BrainDen.com - Brain Teasers

# bushindo

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## Everything posted by bushindo

1. Let's say that you and 19 other prisoners are on a death row. The warden gives you and your fellow prisoners a chance to win your freedom through a game. The game is as follows, 1) When the game starts, the warden will blindfold all 20 prisoners and arrange them in a circle. 2) The warden will put on each prisoner's head either a RED or a BLACK hat. The warden will choose the color for each prisoner by flipping a fair coin. 3) The warden will then remove the blindfolds. Every prisoner will be able to see the hats on the other 19. Each person will not know the color of his own hat. There
2. ## Quick Draw Aces

This is what I did
3. ## Quick Draw Aces

This is a really nice puzzle.
4. Brilliant and elegant solution, CaptainEd. It also has the bonus of generalizing easily to higher dimensions. I'm in awe.
5. Here's a method for generalizing the solution to the OP to any arbitrary number of dimension
6. Minor correction to the last paragraph in the spoiler.
7. Here's a discussion of why the 15 people won't all abstain during the same turn.
8. Here's an alternative method to solve the 3-D problem in the OP. Unlike plasmid's elegant solution, this one uses conditional translation and rotation. I would like some clarification. When you say 'generalize to higher dimensional space', do you mean 1) Given a random number generator that uniformly produce numbers between 0 and 1 and a description of ANY high dimensional region (e.g., a sphere in 3D, a circle in 2D, a triangle in a plane embedded within 3D space as described in the OP, etc.), produce a method that uniformly sample coordinates within the described high dim
9. I apologize for posting a solution that is the same as plasmid. I read the spoiler title which said that the method is 'kludgey', and assumed that interleaving digits on numbers with infinite digits isn't kludgey, so his solution can't be the one I was thinking of. You know what people say about decomposing the word 'assume'. I feel that way right now.
10. It is possible to uniformly generate numbers in a 3-dimensional region from a single draw of a random number generator without discretizing the 3-d volume into small, finite regions.
11. Maybe i'm missing something somewhere...
12. Apparently you and I both had bugs in our codes. My bug has no other explanation besides a sloppiness on my part. Mea culpa. This board never fails to amaze me. Good work, superprismatic.
13. Great work, k-man. The exhaustive proof is a very nice bonus. This board never fails to amaze me =)
14. Ah, I see I was sloppy in phrasing this problem. By random speakers, I mean that these people randomly answer Yes or No to any question. That should bring the puzzle back along the intended line.
15. You are an explorer traveling in the Amazon rain forest. You need to explore a particularly dangerous region of the forest, so you drop by a local village of Tourguidians to hire a native as an expedition guide. The Tourguidians are the best guides to the Amazon forest. However, they are divided into 2 sub-groups: the truth tellers and the random speakers. The truth tellers will always respond to questions with the truth, while the random speakers will randomly tell the truth or lie to any question. There are 11 Tourguidians in this particular village, 6 of whom are truth tellers, and 5 ar
16. This is a joke, right?
17. I just tested this new strategy. It works very well. Again, a generous interpretation of 'tools in the average household' is required.
19. Anyone see a mistake? Good work, EventHorizon. Nice job going beyond the call of duty. As a prize, you get both your freedom, and the 10th rat for a pet .
20. Suppose that you are a prisoner on the death row. The warden offers you a chance for freedom through a game. The game is as follows: 1) The warden shows you an array of 30 identical beakers, each containing an identical amount of clear fluid. 2) You are told that 28 beakers contain simply water. 2 beakers (you don't know which ones) contain deathly poisons which can render death in exactly 1 minute. 3) You are offered 10 live rats and 10 empty flasks. You can take turn testing for poison using the rats. 4) At each turn, you must mix fluids from any number of the 30 beakers into one
21. For a generous interpretation of 'tools in the average household'
22. Please note that there is no requirement that p(x) be a distribution with limited support (finite domain). The examples of the uniform distribution and binomial distribution that I gave have finite domain, but the gaussian example has unbounded support (-infinity to infinity). The gaussian distribution can potentially generate any number from -infinity to infinity, though certain numbers tend to show up more often. This is just as well, because while the OP states that any number from -infinity to infinity may be generated by this mysterious density distribution, it doesn't say that all number
23. Some comment on this approach
24. I think the fact that we can not produce a single percentage for the performance of this strategy is telling. It may be suggesting that the performance is approaching 50% from above, similar to how .9999999.... is approaching 1 from below.
25. Is it possible for the 2 generated number to be the same?
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