1.You are a contestant on the game show Let's Make a Deal, and emcee Monty Hall has a game for you to play. On stage are three huge doors, and he informs you that hidden behind one of the three doors is a brand new sports car, behind another is a donkey, and behind another is 400 pounds of bananas. (This may seem obvious, but your goal is to get the car, not the donkey or the bananas.) He asks you to choose one door, and you will win the prize behind that door. You choose, but before he reveals what you have won, Monty reveals what's behind one of the doors you did not pick, and it's not the car. Before revealing what lies behind the remaining two doors, he makes you one final offer: if you wish, you may switch from your choice to the other remaining door. The question is: Should you switch, should you not switch, or does it matter?
2.A professor tells her assistant that she dined with three people last night. She also tells him that the sum of the three people's ages is twice the secretary's own age and that the product of the three people's ages is 2,450. Then, she asks him to tell her the ages of the three people. After a while, the assistant tells the professor that he doesn't have enough information to solve the problem. She agrees and adds that she is older than all three people with whom she dined. The assistant, who knows her age, promptly gives the professor the correct ages. The question is: What are the ages of all five people in this story?
3.You stand at a fork in the road. Next to each of the two forks, there stands a guard. You know the following things: 1. One path leads to Paradise, the other to Death. From where you stand, you cannot distinguish between the two paths. Worse, once you start down a path, you cannot turn back. 2. One of the two guards always tells the truth. The other guard always lies. Unfortunately, it is impossible for you to distinguish between the two guards. You have permission to ask one guard one question to ascertain which path leads to Paradise. Remember that you do not know which guard you're asking -- the truth-teller or the liar -- and that this single question determines whether you live or die. The question is: What one question asked of one guard guarantees that you are led onto the path to Paradise, regardless of which guard you happen to ask?
4.An old king is about to die and he has no offspring to inherit the crown. So he summons the three wisest men from his kingdom and puts them to a test. He tells them that he is about to put them in a room and have his aide put a hat on each of them. Each hat may or may not have a dot on it, but at least one hat will have a dot. They may not touch the hats, nor communicate in any way. The first one that correctly identifies whether his hat has a dot will become the next king. If he is wrong, or if he breaks the rules, he will be killed. Then he sends all three wise men into the room.
The king then tells his aide to put dotted hats on all three.
A few minutes later one of the wise men returns and announces proudly that he has a dot. How did he know?
(complicated answer, try it only if you are a genius)
5.Suppose you're taking a multiple-choice quiz. One question has three choices. Not knowing the answer, you randomly guess A. The instructor then announces that C is incorrect. Should you switch to B before turning in your paper?
1. Is always 50 percent. I know that in the movie "21" were this riddle came from, the guy said that you should change doors. This was a dumb riddle that had nothing to do with probability change. 21 is a good movie but that part was just plain dumb because it had nothing to do with math and everything to do with spychology (that is what I have come to understand.) If he did have something to do with math then the movie was wrong and just trying to sound intelligent. Movies have a tendency of doing stuff like that.
Ok well I was wrong abotu number one. Most of the people who figured this one out are probally only going by what happened in the movie. The real challenge for everyone who got it right is to explain why you have a better chance by changing doors. I already cheated by looking up the answer and I regret what I said about number 1 completely.
Yes, I do understand that they explain the answer in 21, I did not pay clsoe attention to the reason and figured it was just a movie trick. Boy how stupid I feel right now. >.<
I'll only answer three and four, because the others are answered already.
3. "If I asked the other guard which path leads to paradise, then which path would he point me down?" Take the opposite path. 4. Wiseman A put himself in Wiseman B's position, assuming A doesn't have a dot. B would say "If C had a dot, and I didn't, then he would immediatly know that he had the dot, since neither A or B has a dot. But since C isn't declaring victory, then I have a dot on my hat." A, seeing this, would know that B would have thought of this and answered immediatly, but since he didn't, A must have a dot as well. (it's confusing, i know)
1. Doesn't matter. After one door is elimited, there are two left. 50%-50% chance. The past has no effect on present chances. If I were to flip a coin 10 times and get heads, it wouldn't be any more likely to get tails on the elenventh flip. And way to steal this from 21... 2. There are six people in this story: the three diners, the secretary, the professor, and the assistant. 3. If I were to ask that guy, what would he say? Take the other route. - * + = -. 4. Zerlock explained it better than I could. 5. Same as 1. 6. E N T. First letter of the numbers 1-10.
if you asked for number three they would say "he is" no matter what you say so for three you would say "if i want to go to paradise what path would the other gaurd tell me to go?" umm lets say right:death leftaradise the liar would say " the other gaurd would tell you to go right" which is not rue because he's the liar gaurd so the thruth teller would say: "he'd tell you to go right" which is correct because the other gaurd is the liar and your talking to the truth teller so ask that awnser to any gaurd and they will tell you the wrong awnser so if any of the gaurds say left for example go right! or left wich evere they dont say.... HA!
