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bushindo

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Everything posted by bushindo

  1. bushindo

    I forgot to say that at the beginning of step 4, the Easter Bunny then removes everybody's blindfold. That shouldn't detract from the puzzle, though, as that fact is implied in later details. The Easter Bunny does draw random hat color for everybody based on independent coin flips. Please assume that the reindeers are sentient and can write. No cheating using ipads, reindeer eyes, Rudolph's big red nose, etc. At least that's what I think. It is possible to find a strategy with positive expected winning. The strategy does not require much charting or computation. In fact, you j
  2. bushindo

    In this economic downturn, Santa is having a bit of financial trouble preparing for his yearly trip. There are a couple of outstanding lawsuits against Santa Inc. for broken roofs and busted chimneys; the North Pole Toy-Assembling Elves Union (NPTEU) is demanding a raise; prices for toy raw materials are skyrocketing; and Mrs. Claus just blew the family budget on a bunch of iPads for the reindeers. Knowing this, the Easter Bunny is offering Santa a chance to make money through a game. The game is as follows: 1) The Easter Bunny is the game host. Santa and his 9 reindeers (Dasher, Dancer, Pr
  3. bushindo

    Just read Jobe17's solution. Wish I thought of that. Thanks for the superbly constructed puzzle. I really enjoy it. It was devilishly challenging/fun to work through.
  4. bushindo

    Well, if that's the case, then here's a strategy,
  5. bushindo

    More clarification: Suppose that an infected member is in a room with a non-infected unconscious member, presumably he would need an excuse to touch the unconscious person. What would the infected member say about the result of his scan? What happens when you connect two conscious crewmember together, one of which is infected, and the other being non-infected?
  6. bushindo

    Some clarification please: 1) The OP indicates that video and audio communication are available between you and all areas. That seems to imply that you can simply pose questions to the crew members and have them respond. Does that mean that the non-infected crew members will act as truth tellers? Would the infected members then act as random answerers? 2) Suppose that a crew member is infected, and then is cured by a serum. Would he know that he was infected last round?
  7. bushindo

    Nice solution. Clear and insightful as always.
  8. bushindo

    Welcome to the den. This solution assumes that we know exactly what X is, so that we can distinguish between X, 2X, 3X, and so on. That is not true. We know that the odd coins are heavier than the normal coins, but we don't know how much heavier. Also, please put your solution in spoiler tags next time. Also, apparently I mistyped the number of coin piles in this puzzle. There should be 9 piles (not 10 piles) of coins total, each pile with 10 coins. 7 piles are normal coins, and 2 piles are fake coins. The remaining parameters are the same. Sorry about that. That correction should make the
  9. bushindo

    Suppose that you have 10 piles of coins. Each pile has exactly 10 coins. Eight piles consist of normal coins, which weight 100g each, and the remaining two piles consist of fake coins, each of which is heavier than 100 g. All the fake coins have identical (and unknown) weight. You are given a digital scale, which can take any number of coins and return the total weight. Please identify the 2 piles with fake coins in only 2 weighings. EDIT: I apologize for the double post. I have no idea why this puzzle shows up twice as two topics. If any mod sees this, please delete this duplicate topic
  10. bushindo

    This puzzle has been partially solved by araver. The strategy still isn't as optimal as it could be, so for the sake of completeness I'll clarify the remaining challenge. Given the problem in the OP, find a strategy that has a winning rate that is 75% or higher.
  11. bushindo

    This is excellent. The strategy above is more optimal than mine, which can only win 1/16 times (256 times that of random guessing). Good work.
  12. bushindo

    Yes, I did not ask for the optimal strategy on purpose. You're very sharp. This puzzle is more like an ah-ha type of puzzle. It does not, and should not, require excessive charting or computing. EDIT: I apologize for the double post. Something seems to be wrong with my browser.
  13. bushindo

    Yes, I did not ask for the optimal strategy on purpose. You're very sharp. This puzzle is more like an ah-ha type of puzzle. It does not, and should not, require excessive charting or computing.
  14. bushindo

    The next Greedy strategy tries to win the middle cases (w=3,w=4) and group everyone errors in the losing cases: Depending on z choose: z=0 - Red* z=1 - Blue z=2 - Red z=3 - abstain z=4 - Blue z=5 - Red z=6 - Blue* *-same chances if instead of color, abstain is chosen. This greedy strategy has a 2*(7+35)=84 out of 128 winning cases = 65.625% It wins for B={1,3,4,6} instances. Its not so good compared to 112 out of 128=87.5% for the perfect-Hamming strategy (if we knew the distribution of hats as well), but not far from that either. Depending on z choose: z=0 - Blue z=1 -
  15. bushindo

    Suppose you and 11 friends are invited to play a game. The game is as follows: 1) All of the 12 participants are blinded folded and have either a red or blue hat placed on each of their heads. 2) The host then randomly arrange them in a circle in such a way that each participant can only see the 4 neighbors immediately to his/her left and the 4 neighbors immediately to his/her right. 3) The blindfolds are removed, and each participant can look at the hat of his 4*2 = 8 immediate neighbors. 4) Each person must then write down a guess for his/her hat. Each guess must either be 'red'
  16. bushindo

    The quote 'nominees always guess with the odds' is a bit ambiguous and makes it difficult to compute the winning rate of this strategy. Can you clarify? If everyone abstain, that would be considered a loss for the participants.
  17. bushindo

    Thanks for the comments, araver. They are insightful as always. I have another challenging puzzle of this type that you might enjoy. I'll post that puzzle up after my current puzzle 7 Britishmen, 7 Frenchmen, and 7 Italians is solved. That shouldn't take long . Stay tuned.
  18. bushindo

    . And sorry for the accidental reposts, something goofy when I logged in.... Sorry to hear about the ridiculous charts I'd like to note that each participant are put into a different room, so he can not hear that has transpired with his fellow participants.
  19. bushindo

    7 Britishmen, 7 Frenchmen, and 7 Italians are invited to play a cooperative game. The game is as follows: 1) The game host puts each of the 21 participants into a separate room, blindfolds him, and places either a red or blue hat on his head. 2) The host then tells each participant the following: how many red hats are there total among each of the other two races, and how many red hats total among the participant's other 6 countrymen. For instance, if the host is talking to a Frenchmen, he would say to the Frenchmen, "Among the 7 Italians, there are a total of x red hats. Among the 7 Bri
  20. bushindo

    That would be here
  21. bushindo

    I agree with araver that probabilistic methods can not beat deterministic methods. With some thoughts, it seems that 4/32 as the winning rate is the best we can do with this situation. It is possible to extend the deterministic ideas to more general cases, but for this case with 5 players, it is not necessary and the puzzle is not as challenging as I intended to be. Puzzle making is quite tough . Let me go back and reconstruct this puzzle.
  22. bushindo

    Great! Now we can show that we have positive expected winnings. The bonus question about the optimal strategy is still open though. I'd like to hear about your N=4 strategy.
  23. bushindo

    Suppose you and 4 friends are invited to play a game. The game is a variation of the hat puzzle with monetary incentive. The game is as follows: 1) You and your 4 friends each pay 10 dollars to participate in the game (50 dollars total). 2) All participant is then blind folded and have either a red or blue hat placed on each of their heads. 3) The host then randomly arrange them in a circle in such a way that each participant can only see the 1 neighbor immediately to his/her left and the 1 neighbor immediately to his/her right. 4) The blindfolds are removed, and each participant c
  24. bushindo

    It is possible to get above 90%
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