bonanova

That's the beauty of this one. You're only missing the best answer.

It's time to paint the prison. The warden wants the cells cleared for the convenience of the painter. He devises a scheme by which his 100 prisoners either will be all freed or all executed. Either way, the painting will be made easier. His scheme offers a survival probability that seems terribly small. In a room he places their names, on sheets of paper, in 100 wooden boxes, numbered 1-100 and lined up on a table, one name to a box. Prisoners are led into the room one by one and are told to look inside the boxes in search of their name. But each prisoner can open at most 50 boxes. Successful or not, each prisoner must then leave the room, exactly as he found it, and he is permitted no further communication with the others. They may plot a strategy in advance. It needs to be a clever one, because every prisoner must find his own name in order for any of them to survive. Your fame as a logician has reached the prison and you have been called in to help. They want you to provide them with a strategy having a survival probability that exceeds 30%! They have connections on the outside, they remind you, and they know where you live.

Due to temporary magical powers you find yourself undefeated in the US Open tournament, slated to play none other than Novak Djokovic for the title. Now it would not be fair to Djokovic -- and there would be no puzzle -- if you could keep your powers for the entire final match. You are informed that, at some point before the end of the match, your powers will go away, and you must finish the match using only your native skills. However, because you possess great logical skills you are granted to choose what the score will be when your powers end. In order to maximize your winning chances, what score (sets, games and points) would you choose? (Finals matches are best 3 of 5 sets.)

BMAD this is a great puzzle. I hope someone solves it, I'm at an end, with it.

I guess any number of rules (which may be mathematically equivalent) give that answer. Would like to hear from istemihan on his.

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.

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 tube and niche remain stationary while (only) balls move. Are these assumptions in line with the OP?

Great stuff.

Very cool.

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.

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.

Are KIP, etc., abbreviations for the color names? Interestingly, Google translates "mor" as livid.

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 last guest to receive the bottle for the first time) wins the bottle of wine. Numbering the positions clockwise (with the host being #1) which position will you sit in to win the bottle with greatest probability?

Nothing fits, but guessing this:

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."

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?

And

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 / weapon / location combinations for the four games.

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

Curious about your result. If you average over many trials are your expected winnings positive?

Do you have the right number of characters in the ciphertext?

Simple. Binary Hex Caesar. Or not.

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.