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Everything posted by bushindo

  1. bushindo

    Suppose that there are 16 people standing in a straight line in a room. Each person is either a truth teller (always tell the truth) or a naysayer (always answer NO). You are in a different room, and your task is to determine the positions of all the truth teller in this line. You can not see the 16 people, as they are in the other room. You are allowed to take 'turn' to determine their persona. During each turn, you can address 1 single YES/NO question to ALL 16 people. The question will be relayed to the 16 people, and the total number of YES will be relayed back to you. Assume that numb
  2. bushindo

    Good work, k-man and araver. As usual, araver contributed beyond the requirement of the OP and taught me something new. I have another puzzle up that you both probably will enjoy.
  3. bushindo

    Suppose that you are in a room with 16 light switches, which are arranged in a line on the wall. Each light switch is connected to a unique lightbulb in another room. However, some of the 16 lightbulbs are burned out, which means that the 16 light switches you see consist of functional and non-functional switches. The light switches are currently all set in the OFF positions. It is also known that the 16 switches are arranged in such a manner that within any 7 consecutive light switches, there are an odd number of functional switches. Assume that setting a functional switch to the ON position
  4. bushindo

    And, it follows trivially Nice work! Once again you made a nice contribution to this topic. Thanks!
  5. bushindo

    Thank you for the puzzle. I liked the cycle-3 alternator very much. Made it different from any other problem I've seen so far. I pondered for a little while if you can narrow down the alternator too at the same time. Probably not, but still pondering. Thanks for working on the puzzle. This answer is entirely satisfactory and I'd consider the OP solved. The note you made at the end made me ponder about it a bit too, Araver's post notes that we could phrase the question in such a way that liars and truth tellers will give us the same answer. That should remove th
  6. bushindo

    Suppose that you encounter 4 people, each of whom is either a truth teller (always tells the truth), a liar (always tell lies), a random answerer (always answer randomly with 'Yes' or 'No'), or an alternator. The alternator, upon being asked the first question, will randomly choose to be a truth teller, a liar, or a random answerer and then answer the question with that persona. Every time the alternator is asked a question thereafter, he'll switch his current persona in the following cycle: truthteller -> liar -> random answerer -> truth teller ..., etc. For instance, if the alternat
  7. bushindo

    That's an interesting issue you bring up, I'll have to think about it some. I'm glad you like the puzzle. I greatly enjoy your insights on this puzzle. I have another one that is similar to this but with a twist. However, I'm going on vacation tomorrow and I probably won't be able check this board for the next few days, so I'll post the puzzle next week.
  8. bushindo

    Step 2 - Final adaptive questions (at most 3) -------------------------------------------- All but one case in the table have at least 1 sure position and at least 1 truth-teller among these positions. Target that one known truthteller (let's call him Oracle) with the rest of the questions. First, let's eliminate most of the cases. If there are 3 or more sure positions, then at most 4 unknowns remain. Therefore 3 questions targeted at the Oracle about 3 unknown positions give a total of 6 sure positions and the last can be deduced by whatever type (R or T) is missing from the (3R, 4T)
  9. bushindo

    Yes, we can't ask anyone what answer someone else will give to a particular question, unless we are sure that we are either asking about a truth-teller / liar or asking the question to a random answerer.
  10. bushindo

    Let's say that the liars and the truth tellers do not know what the random answerers would respond to any given question. I think the question is more challenging that way.
  11. bushindo

    I didn't think about summing a series neither. Do you mean summing the chance that John won given that Bill has 0 points, 1 points, and so on? I didn't think about it that way, although now I wonder why I didn't think of that before. Recursive functions are actually fit this problem quite well. It only takes a couple of lines as in the following pseudo-code. And yes, math is very cool!
  12. bushindo

    But I'm very far from actually writing such a successful strategy (at least the first part of it), so for now I guess I'm just bragging I eagerly look forward to this strategy =)
  13. bushindo

