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  1. Hey everyone, I'm always in the hunt for some clever riddles. I'll offer up some that I've enjoyed, and then open it up to anyone else to chime in. If we could, I'd appreciate if we could limit ourselves to true logic-puzzle/math riddles, no joke riddles or lateral thinking riddles. (someone can create another thread for that, if they so choose) Also, please "spoiler"-out any hints, solutions, or explanations. Alrighty, now that we've got that out of the way, here are a couple of my favorites: in roughly ascending order of difficulty (though that is fairly subjective): 1. Describe the set of all points on the earth such that walking south for a mile, then walking east for a mile, then walking north for a mile will render the walker back at the starting point. (assume a perfectly spherical earth) 2a. A man tells you he has two children, and that he has a daughter named Alice. What is the probability that he has two daughters? (assume boys and girls are each born with 50% probability) b. A different man tells you he has two children, and that he has a daughter named Stacey who was born on a tuesday. What is the probability that he has two daughters? And if it is different, than part (a), why is this? 3. If there are N cars (with random starting points) traveling in the same direction at constant, (strictly positive), and unique speeds on an infinitely long 1-lane road until the proximity of the car in front mandates that a car slows to the match the speed of the car in front, after an infinite amount of time elapses, what is the expected number (as a function of N) of "clumps" of cars? 4. Three perfect logicians are forced to play the following game: each logician is given a hat that is either white or black. They cannot see their own hat, but they can see the hats of the other two players. No information is exchanged. After a brief time, they are escorted into separate interogation rooms where they have the opportunity to say either "white" or "black" or remain silent. If everyone remains silent, they are all executed. Similarly, if any one person says a color other than the color of his hat, they are all executed. However, if at least one of them correctly identifies their hat color, and no one incorrectly names a color, they are all given a million dollars, and sent on their way. What should they do to maximize their chances of survival? Assume nothing about the distribution of white and black hats, but you can assume that the fact that they are all perfect logicians is common knowledge. 5. You are standing in a room with three doors marked A, B and C. Two of them lead to Hell, and one to Heaven. There are 3 identical looking men, wearing hats marked 1, 2 and 3. One of them will answer truthfully to every logically answerable yes/no question. One will lie to every logically answerable yes/no question, and one of them will answer randomly to any question. (All of them will answer randomly to an unanswerable question.) All three people have perfect information about eachother, and perfect information about the doors. Unfortunately, they are somewhat uncomfortable with English, and while they will understand your questions, they will respond only with "Hi" and "Ho" meaning 'yes' and 'no', but you don't know which means which. (They may even mean different things to different people!) You may ask up to 3 questions, each one directed to a single person (though you may ask a single person multiple questions). What should you ask to guarantee you find the door to Heaven? examples of unanswerable questions: What is the value of 2+2? (not a yes/no) What would the person who answers randomly say if I asked them...? (not knowable) Good luck! If anything is unclear, I'll try to be diligent about clarifying any questions that crop up over the next few days. Can't wait to see some of your riddles!
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