Question: There are 100 prisoners lining up to go to jail. Each prisoner is wearing a hat that is either black or white. The prisoners don't know their own hat color, just the hat color of those in front of them in line (the first prisoner in line can't see anyone's hat and the last prisoner can see everyone's hat except their own). Starting from the back, one of the guards asks each prisoner what color their hat is. If they are correct they get to go free but if they are wrong they go to jail.If the prisoners get to discuss a plan, how can at least 99 of them be saved?
Answer: The back prisoner will yell "black" if there is an odd number of black hats in front of him and "white" if there is an even number of black hats in front of him. The next prisoner will then count the number of black hats in front of him and if it was odd and is now even, or vice versa, then that person knows what color their hat is. The next person then knows their hat color based on what the people before them said and how many black hats are in front of them. In this way the front 99 prisoners will know their hat color and will be set free. The prisoner in the back who goes first has a 50 percent chance of being set free.
Question: There is a basket full of hats. 3 of them are white and 2 of them are black. There are 3 men Tom, Tim, and Jim. They each take a hat out of the basket and put it on their heads without seeing the hat they selected or the hats the other men selected. The men arrange themselves so Tom can see Tim and Jim's hats, Tim can see Jim's hat, and Jim can't see anyone's hat.
Tom is asked what color his hat is and he says he doesn't know.
Tim is asked the same question, and he also doesn't know.
Finally, Jim is asked the question, and he does know.
What color is his hat?
Answer: The hat is white. If Tom doesn't know his hat color then the other two men's hats cannot be both black otherwise he would know his is white. When Tim doesn't know his hat color either, that means Jim's hat could not be black otherwise Tim would have to know his hat was white to fulfill the information discovered through Tom's answer.
Question: Two men find an old gold coin and want to have a coin toss with it to decide who gets it. The only problem is the coin is heavier on one side so it comes up heads more than tails. What is a fair way for the men to toss the coin and decide who gets the coin?
Answer: They just have to flip it twice. They call the first toss either heads or tails, then the next toss they automatically pick the opposite (ie if one man calls heads on the first flip, he automatically picks tails on the second and vice versa). If they both win one toss (a tie) out of the two, they just have to repeat until one of them wins both tosses.
Question: A man in New York City has $10. He spends $6.50 on flowers, and $3 on lunch (hot coffee and a hot dog). He then gets on the subway which will take him 7 stops for 50 cents. But he is forced to get off of the subway just 5 stops away from where he began.
Why is this?
Answer: When he gets on the subway it is 6 stops away from the end of the line (end of the track). So when it reaches this point it begins to work backwards. So when it goes back one stop he has traveled 7 stops but is only 5 away from where he began.
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