## Lockbox Mk. II solution thread

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phlip
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### Lockbox Mk. II solution thread

My solution:

OK, so I'm going to make a few assumptions:
* Both Romeo and Juliet are reliable, will never lose the mail or forget to reply, and that this is common knowledge.
I make this assumption because otherwise the PO could steal every piece of mail between the two... that way, neither would know the mail had gone missing, they wouldn't know about their missing incoming mail, and they have no reason to think their outgoing mail never arrived (the recipient could have just ignored it).
* The prohibition of the customers finding out that the PO has stolen something doesn't extend to the contents of any box that's sent... this isn't specified either way, so I take it we get to choose. However, this version is more interesting (not letting them get noticed steal the contents of the box can be solved really simply by sending the ring in a box along with a letter asking for a receipt. If Romeo doesn't get the receipt, he knows something's up.)
* Since they're rich enough to afford infinite-value rings, they can probably also afford really good locks, that would take over a fortnight for the best lockpicker to crack. The existence of such locks... well... I'm also assuming. I guess Romeo could sell an infinitesimal portion of the ring to get the money (say it's made of some hyper-gold, that sells for \$∞/g). Juliet could take out a loan, and pay it back with an infinitesimal portion of the ring when she receives it.

Romeo first sends a letter to Juliet which contains the details of this whole plan. Juliet replies to it.

The PO can't steal the first letter because then Romeo won't get a reply, and they can't steal the second because Romeo's expecting it, and would notice if it didn't arrive. Either way, Romeo doesn't get his reply, and knows the PO's been tampering with the mail. Romeo now knows Juliet knows the whole plan.

Then, they do the solution to the original lockbox problem... but first Juliet has to get the stuff necessary, which might take a while... (Romeo could prepare in advance before sending the first letter, of course). Once Juliet has bought her incredi-lock, she sends another letter to Romeo. Romeo then takes a box with room for two locks on it, puts the ring inside, puts on one lock and sends it to Juliet, Juliet adds a lock and sends it back, Romeo removes his lock and returns it, Juliet removes her lock, takes out the ring, and sends back a letter to say it all worked. Because both parties are in on the plan, if the box is stolen at any point, the intended recipient will know within a fortnight. Each lock spends at most a total of 2 weeks in the hands of the postal service, so the locks rated for a fortnight I mentioned will be strong enough.

(The first step of this was originally going to be a TCP-oid three-way handshake, but I realised the third step could be dropped... Juliet doesn't need to know for absolute-certain that her first reply arrived... only Romeo does, and his expectation of it arriving will ensure that it will, because the PO can tell that he's waiting for it... they read the plan too, after all.)

Though, I'm interested to see what solutions people can come up with if the super-lock existence assumption is dropped...

Code: Select all

`enum ಠ_ಠ {°□°╰=1, °Д°╰, ಠ益ಠ╰};void ┻━┻︵​╰(ಠ_ಠ ⚠) {exit((int)⚠);}`
[he/him/his]

zed0
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### Re: Lockbox Mk. II solution thread

phlip wrote:The PO can't steal the first letter because then Romeo won't get a reply, and they can't steal the second because Romeo's expecting it, and would notice if it didn't arrive. Either way, Romeo doesn't get his reply, and knows the PO's been tampering with the mail. Romeo now knows Juliet knows the whole plan.

The PO steals the first letter, then gets someone with female writing to reply to Romeo. The PO now knows Romeo's plan and follows through as if they were Juliet.

a_passing_lunatic
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### Re: Lockbox Mk. II solution thread

Using the same assumptions but without the super-locks:

I was thinking some kind of timer, or some kind of timer combined with a large bomb which goes off when it's opened too soon, but in the first case you'd still need super locks, and in the second, the post office still wins, even if it's flattened in the process.

So, my idea is this: Romeo sends Juliet a letter, asking for a reply in confirmation that she got it, that she should expect a parcel in some number of weeks. He then slips something into the ring, and marks it 'box', and sends it. I'm not sure how to guarentee no post-office switcheroo, though. I mean, given that he's sending it as a box, he can't tell her to expect a ring.

Mouffles
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### Re: Lockbox Mk. II solution thread

Assuming that Romeo knows exactly where Juliet lives, and has access to some modern technology, he could just put a GPS tracking device with the ring in the locked box from the original solution. As long as he tells the postal service, they will have to deliver it.
In the spirit of taking things too far - the 5x5x5x5x5 Rubik's Cube.

taemyr
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### Re: Lockbox Mk. II solution thread

Mouffles wrote:Assuming that Romeo knows exactly where Juliet lives, and has access to some modern technology, he could just put a GPS tracking device with the ring in the locked box from the original solution. As long as he tells the postal service, they will have to deliver it.

This fails because:
Problem text wrote:Furthermore, the postal service is capable of doing or acquiring anything that anyone in the world are, and that they can do anything of which they are capable in as little time as they want.

So they can shoot down existing GPS devices, and substitute their own. Rendering GPS useless.

DrStalker
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### Re: Lockbox Mk. II solution thread

Romeo gets in a box, with the ring and a weeks supply of food and water.

