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?

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,

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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.

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.

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.

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

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.

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.

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.

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.