredLebowski]

A cowboy rides into town on Friday, stays three days, leaving on Friday? HOW!? OMGZ!

[Mikaiel]

I've never bought that though process, I don't understand why just because C has been eliminated as an option it would have any effect on A or B. It seems that after you have eliminated C the choice between A or B would be an independent event from C.

Someone who is good in math could probably explain this, but really from what I can tell it should have no effect.

Let's say you picked box A. At 1st, your chance to get the million dollars is 33.3% (1/3).

That means you have a 66.6% chance of picking the wrong box. Which means there's a 66.6% chance the million dollars is either in box B or C.

Since the host tells you it's not in box C, then there's a 66.6% chance it's in box B, so you should switch.

EDIT : Let's say :

Box A : Nothing
Box B : Nothing
Box C : $1,000,000

There's only 3 possible scenarios :

- You pick box A : The host has no choice but to eliminate box B. Switch = win

- You pick box B : The host has no choice but to eliminate box A. Switch = win

- You pick box C : The host will either eliminate box A or B. Switch = fail

So if you switch, you win 66.6% of the time.

And just 33.3% if you don't.

[Coach A]

We know you can measure 40 minutes by lighting both ends of the rope. So first you light one rope at two ends and the other rope on one end. Then when the first rope burn out, you'll know 40 minutes has passed and the second rope only has 40 more minutes to burn out. If you immediately light the second rope at the other end, that will measure half of 40 minutes which is 20 minutes. That way 40 minutes + 20 minutes = 60 minutes.

yep :cheers:

[pete's montreux]

A cowboy rides into town on Friday, stays three days, leaving on Friday? HOW!? OMGZ!

Ummmmmmmm, the cowboy was Doc Brown? 1.21 JIGGAWATTS!

[EroticVanilla]

Let's say you picked box A. At 1st, your chance to get the million dollars is 33.3% (1/3).

That means you have a 66.6% chance of picking the wrong box. Which means there's a 66.6% chance the million dollars is either in box B or C.

Since the host tells you it's not in box C, then there's a 66.6% chance it's in box B, so you should switch.
Your explanation wasn't helpful, but looking it up on Wiki showed me why it made sense.

Though from further reading there seems to be a flaw in your explanation as well, read about it here (http://en.wikipedia.org/wiki/Monty_Hall_problem#Probabilistic_solution)

Edit: Granted in the parameters given in this scenario your right

[InspiredLebowski]

Ummmmmmmm, the cowboy was Doc Brown? 1.21 JIGGAWATTS!
I don't know about all that but I just downloaded a Stevie Ray at Austin City Limits, part from 83 and part from 89. Good ****ing shit.

[pete's montreux]

I don't know about all that but I just downloaded a Stevie Ray at Austin City Limits, part from 83 and part from 89. Good ****ing shit.

The horse's name is Friday, derrrrrrrrrrrrrrrrr.

Can't go wrong with Stevie Ray, really. Unless you get some of his late 80's shows where he's high and drunk and plays like shit.

[plowking]

8.. A King tests 3 logicians. He has 8 hats. 4 Black and 4 White. He asks the logicians to close their eyes. While that is being done, he hides 2 of the hats behind him, and puts 2 hats on each logician. When the logicians open their eyes, they can only see the hats of the other 2 logicians, but can't see their own hats nor the hats the king hid.

The king then starts asking them if they can tell which hate they have on:

Logician A: "No Idea"
Logician B: "Don't know"
Logician C: "Not sure"
The King gets mad, and asks around 1 more time
Logician A: "I still don't know"
Logician B: "I've figured it out"

And he gets it correct. What hats was B wearing and why?

I'm guessing Logician B looks around and sees that his two other partners are wearing 2 black hats each, or 2 white hats each, thus he determines that he is wearing 2 of the same color as well.

EDIT: Then Logician B can say which color hat he thinks he's wearing, thus giving the other two the answer as to what they're wearing since they know he'd only speak up if he saw them wearing the same colored hat. So if Logician B says "they are both wearing 2 white hats each", they could determine that the King has 2 black hats behind his back, since they could have a look at Logician B and see he is wearing 2 black hats.

Am I anywhere on the right track?

[plowking]

And for 3 I'm gonna guess Amy and Ron.

[Coach A]

I'm guessing Logician B looks around and sees that his two other partners are wearing 2 black hats each, or 2 white hats each, thus he determines that he is wearing 2 of the same color as well.

EDIT: Then Logician B can say which color hat he thinks he's wearing, thus giving the other two the answer as to what they're wearing since they know he'd only speak up if he saw them wearing the same colored hat. So if Logician B says "they are both wearing 2 white hats each", they could determine that the King has 2 black hats behind his back, since they could have a look at Logician B and see he is wearing 2 black hats.

Am I anywhere on the right track?

Well if that was the case, he would know right away the first time he was asked. But he didn't....you are kind of one the right track...

[Coach A]

And for 3 I'm gonna guess Amy and Ron.
No

[Coach A]

2,3, and 8 remain the only ones un-solved!

