I solved it a little differently than the suggested method.
The suggested solution requires a box that is capable of being locked in both the lid and box by two padlocks. It also requires (Spoiler!) the ring to make two pointless transits, which could be expensive if it was large.
What if, instead, the box was capable of admitting only one padlock? Then Jan would padlock it closed. On receiving the locked box, Maria locks her padlock to Jan's, and returns the box (still locked with Jan's padlock, and not necessarily containing anything.) Then, on receiving the box back from Maria, Jan can form a chain that can be broken by either his padlocks (which he can remove) or by Maria's padlock (which she can remove). Then he can attach the chain to any box. Perhaps he should clip one more of his padlocks only to hers, so she can also select a new box.
Of course, this relies on some properties of padlocks that are not necessarily transferrable to cryptography.
Jan can open his padlock, releasing hers, and transform this to:
Box - J - M - J - Lid
Which Maria can open. An optimization could be:
Box - M - J - Lid
This is available if Maria could fit her padlock through the port in the box simultaneously with Jan's there, and send that back so Jan could remove his initial box padlock.
And the arrangement
Box - M - J - Lid
| |
J M
Would let either start a new box, using the J - M - J or M - J - M chaining as needed.
Nicely done. Understood the chaining solution now. One small assumption in that would be that the chain remains taut enough to not leave any gaps to slide the hands into the box (since the lid's hook is no longer in touch with the box).
That puzzle needed more clarification. The solution talks about having two padlocks affixed to the same box, but I can't imagine any kind of box that can have 2 padlocks affixed to it unless the box is specifically designed to allow 2 locks.
My point is that the puzzle should be updated to inform the reader that designing the right kind of box is a part of the puzzle:
"Jan and Maria each have plenty of padlocks, but none to which the other has a key. Using only the padlocks, keys, and a custom-designed box, how can Jan get the ring safely into Maria’s hands?"
Without a third party showing sales of padlock boxes with and without space for two or more locks, there's no actual way of being SURE which is more common.
Even if there are ten times as many boxes available that only have space for a single lock, what matters in the case of the puzzle is, a box with space for two or more locks is readily available. Suggesting in the puzzle "by the way the box has space for two locks" really kind of destroys the "puzzle" aspect.
Two points -- one, that's outside of the problem statement, so no, you can't use cryptography. Two, public-key cryptography uses an exact analogy of the physical-world method, so if you have access to a cryptographic solution you've already solved the problem.
There isn't really an analogy here, it just seems like it.
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.
My sister's solution: Send the ring in a box with a combination lock ;)
Edit: Ah, charlesdenaul already proposed that. You wouldn't need cryptography, as the problem doesn't state that the postal service also monitors the Internet.
After she gets the package. If the post staff just break into your house to take your stuff based on internet communication, they'd find out about your ring the next time one of you mentioned it, among other problems.
I presume email, and that GP misspoke when they said "model" and meant a file that the key could be modeled and printed from. That being said, that solution definitely skirts the intention of the puzzle, but would certainly work given the restrictions the puzzle did list.
:). OTOH, as someone interested in high latency communication protocols I wish cryptographers would hesitate to suggest a three round trip protocol at postal latency.
My solution is that Jan should send the ring in a padlocked wooden box with an inner protective but unlocked box and Maria should apply a saw to the outer box.
(To be fair, I can certainly imagine that in Kleptopia they know how to make excellent boxes).
Even simpler: send it in a padlocked cardboard box which Maria can rip open with her hands. Nothing in the problem statement says that the box itself has to be resistant to attack.
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" ...
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.
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.
Then you put a tiny corundum crystal inside a tiny padlocked box, and permanently affix it to the ring. (Or perhaps the ring has a lockable box portion.) Now the ring cannot be stolen without also stealing an object that is inside a padlocked box. Safe to mail.
