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 and 5 are quite literally have the exact same problem, just worded differently. Just take the three doors one. There are three doors. One of them has a car, so a 1/3 chance. Lets say you chose door number one. He reveals door #3, with no car. The odds are now 1/2 in either door. So, it really doesn't matter if he switches or not. The same goes for the Multiple choice quiz. Just replace door with answers A,B, and C.
1:It doesn't matter at all. 2:It switches her to him, I don't know answer but I think that's part of how to solve it. 3:Which one is the liar? 4:Lose it and tell one of them what dot there is? 5:No 6: one two three four five six seven eight nine ten
divine, all good guesses but sadly, 3 and 4 where wrong 3 would be a possible solution but you still do not know which path to take, and if you read number 4 than you will see if they are wrong, they die
K 3: Ask the guard which one leads to paradise, but liar or truthful he would want to kill you, then take the opposite? 4:I'm not gonna try that again.
4. Atleast one has a dot on it, correct? It's simple. If the men went in turns, it would play out like this. 1: He sees a white hat and a dotted hat, not knowing if their is more than one, he cannot answer. 2: Sees a dotted hat and a white hat, can't answer. 3: Sees two white hats. With the process of elimination, he knows he has a dot.