He posts himself to Juliet.

The post office can't fail to deliver the box without Romeo knowing.
There are two types of people in the world: 1) those that can extrapolate from incomplete data.

Mouffles
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### Re: Lockbox Mk. II solution thread

DrStalker wrote:Romeo gets in a box, with the ring and a weeks supply of food and water.

He posts himself to Juliet.

The post office can't fail to deliver the box without Romeo knowing.

Romeo and Juliet are indefinitely grounded inside their homes
In the spirit of taking things too far - the 5x5x5x5x5 Rubik's Cube.

Seraph
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### Re: Lockbox Mk. II solution thread

Mouffles wrote:Romeo and Juliet are indefinitely grounded inside their homes

Then Romeo should just ship his house.

HarbingerOfTheDarkHeavens
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### Re: Lockbox Mk. II solution thread

Ok, maybe this is just me thinking Olde Tyme solutions... but I think I have the simplest bit of trickery here.

Romeo, writes his first letter to Juliet, asking for a reply, and claiming that he wants to send a couple of letters before he sends the ring to establish some "trustworthy-ness" with the post office. He also states in this letter that he is sending this first letter in a box so that Juliet may save his letters to her and look at them whenever she pleases. The paper he has written the letter on is rolled up, slipped through the priceless ring, and then the ring is covered with wax and sealed with Romeo's crest. The post office must send the letter and it's reply from Juliet. Assuming they read the letter (and can replace the wax and Romeo's crest stamp) they still would not assume that he would cover the ring with wax and use it thusly (also, being that they are lowly postal workers they probably wouldn't even know what a priceless ring looks like.) After Romeo gets his reply he sends another letter (also with a request for a reply) to Juliet telling her that she already has the ring, and all she needs to do is clean it (boil it in hot water or something).

If you think that the PO would notice the ring around the letter. Romeo could put it in a secret panel in the bottom of the box, and he could also make the box seem more innocuos by filling it with other gifts (roses, chocolates, some cheap jewelry, possibly a bobcat {if he wants to pay postage for a big enough box}).

My point is to get the ring to her first, before the post office expects it.

ptveite
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### Re: Lockbox Mk. II solution thread

Phlip, for the record, I think that you are making some assumptions that aren't stated, namely that both Romeo and Juliet will know when something is from each other vs. the postal service. Maybe some sort of assumption about their being able to recognize the other's handwriting and having the handwriting be un-forgeable.

Macbi
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### Re: Lockbox Mk. II solution thread

Romeo cannot send it.
The post office just impersonates Juliet.
Proof:
The post office can always do this since they can do anything Juliet can.
quintopia wrote:postal service is capable of doing or acquiring anything that anyone in the world are

Juliet does not find out since nothing is ever delivered to her, and Romeo does not since he cannot tell the difference between the post office and Juliet.
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chaosspawn
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### Re: Lockbox Mk. II solution thread

My first initial throwaway thought: Romeo shoots the package out of a cannon to Juliet's house, she pays for damages easily since the ring is infinitely valuable.

Here's my attempt:
Romeo gets a telescope. Romeo sends a letter to Juliet telling to sit on bedroom balcony in exactly one week, and encloses something like a box of chocolates, and tells her to eat them on the prescribed date, in a specific order. He finishes by saying that if he sees her there then he will send the ring to her. The post office will know that Romeo has the telescope and can see Juliet, thus they will let the letter go through.

The trick here is: hidden inside one of the chocolates would be the ring. Thus it would have already been sent before the post office would think to look for and steal it. Also the "in a specific order" bit and such is merely an attempt to further obfuscate the ring, making it look like this is only a confirmation letter, that the post office should let pass before trying to steal the mail.

Edit:
I think the solution requires either a way of independent confirmation of receipt (the telescope). Or only one party (Romeo) knowing that the ring will be sent. Juliet can't know because the post will be able to read all communication between them, thus know anything that she would. Thus there can only be either one party knowing, or all parties knowing.

However, rereading the problem again, I noticed it said Romeo already sent the first letter telling her he would send the ring. Under this circumstance it is impossible, as the post office will intercept this letter and Juliet will never get it int the first place. So anything Romeo sends thinking is to Juliet is really to an agent of the post office.
This space intentionally left blank.

QuestionC
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### Re: Lockbox Mk. II solution thread

It appears to just be an issue of writing an unforgeable document. This can be done with RSA encryption.

Assuming Romeo knows Juliet's public key.
• Romeo sends her the ring, and asks that the thank you note be signed using her private key.
• Romeo waits two week for a thank you note from Juliet which uses her RSA signature.
• If he doesn't receive the thank you note, or it is not properly signed, he knows the mail has been tampered with.

Assuming Romeo does not yet know Juliet's public key... then assuming they have any level of private information, this can be done.
Juliet, remember you that verse I sung to you in private that sweet night under the August moon? Use it as a one-time pad to encrypt a message so I can know your public RSA key.

If Romeo and Juliet have absolutely no 'secrets', and all physical means can be forged, then this seems hopeless, and at the same time really unfair.

