Seven Puzzles You Think You Must Not Have Heard Correctly (2006) [pdf]

Post by SilasX » Mon, Aug 29, 2016, 7:39 PM UTC

lmkg wrote: post #123

SilasX wrote: post #108

Earlier quoted context omitted.

I don't understand: the solution text claims that some permutations are guaranteed to work every time[1]. But you still have to initially land in one of "your" cycles, right? [1] "If it happens that the permutation has no cycles of length greater than 50, this process will work every time and the prisoners will be spared."

You always land in "your" cycle, because you start with the box with your name on it. All sequences of box-opening that use the method described must eventually cycle, because both box-to-name mappings are 1-to-1. Because it's a cycle, the sequence must eventually lead back to the box you started with. Since you start with the box with your name on it, then whatever cycle you landed it, it definitely contains the box…

Post by mikeash » Mon, Aug 29, 2016, 7:54 PM UTC

logfromblammo wrote: post #65

mikeash wrote: post #53

Earlier quoted context omitted.

Jan takes a normal box and locks it. He declares the space enclosed by the box to be the "outside," and the world to be "inside."

Unfortunately, the mail thieves declare "outside" to be the volume in conformal space on the side of the boundary definition that contains the point at infinity, and "inside" to be the volume that does not, and thus steal the ring.

Post by delinka » Mon, Aug 29, 2016, 7:59 PM UTC

joveian wrote: post #125

delinka wrote: post #84

Earlier quoted context omitted.

I noticed that one proposed solution is pretty pointless: attach a key to the hasp of the first locked box. The key can then be copied ("stolen" in today's copyrights-holder's parlance) by anyone along the mailing route, and the first person to use the key gets the ring. This, aside from the fact that the key on the hasp is not "inside a padlocked box" ...

Should work fine if the locked box is sent first...

Post by hundt » Mon, Aug 29, 2016, 8:01 PM UTC

SilasX wrote: post #132

lmkg wrote: post #123

Earlier quoted context omitted.

You always land in "your" cycle, because you start with the box with your name on it. All sequences of box-opening that use the method described must eventually cycle, because both box-to-name mappings are 1-to-1. Because it's a cycle, the sequence must eventually lead back to the box you started with. Since you start with the box with your name on it, then whatever cycle you landed it, it definitely contains the box…

I guess that's what I'm confused about: when we start, the boxes we map our names to have nothing to do with the name in the box. Just because my cycle includes the box I got assigned to, doesn't mean that cycle includes the box with my name inside it. If my name maps to 89, then sure, I accept 89 is a LT-50 cycle, but why does it mean that that cycle actually contains my name (as opposed to the box we assigned me to…

Post by Guillaume86 » Mon, Aug 29, 2016, 8:16 PM UTC

thomasahle wrote: post #43

sskates wrote: post #38

Earlier quoted context omitted.

Each individual still has a ~50% chance of being unable to find their name using the query sequence protocol. By agreeing to the same query sequence their success modes and failure modes are now linked. If there's a cycle of 51 or greater, all of those individuals in that cycle are guaranteed to fail, while if they're in a cycle of 50 or less, all of those individuals are guaranteed to succeed. What this protocol doe…

You are right, but we can also agree on a common query sequence in advance that doesn't use the 'results' of the queries. What about using what we find makes this so much more efficient?