51–60 of 220 posts
One that I heard last week: There is an 8x8 checkerboard in a room with a coin placed on each square. Each coin is either facing heads or tails up, and the face is determined randomly. Before you can inspect the board, a "master" comes in, picks a square of interest, and must make a manipulation to the board by flipping one of the 64 coins. He then exits the room. You are now allowed to enter, and must read out which…
SPOILER 1 Names in boxes I don't understand how this works. The answer says it works to a certain percentage if there are no cycles longer than 50. But even if chance has it that there are two cycles of length 50. Then it seems the chance would be very large that one of the 100 prisoners would en up in the "wrong" loop and thus not find their name?
I don't understand the answer at all. Are they suggesting that the prisoners have somehow labeled the boxes? Or do they agree to assign names to the boxes via some other way - like make an alphabetic list of prisoners and assume that is the order of the "names on the boxes"? I suppose I just answered my own question, but I'm still not sure ;-)
The crucial part here is that it's not guaranteed to work - but it gives prisoners 30% chance to survive, as opposed to some infinitesimally small number if each picks 50 boxes on random.
Earlier quoted context omitted.
The wording of the problem is "anything sent through the mail will be stolen unless it is enclosed in a padlocked box".
Jan constructs an enormous box around the entire country of Kleptopia, and places his own padlock on it from the inside. Then he mails the ring with no additional security measures. The problem is fatally flawed by not explicitly stating that boxes locked with padlocks are also not stolen, despite not being enclosed in a padlocked box.
#2 is super interesting! I wonder if it generalizes to higher dimensions.
Thank god I could solve "Love in Kleptopia". Would have been embarrassing being a founder of a security company.
Interesting to me that there is an analogy with a 1000 year old puzzle. https://en.wikipedia.org/wiki/Fox,_goose_and_bag_of_beans_pu...
The apparent similarity between these two is due to there being multiple trips in both -- across the river in one, and through the mail in the other. But the reason for the multiple trips are entirely dissimilar, and so the similarity is purely superficial.
The 'dot-town suicides' is a more general version of a puzzle I know, "The Island with Blue-Eyed People". The solution is an induction, which is unusual in these kinds of problems.
Why can't the visitor say "There are X red, X blue, and 1 yellow?" No one knows about the yellow, thinks it is themself, they all commit suicide on the spot.
Edit: had a paren instead of opening quote.
SPOILER 1 Names in boxes I don't understand how this works. The answer says it works to a certain percentage if there are no cycles longer than 50. But even if chance has it that there are two cycles of length 50. Then it seems the chance would be very large that one of the 100 prisoners would en up in the "wrong" loop and thus not find their name?
I don't understand the answer at all. Are they suggesting that the prisoners have somehow labeled the boxes? Or do they agree to assign names to the boxes via some other way - like make an alphabetic list of prisoners and assume that is the order of the "names on the boxes"? I suppose I just answered my own question, but I'm still not sure ;-)
Thank god I could solve "Love in Kleptopia". Would have been embarrassing being a founder of a security company.
Assuming cryptography exists in Kleptopia, couldn't he use a padlock with a combination and transmit this electronically?
One that I heard last week: There is an 8x8 checkerboard in a room with a coin placed on each square. Each coin is either facing heads or tails up, and the face is determined randomly. Before you can inspect the board, a "master" comes in, picks a square of interest, and must make a manipulation to the board by flipping one of the 64 coins. He then exits the room. You are now allowed to enter, and must read out which…
I think you're referring to this puzzle: http://datagenetics.com/blog/december12014/index.html The version you gave is missing information and so can't be solved as stated.