Of course, this solution assumes the two have a lot of time to crunch numbers, or at least have laptops.

yelly
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### Re: Lockbox Mk. II solution thread

QuestionC wrote:It appears to just be an issue of writing an unforgeable document. This can be done with RSA encryption.
Furthermore, the postal service is capable of doing or acquiring anything that anyone in the world are, and that they can do anything of which they are capable in as little time as they want.

The PO get a quantum computer, or just do some factoring (which is undoubtedly possible, even if it takes forever), as fast as they want.
I guess any kind of encryption etc. won't work, as we don't have an unbreakable code yet (that doesn't require finding a way to get photons between the houses).
...
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HarbingerOfTheDarkHeavens
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### Re: Lockbox Mk. II solution thread

I think we are wrong when we assume that verification of transmission cannot be accomplished. Yes, the post office may be able to forge signatures, handwriting, etc. I would put forth though, that they would have great difficulty answering personal test questions meant for juliet (ex. Where is the freckle on my body that you told me you love so much on our third date?). Another possible solution to the secure communication problem could be Polaroid photographs of Juliet with the day's newspaper, standing next to a sundial (on her roof maybe) holding in her other hand the letter she is mailing (hopefully holding it close enough that Romeo could tell if the letter he recieves with the polaroids matches the letter in the pictures). My final suggestion would be to send her a video-capable cellphone, set to block all incoming calls except from his number.

Macbi
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### Re: Lockbox Mk. II solution thread

Quoting myself:
Macbi wrote:The post office can always do this since they can do anything Juliet can.
quintopia wrote:postal service is capable of doing or acquiring anything that anyone in the world are

She can answer those questions, hence so can they.
Simmilar for the other two.
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Cosmologicon
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### Re: Lockbox Mk. II solution thread

QuestionC wrote:If Romeo and Juliet have absolutely no 'secrets', and all physical means can be forged, then this seems hopeless, and at the same time really unfair.

Agreed, but if they do have a secret, it seems trivial. All Romeo has to do is send the ring and ask for a confirmation letter that includes the secret. No encryption or even preparation necessary.

EdgarJPublius
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### Re: Lockbox Mk. II solution thread

As far as I can tell, the solution requires some sort of Turing test with which Romeo is able to tell the difference between Juliet and any given employee, contractor or other resource of the Postal Office. Since they have never met in person, this will have to rely on previous letters between the two that have not been intercepted and have been destroyed in an unrecoverable manner such that only Romeo and Juliet know the contents but those contents cannot be recovered by any third party.

Another option is to somehow trick the post office into not reading a letter.
Or sending letters through some intermediary that are unlikely to be intercepted (I.E. giving the letter to a visitor to be mailed to some-one who can give it directly to Juliet, since the post office will likely expend resources intercepting all letters sent to and from Romeo and Juliet.)
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quintopia
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### Re: Lockbox Mk. II solution thread

Hmm, surprising that this got its own solution thread. Anyway, I just thought I'd throw out that all ideas that involve using some previous bit of information cannot work, because the problem states that they have never physically met before. This means the requirement that the post office has handled all communication between them extends indefinitely into the past. In other words, the post office, being capable of copying down the text of letters instantly, can be assumed to have a record of all prior communications of everyone, and, as soon as the letter about the ring is sent, can go back and read such communications. Furthermore, the problem would be trivial if we assume that the ring is already sent by the time the post office finds out about, which is why the problem states "Romeo wants to send a ring" and "the post office found out about it [already]." In other words, the post office finding out about the rings is in the past, and the actual sending of the ring is in the future.

Also, remember that there are certain assumptions about what the post office cannot do which may be considered reasonable. Namely, things that no one in the real world can do (or will foreseeably ever be able to do). The only specification is that if anyone can do it, they can, and instantly.

quintopia
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### Re: Lockbox Mk. II solution thread

EdgarJPublius wrote:Another option is to somehow trick the post office into not reading a letter. Or sending letters through some intermediary that are unlikely to be intercepted (I.E. giving the letter to a visitor to be mailed to some-one who can give it directly to Juliet, since the post office will likely expend resources intercepting all letters sent to and from Romeo and Juliet.)

Remember that the ring has infinite value. Thus, any finite amount of extra resources expended can be justified toward its acquisition.

phlip wrote:I guess Romeo could sell an infinitesimal portion of the ring to get the money (say it's made of some hyper-gold, that sells for \$∞/g). Juliet could take out a loan, and pay it back with an infinitesimal portion of the ring when she receives it.

Why not just assume Romeo and Juliet are capable of making anything they would buy in such a manner? The result is the same, but it's a lot easier to state.

phlip wrote:Then, they do the solution to the original lockbox problem.

The solution to the original lockbox problem will NOT work at any point. It requires that a box be sent with a hasp that is devoid of lock. Knowing that allowing such a box to go through will result in the successful conclusion of the original lockbox solution, the post office will add their own indestructible, unpickable, etc. lock to the empty hasp and send the box on. They have met their requirements and no one will ever have access to the ring again unless and until the post office decides to remove its lock.

miraidesuka
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### Re: Lockbox Mk. II solution thread

I'm surprised no one's mentioned The Purloined Letter yet.

