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 - Firstly, this wasn't "stolen" from the movie 21, it's a really old puzzle. The answer is switch. The door you originally pick has a 1/3 of having the car behind it. The other 2 have a 2/3 chance between them. So once one of the doors has been opened, the other door now has a 2/3 chance. Imagine if there were 100 doors and one car. You pick a door, and then Monty opens 98 of the other doors to reveal donkeys. Would you keep the door you picked, or switch? Obvious now, isn't it? 2 - I can't work this out. 3 - Ask either of them "which path would the other guard so leads to paradise?" The truthful guard would point to the path leading to death, knowing that's what the lying guard would say. The lying guard would also point to the path leading to death, because he'd lie about what the truthful guard would say. 4 - OK, unless I read the question wrong, all 3 have a dot on their hat. So, the wise man who wins (call him A) thinks this way: If my hat didn't have a dot, then men B and C would both see a hat with a dot and a hat without a dot. So both would know they MUST have a dot, because otherwise the other 2 would see to blank hats and know THEY had dots. So because none of the other men have spoken up, man A knows he has a dot. This riddle of course assumes that the wise man is actually wiser than the other 2, cos in theory all 3 would reason exactly the same way, and it would just be a matter of who gets it first. 5 - Same as question 1 6 - T - ten
heres a riddle..an immature riddle... There once was a man from Norway Who got his balls stuck in a doorway Along came his wife With a big butcher knife And now they lay in the hallway
1. it doesn't matter if u stay or not, they didn't give u any more info then b4 other than the fact that the host may be nervous, in which cash 2/3 u should stay(i agree with jikek)
2.i could prob figure it out but am not in the mood 2 wast the time
3.just say "if u were the other guard, what road whould u pick" both will say the same thing and thus giving u the right path
4. 2 answers 1)study expressions 2) they didn't say u can't look at the hat while they r putting it on or othewise i.e. a mirror
Number 1 and 5, you should switch, you can look at it this way there are 3 doors, lets explore every possible situation Door 1 and Door 2 are goats while Door 3 is a car (PRETEND YOU DIDN'T KNOW THIS BEFORE PICKING) Lets say you pick Door 1, they eliminate Door 2 because its a goat, if you had switched, you would've gotten a car. Lets say you didn't pick Door 1, and instead picked Door 2, then they would eliminate Door 1 (since they eliminate a Door without the car), should you switch, you would get the car If you understood everything so far, Choosing Door 1, and 2 then switching gets you the car. If you had chosen Door 3 (the one with the car), and they eliminate one of the doors and you switch, then you would get a goat. Lets see our results, OUT OF THREE POSSIBLE PATHS YOU COULD HAVE GONE THROUGH, IF YOU HAD SWITCHED, YOU WOULD HAVE GOTTEN THE CAR TWO OUT OF THE THREE PATHS. Netting you a 66.67% as opposed to the 33.33% chance of getting the car if you did not switch.
I think 4 could have an answer that makes more sense and is easier to understand. Me and my friend came up with an answer. This works if the men go in the room one by one or all at the same time. Since the aide placed 3 hats, each with a dot on the mens heads, and the rules specify that they cannot communicate or touch the hats, which makes it difficult to determine from one of their possitions who has the hat. However if one of the wisemen simply tilted his head and the hat fell off, he didn't touch it or communicate with the others and he can now find his hat with a dot on it, whilst not breaking the rules.
Another way would work assuming they were all three in the room at the same time. If one wiseman glanced at the other two, which looking is not communication so still adhearing to the rules, he would notice that they both had dots. Using that he could safely assume he had a dot on his by breaking down the rules. The king never said that at least 1 hat would be blank, that then opens the possability that his hat can also have a dot on it. And with the rule of no communication or touching the hats he could then assume that they all had dots and tell the king he had a dot. Had he guessed wrong he would have been killed, and had he broke the rules he would have been killed. But being a wiseman he was able to safely determine that by chance he too had a dot.
you should switch because change changes everything, meaning okay what u chose is a mystery but with one of the choices you didnt make being obvioulsy incorrect that leaves you with 2 choices, from far back it looks like a 50/50 chance, but really it is a 2/3 1/3 chance, with you now being given another choice the obvious conclusion is to change because the teacher or game show host has no choice but to let you know one of the other ones are incorrect which thus gives leaves you with two thoughts one do i have the correct answer/did i pick the right door or did the teacher or game show host not say b was incorrect you show you what was behind the other door because it is the correct choice, but like i said change changes everything, id switch
3 you ask the guard if the other guard lies every once in a while, the liar would say yes and the truth tell would say no because the liar lies all the time not just once in a while
4 its quite simple actually, none of them figure all three of them will have dots so when the aid puts the hats on them they look at each other. its a,b,c question a looks at b and c sees they both have dots, b looks at a and c and notices they both have dots, c then looks at a and b and sees they both have dots. its all about the first person who realizes that no one spoke up meaning that they both see dots on the other peoples hats. in other words since they didnt think all three of them had dots, so with A,B,C noticing that the other 2 ppl have dots but if the other two arent speakin up then i must have a dot too then speaks up and claims i have a dot on my hat.
4. That if its a black hat you can not put a dot in it so the king had a hole right at the top but it was very small tiny a tiny bit bigger than the ant and he could just feel the wind on just that spot on his head so thats how he knew
Ah, for Q1, it may look 1/2, but it's not. There is a 2/3 chance that you picked a bad prize, so when he reveals the bad prize, if you change, the odds are somehow 2/3 in your favour. Trust me, it was on the BBC. Try it with some stones, a coin, three cups and a friend. Two times out of three, you win.
