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Everything posted by bonanova

  1. BMAD this is a great puzzle. I hope someone solves it, I'm at an end, with it.
  2. I guess any number of rules (which may be mathematically equivalent) give that answer. Would like to hear from istemihan on his.
  3. You guys are amazing on these. Best I can do appreciate the answers once they're solved. I love analytical / math / probability stuff and completely lack creative / intuitive skills. Maybe I'll try making up some like this, but the effort may not be fruitful. They are fun.
  4. I think "remain equidistant between the balls" is difficult to understand. Literally it means the distance between the niche and the balls is the same. The same as what? And if distances remain the same, how can anything move? I think what is meant is that initially the niche lies between the two sets of balls. I also think the only way for a black ball to change from being to the left of a white ball to being on its right is to lie in the niche while the white ball moves over it to the left. I also think the niche must contribute to the length of the tube by one unit (ball width.) And the t
  5. Credit for the puzzle doesn't go to me. I didn't recall specifically the roulette wheel version, bubbled; rather, I saw an even different embodiment recently in Quora. I knew already of the uniform distribution of results and thought it would be fun to discuss it here. so I created a bottle spinning flavor text for it. I recall my first and only game of spin the bottle, back in high school. It was memorable because my single kiss of the evening was with the homecoming queen, a beautiful Uma-Thurman-like blonde named Hope. Calculate the odds of that.
  6. Yes. The host cannot win. No satisfactory analysis yet. Try the case with three guests (two guests is trivial) and compute the probability that after n spins you have not received the bottle.
  7. Are KIP, etc., abbreviations for the color names? Interestingly, Google translates "mor" as livid.
  8. Eight friends at a party, including the host, sit in a circle on the floor. There's a nice bottle wine that has not been opened that one of the seven guests should take home. The host will spin the bottle and pass it to the person on his left or right, depending on the direction the bottle points when it stops. The guest who receives the bottle will do the same - spin the bottle and in the same way pass it to his left or right. The game continues as long as there is at least one guest who has not received the bottle. Whoever receives the bottle when that is no longer the case (whoever is the l
  9. Nothing fits, but guessing this:
  10. Is there any dispute of the claim that money cannot be won by flipping a fair coin?* That is, there is no winning (or losing) strategy? * Other than with "heads I win, tails you lose."
  11. Just to clarify, does this ask whether you could extract the black balls if the chute could hold fewer than 11 balls and if so what is the smallest such number?
  12. In four successive games of Clue the following statements became true: [1] In one game Miss Scarlet used the wrench, but not in the Library. [2] In one game the rope was used in the study, but not by Colonel Mustard. [3] In one game the gun was used in the conservatory [4] In one game Professor Plum was the culprit, but not in the Library [5] In one game Colonel Mustard was the evildoer, but not in the conservatory [6] In one game Mrs. White was the perp, but she does not like ropes. [7] In one game the lead pipe was the weapon, used perhaps but not necessarily in the kitchen. Name the culprit
  13. 1. The first question with B as the correct answer is: A. 1 B. 4 C. 3 D. 2 2. The answer to Question 4 is: A. D B. A C. B D. C 3. The answer to Question 1 is: A. D B. C C. B D. A 4. The number of questions which have D as the correct answer is: A. 3 B. 2 C. 1 D. 0 5. The number of questions which have B as the correct answer is: A. 0 B. 2 C. 3 D. 1
  14. Curious about your result. If you average over many trials are your expected winnings positive?
  15. Do you have the right number of characters in the ciphertext?
  16. Simple. Binary Hex Caesar. Or not.
  17. You are seated at a table on which lie ten coins, each capable of showing a head or tail. You are wearing gloves and the room is dark. Your task is to create two non-empty groups that show the same number h of heads. h may have any value from 0 to 5. You may use any or all of the coins, exactly three of which currently show heads. Proceed. The clock is ticking.
  18. I don't know of a strategy to win coin tosses. I would expect to go broke or double my money with equal likelihood. Even so, here's what I would probably do:
  19. I never was never able to figure Keno odds, but after placing a few $1 bets in Vegas a few years back I vowed to stay away. My intuition was the payoff was ridiculously low. I since have seen that was a wise move on my part. In case you've never done the calculation, I'll offer you the option of four different games and ask you to determine the expected return. There are 80 numbers, from which you pick from 1 to 4, and from which the casino picks 20, at random. Your winnings depend on the number of "matches" between your numbers and the casino's. In each case you bet $1, which the house keeps
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