*Assume that Romeo and Juliet know that they are going to get letters on a weekly basis, and that any absense in letters is a sign that the post office has intercepted their communications.

*Assume a non-omnipotent post office, and that Romeo and Juliet's first letters are sufficiently private, since the post office isn't interested in the affairs of minors at first.

*Assume Romeo has been able to send at least one letter to Juliet.

*Assume that Romeo acquired the ring some time after war split the two lovers apart.

*Assume that the post office learned the value of the ring and of Romeo's intentions to send it to Juliet only after he'd acquired it himself. (How could it have arrived at an unreachable location otherwise?)

My solution:

Romeo's first letter is a normal, inane, lovey-dovey letter that reveals nothing about sending a ring to Juliet. Concealed on the letter, a second letter written in invisible ink gives Juliet instructions for passing encrypted messages between them. Included in this is a set of codewords that Romeo and Juliet can use from this point on. Since the post office would leave Romeo's original letter alone, or at least not subject it to any high level of scruitiny; it passes unnoticed. From that point on, Romeo and Juliet write encrypted letters along with every regular letter. At this point even if the post office were to discover a second letter written in invisible ink, creating a forgery would alert Romeo or Juliet to the fact that their communications have been intercepted (since the post office doesn't know the keyword that should be included or which word in the series the keyword is) if a letter comes through missing a keyword, all Romeo or Juliet has to do is not reply. At which point, Romeo can start the encryption series over again, or start from another letter on the secret keyword list. As long as the secret list remains betweens Romeo and Juliet

Romeo and Juliet continue communicating in this way, and begin exchanging trinkets along with their letters -- the first of which Romeo conceals a dummy ring in. They establish this pattern for a given amount of time so as to confuse the post office. In his next letter, Romeo asks Juliet to check and see if the dummy ring was sent along with the first trinket, by this time, Romeo will be sending a second trinket which won't contain anything.

If the post office is intercepting the letters and the trinkets, Romeo will find out from Juliet when he receives his second trinket. If the trinkets are getting through without the post office intercepting them, Romeo simply sends the genuine ring concealed within the third trinket, confident that the post office will ignore it. If Juliet hasn't received the ring, Romeo knows that the post office is intercepting the fakes.

If the post office has been intercepting messages up to this point though, I'm pretty sure Romeo and Juliet are fracked no matter what they do.
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Ansain
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### Re: Lockbox Mk. II solution thread

zed0 wrote:
phlip wrote:The PO can't steal the first letter because then Romeo won't get a reply, and they can't steal the second because Romeo's expecting it, and would notice if it didn't arrive. Either way, Romeo doesn't get his reply, and knows the PO's been tampering with the mail. Romeo now knows Juliet knows the whole plan.

The PO steals the first letter, then gets someone with female writing to reply to Romeo. The PO now knows Romeo's plan and follows through as if they were Juliet.

Romeo could simply ask Juliet to confirm her identity by writing something that only they know, to make sure she gets the original package.

however another crucial flaw in the plan is when the lock box returns on day 2 with the post offices lock on it in hopes that romeo will send it back without his own lock.

This is countered if romeo waits two weeks before sending the box again however, because Juliet would know that she did not get the package she was expecting. So in order to make the plan work Romeo needs to plan in advance the days on which each package is sent to ensure that the post office did not steal it.
Why put off till today what you could just as easily get done tomorrow?

I can mathematically prove that 1 equals 0!.

Parts a-x in my plan weren't that important anyways.

quintopia
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### Re: Lockbox Mk. II solution thread

Ansain wrote:This is countered if romeo waits two weeks before sending the box again however, because Juliet would know that she did not get the package she was expecting. So in order to make the plan work Romeo needs to plan in advance the days on which each package is sent to ensure that the post office did not steal it.

False. As I mentioned before, the post office will not return the box to Romeo, since that could result in them breaking their mission statement. They will add their own lock and let it continue to Juliet. She will receive the box, and know that the post office has added a lock, but will be helpless to do anything about it. Juliet will never receive the ring. Thus, any working solution will not have any extra places for locks to go, as this will allow the post office to accomplish their secondary goal of preventing Juliet from getting the ring (as keeping the game going and open to future winning is preferable to admitting defeat and losing the invaluable ring).

miraidesuka wrote:oncealed on the letter, a second letter written in invisible ink gives Juliet instructions for passing encrypted messages between them.

How, pray tell, does Juliet know the existence of this concealed letter? If she is capable of guessing that an otherwise ordinary letter contains a concealed message just by looking at it, then so is the post office. Of course someone who conceals hidden messages is up to something, so they will copy this message in keeping with their practice of keeping backups of all delivered messages.

miraidesuka wrote:*Assume a non-omnipotent post office, and that Romeo and Juliet's first letters are sufficiently private, since the post office isn't interested in the affairs of minors at first.

Considering I assume that the post office is so corrupt it records every message since the beginning of time, and still have formulated a solution, this assumption is not necessary.