    I don't think that this question is "so poorly written that it renders the answer meaningless". I understand the puzzle just fine, as do The Genius of Genius, Dhanannjay Deo, rob_3, and I suspect many others. This is a very nice puzzle that demonstrates the elegance of recursive functions, and makes a valuable contribution to this Logic/Math puzzle forum. We have been through this before. I recommend that you read these excellent responses from and to your last post.
  14. bushindo

    A recursive code shows that
  15. bushindo

    Some clarifications please: 1) Does the fact that John is 20% better than Bill means that John is 20% more likely to win a point (e.g., John would on average win 6 out of every 11 points) ? 2) Does serving change the odd of a person winning the point? If so, how does that change?
  16. bushindo

    This is an extension of my last which was flawed but still had some value to the board thanks to contribution from araver. Suppose that you encounter 7 people, each of whom is either a truth teller (always tells the truth), a liar (always tell lies), or a random answerer (always answer randomly with 'Yes' or 'No'). You know that in this group of 7, there are 3 random answerers, 2 truth teller, and 2 liars, but you don't know which person is which. The puzzle is to identify the 3 random answerers with the following information: 1) You can only ask yes/no questions to 1 person at a time
  17. bushindo

    Good work, araver. You made some valuable contribution from an otherwise flawed puzzle. I'm glad you enjoyed it. I sure enjoy reading your proof. This is a good start, but it is virtually impossible to distinguish between mirror pairs. Suppose we narrow the problem to either possibility 2 or 3 in your example, it is virtually impossible to determine which is the correct one from there.
  18. bushindo

    Yes, if that happens, the truth teller's head will explode. Actually, more seriously, I just realized that I made a mistake in constructing this puzzle. Turns out in the worst case I can narrow the 6C3 = 20 possible configurations down to 2, but no further. Therefore a solution is not possible, at least not for me. If a mod can delete this topic, I'd appreciate it very much. Sorry to those who spent time thinking about the problem as it was posted.
  19. bushindo

    Suppose that you encounter 6 people, each of whom is either a truth teller (always tells the truth), a liar (always tell lies), or a random answerer (always answer randomly with 'Yes' or 'No'). You know that in this group of 6, there are 3 random answerers, 1 truth teller, and 2 liars, but you don't know which person is which. The puzzle is to identify the 3 random answerers with the following information: 1) You can only ask yes/no questions to 1 person at a time 2) You can ask the same question of different people, or address different questions to the same person. 3) Everytime you ask
  20. bushindo

    In the original setting of the problem: "In a future not so far way, Earth archaeologists find on a far away planet a fragment from a long lost civilization. This fragment involves an unknown operation *|*. Unlocking its secrets may lead to a breakthrough in understanding their civilization. " Please allow me to state (and add to the OP) 2 informal assumptions I made when posting the original setting of the problem: 1) We're talking about aliens so they *might* possess different insights than humans. 2) It's a fairly used operation on their world, so one *might* expect the symmetry /sim
  21. bushindo

    Also, can you please let me know how did you come up with such a complex formula? Do you have some standard method for these kind of problems or you are using some computer algorithm? Edit: added spoiler. Actually, the example above does work for 1 *|* 0; ( 1700 + 1309*(1) + 182*(1) + 985*(1) ) = 4176, which is equal to 2 modulo 2087. I did not notice the post that required the operation to be commutative. That can be easily fixed. This is one example that fits all 6 clues and is commutative
  22. bushindo

    Here's one solution that fits the existing 6 clues. Plenty more where this comes from =)
  23. bushindo

    Ah, that's it. Good work! Thanks for working on this problem.
  24. bushindo

    Excellent! Thanks for the explanation of your strategy. I'm glad you enjoyed it. I think something has gone amiss here. This solution does have a cycle of 60, so it properly takes y back to itself on the 60th power. The powers of P in between 0 and 60, however, don't match the data though.
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