[Bosnian Sajo]

A women shoots her husband, holds him under water for 5 minutes, and then finally hangs him. Later that evening, they go out an enjoy a lovely dinner.

How can this be?

[EroticVanilla]

A women shoots her husband, holds him under water for 5 minutes, and then finally hangs him. Later that evening, they go out an enjoy a lovely dinner.

How can this be?
She took a picture of him.

BTW did anyone get shot-up in you school.

[IlliniFan]

A women shoots her husband, holds him under water for 5 minutes, and then finally hangs him. Later that evening, they go out an enjoy a lovely dinner.

How can this be?
I see what you're trying to do but this little riddle doesn't work.

[Bosnian Sajo]

She took a picture of him.

BTW did anyone get shot-up in you school.


Nope, apparently the kid will come once the police leave the school, although the police are spying on him 24/7 so I doubt anything will happen.

[Coach A]

3 remain unsolved

[gino0o]

Victor and Kelly

[Jakeh008]

Repost the last 3 so i dont gotta find what they are

[Coach A]

Victor and Kelly

Correct!



#2 and #8 are the only unsolved ones

[sirkeelma]

8.. A King tests 3 logicians. He has 8 hats. 4 Black and 4 White. He asks the logicians to close their eyes. While that is being done, he hides 2 of the hats behind him, and puts 2 hats on each logician. When the logicians open their eyes, they can only see the hats of the other 2 logicians, but can't see their own hats nor the hats the king hid.

The king then starts asking them if they can tell which hate they have on:

Logician A: "No Idea"
Logician B: "Don't know"
Logician C: "Not sure"
The King gets mad, and asks around 1 more time
Logician A: "I still don't know"
Logician B: "I've figured it out"

And he gets it correct. What hats was B wearing and why?

Because Logician A and Logician C wears the same hat.

[RoseCity07]

This word starts with an "e" and ends with an "e", and usually has one letter in it. What's the word?

[plowking]

This word starts with an "e" and ends with an "e", and usually has one letter in it. What's the word?

I'm guessing envelope? lol

[RoseCity07]

I'm guessing envelope? lol

Yes. It's a pretty easy one to google.

[gino0o]

This one is really hard.

Four perfect logicians sat around a table that had a dish with 11 oranges in it. The chat was intense, and they ended up eating all of the oranges. Everybody had at least one orange, and everyone knew that fact, and each logician knew the number of oranges that he ate. They didn't know how many oranges each of the other ate, though. They agreed to ask only questions that they didn't know the answers to.

Their queries are as follows:

A: Did you eat more oranges that I did, B?

B: I don't know. Did you, C, eat more oranges than I did?

C: I don't know.

D figured out how many oranges each person ate.

How many oranges did each person eat?

[iamgine]

This one is really hard.

Four perfect logicians sat around a table that had a dish with 11 oranges in it. The chat was intense, and they ended up eating all of the oranges. Everybody had at least one orange, and everyone knew that fact, and each logician knew the number of oranges that he ate. They didn't know how many oranges each of the other ate, though. They agreed to ask only questions that they didn't know the answers to.

Their queries are as follows:

A: Did you eat more oranges that I did, B?

B: I don't know. Did you, C, eat more oranges than I did?

C: I don't know.

D figured out how many oranges each person ate.

How many oranges did each person eat?
Well, considering they had to ask one another, that means A, B & C all ate less than 5 oranges.

D could easily know if he ate 8 oranges. Greedy bastard.

[Mikaiel]

This one is really hard.

Four perfect logicians sat around a table that had a dish with 11 oranges in it. The chat was intense, and they ended up eating all of the oranges. Everybody had at least one orange, and everyone knew that fact, and each logician knew the number of oranges that he ate. They didn't know how many oranges each of the other ate, though. They agreed to ask only questions that they didn't know the answers to.

Their queries are as follows:

A: Did you eat more oranges that I did, B?

B: I don't know. Did you, C, eat more oranges than I did?

C: I don't know.

D figured out how many oranges each person ate.

How many oranges did each person eat?

A = 1
B = 2
C = 3
D = 5

[Mikaiel]

Well, considering they had to ask one another, that means A, B & C all ate less than 5 oranges.

D could easily know if he ate 8 oranges. Greedy bastard.

B said "I don't know". So he didn't eat just one orange. He would have known it was impossible for him to have eaten more than A so he would have said no. So he ate at least 2.

Same logic --> C ate at least 3.

And since 5 is the only number that comes up only once if you try to list all possibilities, D = 5.

[Coach A]

Because Logician A and Logician C wears the same hat.
Then how wouldn't he know the first time he was asked :hammerhead:

[sixerfan82]

I've never bought that though process, I don't understand why just because C has been eliminated as an option it would have any effect on A or B. It seems that after you have eliminated C the choice between A or B would be an independent event from C.

Someone who is good in math could probably explain this, but really from what I can tell it should have no effect.

Here is the general idea.

You have 3 options, A B and C. One of them is correct and 2 of them are wrong, meaning you have a 33.3% chance of picking the correct answer.