EdgarJPublius
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### Re: Lockbox Mk. II solution thread

Int hat case, the only solution I see is to deliver the ring via intermediaries rather than via the post office.

or else, create a box such that it will only open at specific space-time coordinates (I.e. Juliet's House, In one week) as determined by an internal system capable of determining it's position and time via reception of signals from a randomly selected pulsar or combination of pulsars (or, I suppose, other suitable celestial signal sources) and that upon opening, the box will send a radio signal to Romeo confirming that the package has arrived at the appropriate coordinates at the appropriate time.

The box will, of course, have to be almost arbitrarily large in order to properly triangulate the Pulsar signals, bit I'm sure the Psuedo-omnipotent post office can figure out how to deliver the thing regardless.

Also, except for its own, internal opening mechanism,t he box is unopenable.

I'm sure there's a simpler way to get a similar result, but I felt like over-engineering the thing.

If you really want, you can just wait an arbitrarily long amount of time until a freak macro-scale quantum effect results in the ring translating itself to Juliet without passing through the intervening space
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quintopia
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### Re: Lockbox Mk. II solution thread

About the only thing we can be sure he has seen is her letters and any boxes she has sent in the past. And since it would be unreasonable to think that the post office would randomly send letters and boxes pretending to be her even before there was a ring involved, it is reasonable to assume he knows that the boxes and letters he received before the ring was acquired were, in fact, from her. It is also possible he knows what she looks like, since she may have sent him a postcard letter with her picture on it.

EdgarJPublius wrote:the box will send a radio signal to Romeo confirming that the package has arrived at the appropriate coordinates at the appropriate time.

This won't work, as the post office could intercept it and instantly begin transmitting millions of interfering signals. However, I don't see why it's necessary for Romeo to know the ring arrived, as long as it did.

Also, how would Romeo go about building an arbitrarily large box without leaving his house? How would his employees go about building it without entering the no-man's land? Wouldn't the post office begin building its own arbitrarily large boxes all around, thus restricting the size of Romeo's box?

Also, can anyone find a solution that assumes a pre-Industrial society? (say, Elizabethan, eh?)

SammyIAm
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### Re: Lockbox Mk. II solution thread

Here we go (first post on the forums too):

NOTE: While writing this, I've discovered a bit of a problem. Since the post office intercepted Romeo's letter telling Juliet that he was going to send her a ring, they needn't deliver any more mail from either of them. If either of them sends a letter, the post office will simply write their own reply from here on out. In fact, since Romeo and Juliet have never actually met, there is the possibility that neither has ever received a letter from each other, and they've been corresponding with the Post Office all along. Anyway, assuming Romeo and Juliet have actually corresponded with each other:

For this solution to work, we must make two assumptions. First, we assume that Juliet knows Romeo has intended to send her an infinitely valuable ring, and that she has some means of confirming that any ring she has received is indeed of an infinite value. This seems reasonable since although Juliet cannot leave her house, there is not a no-man's land surrounding her house and she could conceivably call some sort of 3rd party appraisal service. Secondly, it seems fairly difficult for anyone to acquire an infinitely valuable ring, so I'm going to assume that the post office is unable to somehow get an infinitely valuable ring (though technically speaking, if Romeo can do it, so can they).

The Post Office guarantees that they will deliver any letter within a week, but does not have any specific restrictions on what type of letter, or the material it is written on. All Romeo has to do is inscribe his letter (a simple "I love you" should suffice as a "letter") on the ring, and attach sufficient postage. If the Post Office wants to get nit-picky about the shape of what defines a letter, we should be able to allow that the infinitely valuable ring could either fold into a flat square, or is made of a material soft enough to be flattened and re-molded into a ring (in which case Romeo could send, in a separate box after the ring itself, some sort of mold to re-form the ring).

If Juliet does not receive the ring within a week of when Romeo is expected to send it (this could have been defined in a letter at some point, but only if they've corresponded (see note at top)), she knows the Post Office has tampered with the mail. Romeo doesn't need to know if Juliet received the ring or not since the Post Office cannot allow Juliet to know they have tampered with the mail.

Upon receipt of the ring, Juliet checks to make sure it is indeed an infinitely valuable ring. If it's not, she knows the Post Office has tampered with her mail. If it is an infinitely valuable ring, the ring made it through and she can wear it.

Not perfect, but there's only two assumptions, so it's close.

EdgarJPublius
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### Re: Lockbox Mk. II solution thread

quintopia wrote:About the only thing we can be sure he has seen is her letters and any boxes she has sent in the past. And since it would be unreasonable to think that the post office would randomly send letters and boxes pretending to be her even before there was a ring involved, it is reasonable to assume he knows that the boxes and letters he received before the ring was acquired were, in fact, from her. It is also possible he knows what she looks like, since she may have sent him a postcard letter with her picture on it.

EdgarJPublius wrote:the box will send a radio signal to Romeo confirming that the package has arrived at the appropriate coordinates at the appropriate time.