After picking 1 of the 3 choices, the host reveals one of the 'bad' doors, leaving you with 1 good and 1 bad, of which your door could be either.

The host asks you if you'd like to switch.

By NOT switching, you are keeping yourself at a 33.3% chance(aka 1 of 3 doors)

By switching, you are inherently picking the door the host reveal AND the new door, meaning you are picking 2 doors against 1, aka a 66.6% chance.

This DOESN'T mean you are picking the right door, it just improves your chances.

[Rockets(T-mac)]

Here is the general idea.

You have 3 options, A B and C. One of them is correct and 2 of them are wrong, meaning you have a 33.3% chance of picking the correct answer.

After picking 1 of the 3 choices, the host reveals one of the 'bad' doors, leaving you with 1 good and 1 bad, of which your door could be either.

The host asks you if you'd like to switch.

By NOT switching, you are keeping yourself at a 33.3% chance(aka 1 of 3 doors)

By switching, you are inherently picking the door the host reveal AND the new door, meaning you are picking 2 doors against 1, aka a 66.6% chance.

This DOESN'T mean you are picking the right door, it just improves your chances. What I don't get is how does that improve the chance of the prize being in that door if you switch? You said that if you switched doors, that your chance becomes 66.6%, but that doesn't make any sense because the host already said that one of the doors has nothing in it. Each door has 33.3% chance of having the prize when you eliminate one that means the chance switches from 33.3% to 50% not 66.6%, for you to have 66.6% you would need 3 choices, but since one door has been eliminated you only have 2 choices.

[EroticVanilla]

What I don't get is how does that improve the chance of the prize being in that door if you switch? You said that if you switched doors, that your chance becomes 66.6%, but that doesn't make any sense because the host already said that one of the doors has nothing in it. Each door has 33.3% chance of having the prize when you eliminate one that means the chance switches from 33.3% to 50% not 66.6%, for you to have 66.6% you would need 3 choices, but since one door has been eliminated you only have 2 choices.
Here (http://en.wikipedia.org/wiki/Monty_Hall_problem#Popular_solution) is a link explaining how you increase your odds. It took a visual for it to make sense to me.

[Rockets(T-mac)]

Here (http://en.wikipedia.org/wiki/Monty_Hall_problem#Popular_solution) is a link explaining how you increase your odds. It took a visual for it to make sense to me.
Thanks I think I get it now. Since you only had 33.3% chance of getting the right door in the first place, and you learn that one of the doors is empty, then you know that it's better odds to switch.

[raiderfan19]

logician B peaked but didnt want the king to know that so he pretended to not know the first time. Sneaky bastard. ;)

[raiderfan19]

actual answer logician B has a black and a white hat on and the hidden hats are a white hat and a black hat. Logician A and C both have 2 of the same color(either color works). Thats not enough for logician B to fighure out what hes wearing in the first round because he could have 2 of either color on himself. However, after the first round logician knows that he cant have 2 of either color hat on or one of the other logicians would have figured it out in the first round.

Good riddle. It took me a few minutes.

[raiderfan19]

also the answer to number 2 is they will both be in chicago when they meet because they both left from detroit to go to chicago and the second one is going slower so the 2nd one wont catch the first one until it stops in chicago.

[Coach A]

Good job raiderfan you got them both


:cheers:

All have been solved now!

[raiderfan19]

Good job raiderfan you got them both


:cheers:

All have been solved now!
You got any more? I love riddles.

[Kobr]

A man pushed his car to a hotel and lost his fortune. What happened?

[GatorKid117]

A man pushed his car to a hotel and lost his fortune. What happened?

Playing monopoly?

[Kobr]

Playing monopoly?

Yeah.

[Kobr]

Suppose you live in a nation where families only want to have boys. Each couple in this country continues to have children until they finally give birth to a boy. If a couple has a girl, they have another child. If they have a boy, they stop having any more children. What then is the proportion of boys to girls in this fictional country?

[acerlghp]

Suppose you live in a nation where families only want to have boys. Each couple in this country continues to have children until they finally give birth to a boy. If a couple has a girl, they have another child. If they have a boy, they stop having any more children. What then is the proportion of boys to girls in this fictional country?
Still 1:1?

[SourPatchKids]

1. Paul was walking in the middle of an empty road and saw a piece of gold and a piece of meat lying in the middle of the road. He took the meat and left the gold. Why?

2. There were two sexy ladies bathing nude in the river while a heterosexual man was walking by. Why did the man not look?

[Dave3]

2. There were two sexy ladies bathing nude in the river while a heterosexual man was walking by. Why did the man not look?
He was blind.

And for 1. The gold was stuck to the ground or something?

[timlush]

also the answer to number 2 is they will both be in chicago when they meet because they both left from detroit to go to chicago and the second one is going slower so the 2nd one wont catch the first one until it stops in chicago.

Also, it doesn't matter where they are going or how fast, when they "meet", they are in the same place, so they are the same distance from anywhere (New York, LA, etc...)