This won't work, as the post office could intercept it and instantly begin transmitting millions of interfering signals. However, I don't see why it's necessary for Romeo to know the ring arrived, as long as it did.

Also, how would Romeo go about building an arbitrarily large box without leaving his house? How would his employees go about building it without entering the no-man's land? Wouldn't the post office begin building its own arbitrarily large boxes all around, thus restricting the size of Romeo's box?

Also, can anyone find a solution that assumes a pre-Industrial society? (say, Elizabethan, eh?)

Arbitrarily large is an over-simplification, there is a definite minimum size that can be used and it's not a prohibitively large limit.

The radio signal is so that the post office cannot simply intercept the letter (or very large box as it were) because if the box is intercepted (or the signal is jammed) then Romeo will know that the post office has not followed though on their guarantee.

Even if the minimum size of the box larger than the land Romeo has available to him, the box can make use of vertical space as well, which the post office cannot reasonably restrict.

Technically the device could work using very large resonating spheres as signal receivers and a difference engine to process the signals, all technology available to a pre-industrial society (although the knowledge to construct such devides and how to use them are not pre-industrial).

Given that the post office has intercepted and maintains copies of every letter since the beginning of time, there is no information in any letter Juliet sent to Romeo that is not falsifiable by the post office, Juliet cannot pass any Turing test against the Post Office except by chance, a chance she won't get because they can intercept her replies and substitute their own. With the exception of new information, the only ways for the ring to reach Juliet is either for the Ring to be delivered in a manner the post office can't or won't intercept (I.E. via intermediaries etc.) Or if the box is capable of determining that it has reached its destination intact and can inform Romeo of this fact, any other type of letter can be intercepted by the post office and replaced, or the reply can be intercepted and replaced.

EDIT: If you want to get nit-pickety: Romeo sends the ring with no security precautions whatsoever. Because Romeo's earlier letter has led Juliet to expect the ring, the post office cannot obtain it without her realizing that the Post Office has not fulfilled its guarantee. In this case, the post office can want the ring all it wants but knows it can never obtain it.
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### Re: Lockbox Mk. II solution thread

EdgarJPublius wrote:they can intercept her replies and substitute their own

EdgarJPublius wrote:any other type of letter can be intercepted by the post office and replaced, or the reply can be intercepted and replaced.

These are assumptions and are not immediately obvious to me. It is reasonable to assume they have corresponded before, as I said earlier. I mean, without having corresponded before, how could Romeo have decided he liked her enough to give her an infinitely valuable ring? And if they have corresponded before, then with a few other small assumptions, the possibility of the post office duplicating their messages is eliminated.

EdgarJPublius wrote:if the box is intercepted (or the signal is jammed) then Romeo will know that the post office has not followed though on their guarantee.

If the signal is jammed, Romeo cannot determine one way or the other whether the package arrived. Your solution can be made to work, but a radio signal is not the way.

SammyIAm: I can find no flaws in your solution. I didn't even think of specifying the properties of the ring. Although I would state the assumptions you made as follows:

1) Juliet and Romeo have corresponded at least once, and as such, Juliet knows to expect a ring of infinite value by a certain point in time.
2) There exists exactly one ring of infinite value.
3) No one can make a ring of infinite value.
4) People can transform rings of infinite value into letters and back again.
5) Someone can discern whether a ring is of infinite value.

This is a very small number of assumptions. The first 3 are either implicit in the problem statement or absolutely necessary in any solution. Either the 5th assumption, or one which accomplishes the same thing (i.e. a means by which Juliet can determine that the letter she was expecting was, in fact, the one that arrived) is necessary. The fourth is very much a stretch, but the problem said nothing about the nature of the ring, and so it must be accepted.

Any other solutions banging around out there?

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### Re: Lockbox Mk. II solution thread

Here's an idea, although it would take some patience to pull off. It's just another rendition of distracting the post-office while the ring slips by, undetected.

First, Romeo would need a young tree. Not a sapling, something with a circumference of a couple inches at least. Using the old trick of making an axe by implanting an axe-head into a tree-branch, Romeo could hide the ring inside the tree by carefully cutting it lengthwise, implanting the ring, and taping it up, allowing the tree to re-grow together into a suitable-sized piece of wood for box fabrication.

Romeo would start sending letters, paired with momentos, each in a wooden box. (Letters and boxes will make it within a week) Each letter should mention something along the lines of, "I am sending you this teddybear as a test to see if the ring could pass through the corrupt mail system." The gifts and boxes would make it through, if the PO is smart enough to not tamper with Romeo's test-gifts in order to bait him to send the ring. Each box should have some fancy carving or painting as to give the box itself worth, so Juliet won't throw them away. Maybe make them collectable display cases. Whatever.

One of the boxes would then be made out of the tree wood with the ring fused into the middle of the wooden panel, completely unnoticable just by looking at it. After an arbitrary ammount of these boxes and gifts have been sent, Romeo would send a letter that informs juliet that he made the boxes out of heavily perfumed wood, and instructs Juliet to burn all the boxes he has sent her and stir the ashes to release their wonderful aroma. She would then find the ring within the pile of ashes.
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### Re: Lockbox Mk. II solution thread

Good one, but I can make it one better, because if the box is to be destroyed, why bother embedding it in the wood or sending so many boxes? Juliet is expecting a letter from Romeo and knows Romeo's handwriting. He sends her a letter telling her she should receive a box with a ring in it within the week. He locks it in a box of solid and pure sodium, carves a message in its surface, shrink wraps it, wraps it in a clear honeycomb pattern, submerges it in water, and shrink wraps it again, wraps it in honeycomb again, submerges it in butane, and shrinkwraps it again. Any attempt to break into the box now will destroy the entire box, and any attempt to burn through the box will, again, instantly destroy the entire box. Thus, Juliet can do either of these things to open the box and get the ring (first confirming that the message carved in the sodium is indeed by Romeo's hand), but if the post office does either, then they destroy the box, thus making it impossible to maintain their mission statement.

Of course, none of this would work in a pre-Industrial situation, while my original solution would.

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### Re: Lockbox Mk. II solution thread

Juliet cuts her finger off and mails it to romeo, where he then puts it on her finger.

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### Re: Lockbox Mk. II solution thread

quintopia wrote:Good one, but I can make it one better, because if the box is to be destroyed, why bother embedding it in the wood or sending so many boxes? Juliet is expecting a letter from Romeo and knows Romeo's handwriting. He sends her a letter telling her she should receive a box with a ring in it within the week. He locks it in a box of solid and pure sodium, carves a message in its surface, shrink wraps it, wraps it in a clear honeycomb pattern, submerges it in water, and shrink wraps it again, wraps it in honeycomb again, submerges it in butane, and shrinkwraps it again. Any attempt to break into the box now will destroy the entire box, and any attempt to burn through the box will, again, instantly destroy the entire box. Thus, Juliet can do either of these things to open the box and get the ring (first confirming that the message carved in the sodium is indeed by Romeo's hand), but if the post office does either, then they destroy the box, thus making it impossible to maintain their mission statement.

Of course, none of this would work in a pre-Industrial situation, while my original solution would.

I must have missed your original solution, but I didn't see it here or in the problem thread.

Why can't the post office cut the first two layers (without the last shrink wrap) and then drain the liquid. Then assuming a completely dry area (similar to what romeo would have needed to do this in the first place) open the box and take the ring, then repeat the same procedure to close it. Thus the box is ultimately no more secure than a standard letter/package, as the post office can undetectably open it.
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### Re: Lockbox Mk. II solution thread

I've gotta say that I think this whole discussion is about a logistics problem, not a logic problem. The answer to the old version, that Romeo adds a lock, Juliet adds a lock, Romeo removes a lock and Juliet removes a lock, has a symmetry, simplicity and, dare I say, beauty to it. That's the solution to a logic problem. This is a mess.

But, you know, continue as you were. [/fuddy duddy]
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### Re: Lockbox Mk. II solution thread

quintopia wrote:
EdgarJPublius wrote:they can intercept her replies and substitute their own

EdgarJPublius wrote:any other type of letter can be intercepted by the post office and replaced, or the reply can be intercepted and replaced.

These are assumptions and are not immediately obvious to me. It is reasonable to assume they have corresponded before, as I said earlier. I mean, without having corresponded before, how could Romeo have decided he liked her enough to give her an infinitely valuable ring? And if they have corresponded before, then with a few other small assumptions, the possibility of the post office duplicating their messages is eliminated.

You yourself said that

Considering I assume that the post office is so corrupt it records every message since the beginning of time

and that Romeo and Juliet have never met physically.

Given that assumption, no letter can pass through the post office that the post office cannot intercept and either replace or write their own reply to.

Since the post office must never allow anyone to know they have violated their guarantee, Either Romeo must be able to learn whether the package has arrived at Juliet's untampered with, or Juliet must be made to expect the ring at a certain time, which she cannot be as the post office is capable of intercepting and replacing any such notification.

As for jamming the radio signal, that in its self would tell Romeo something unless the Post Office is in the habit of undertaking random radio jamming, even if they start such jamming as a result of Romeo's package, he can still reasonably infer that the package has arrived and that the Post Office undertook the jamming to prevent him from learning that.
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### Re: Lockbox Mk. II solution thread

quintopia wrote:I would state the assumptions you made as follows:

1) Juliet and Romeo have corresponded at least once, and as such, Juliet knows to expect a ring of infinite value by a certain point in time.
2) etc...

Then the post office can't possibly intercept it without her realising.
Unless they can make a fake, then there's no solution.

jestingrabbit wrote:I've gotta say that I think this whole discussion is about a logistics problem, not a logic problem. The answer to the old version, that Romeo adds a lock, Juliet adds a lock, Romeo removes a lock and Juliet removes a lock, has a symmetry, simplicity and, dare I say, beauty to it. That's the solution to a logic problem. This is a mess.

But, you know, continue as you were. [/fuddy duddy]

The problem is that that doesn't even work classically, as the post-office can pretend to be Juliet.

EdgarJPublius wrote:Since the post office must never allow anyone to know they have violated their guarantee, Either Romeo must be able to learn whether the package has arrived at Juliet's untampered with, or Juliet must be made to expect the ring at a certain time, which she cannot be as the post office is capable of intercepting and replacing any such notification.

Compleatly true, which is important.

If Romeo has a tracking device they deliver that, but not the ring.

Presumeably Romeo could make a tracker that had the ring as an unremovable component, but that probably also has a flaw, as the post office can duplicate it, and smash it as they turn the other one on.
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### Re: Lockbox Mk. II solution thread

chaosspawn wrote:I must have missed your original solution, but I didn't see it here or in the problem thread.

No, I just (intentionally) never posted it.

chaosspawn wrote:Why can't the post office cut the first two layers (without the last shrink wrap) and then drain the liquid.

You're right. That doesn't mean it's impossible to design a box which cannot be harmed without being destroyed, it just means that I didn't consider knives. Fill in the blanks yourself, as the basic premise is sound.

jestingrabbit wrote:I've gotta say that I think this whole discussion is about a logistics problem, not a logic problem.

Either way, it gets engineers' minds working, and there is no forum dedicated to logistics puzzles, so here ya go.

EdgarJPublius wrote:Given that assumption, no letter can pass through the post office that the post office cannot intercept and either replace or write their own reply to.

Which is why I said that it is okay to assume (and in fact, must be assumed) that they have successfully corresponded at least once, and know they have done so. It doesn't matter how this was accomplished, say it's because the post office didn't care enough to copy the letter in its own handwriting at first. As you have so thoughtfully noted, there is no solution without this assumption.

EdgarJPublius wrote:As for jamming the radio signal, that in its self would tell Romeo something unless the Post Office is in the habit of undertaking random radio jamming, even if they start such jamming as a result of Romeo's package, he can still reasonably infer that the package has arrived and that the Post Office undertook the jamming to prevent him from learning that.

Well, if you'd like to allow radio through, then why not just have the post office bring two identical boxes, one of which Romeo sent, into Juliet's house, and deliver the one that Romeo did not send, and leave with the (now opened and radio signal sent) ring-bearing box. If Juliet can't tell the difference, then this would work for them. If she can tell the difference, then the radio signal is unnecessary, as she will know the box wasn't delivered.

Macbi wrote:Then the post office can't possibly intercept it without her realising.

True. But nowhere in its mission statement does the post office promise to deliver contents of boxes. Even if the post office steals the ring out of the box and delivers the box empty, they have kept their promise. So, it is possible for them to steal it.

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### Re: Lockbox Mk. II solution thread

quintopia wrote:
chaosspawn wrote:I must have missed your original solution, but I didn't see it here or in the problem thread.

No, I just (intentionally) never posted it.

chaosspawn wrote:Why can't the post office cut the first two layers (without the last shrink wrap) and then drain the liquid.

You're right. That doesn't mean it's impossible to design a box which cannot be harmed without being destroyed, it just means that I didn't consider knives. Fill in the blanks yourself, as the basic premise is sound.

jestingrabbit wrote:I've gotta say that I think this whole discussion is about a logistics problem, not a logic problem.

Either way, it gets engineers' minds working, and there is no forum dedicated to logistics puzzles, so here ya go.

EdgarJPublius wrote:Given that assumption, no letter can pass through the post office that the post office cannot intercept and either replace or write their own reply to.

Which is why I said that it is okay to assume (and in fact, must be assumed) that they have successfully corresponded at least once, and know they have done so. It doesn't matter how this was accomplished, say it's because the post office didn't care enough to copy the letter in its own handwriting at first. As you have so thoughtfully noted, there is no solution without this assumption.

EdgarJPublius wrote:As for jamming the radio signal, that in its self would tell Romeo something unless the Post Office is in the habit of undertaking random radio jamming, even if they start such jamming as a result of Romeo's package, he can still reasonably infer that the package has arrived and that the Post Office undertook the jamming to prevent him from learning that.

There are many ways in which a radio signal can be blocked, and the post office does not guarantee the arrival of radio signals, thus, they may implement any solution in their power once and for all time to force all information to flow through the post office's hands.

Macbi wrote:Then the post office can't possibly intercept it without her realising.

True. But nowhere in its mission statement does the post office promise to deliver contents of boxes. Even if the post office steals the ring out of the box and delivers the box empty, they have kept their promise. So, it is possible for them to steal it.

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### Re: Lockbox Mk. II solution thread

Wouldn't Romeo simply wear a PO's uniform and deliver the package himself?
Or if that didn't work, enroll a trustworthy friend in the PO and have him deliver it.

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### Re: Lockbox Mk. II solution thread

By the problem statement, Romeo is grounded indefinitely and the post office as a whole (meaning any employee in it) wants to acquire the ring. I.e., there are no trustworthy friends in the post office, and anyone who joins the post office is instantly corrupted.

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### Re: Lockbox Mk. II solution thread

quintopia, I suggest you go ahead and post your solution now. The longer you hold off, the more people will expect of it, and the angrier they'll be if it disappoints them. The puzzle seems to be open to enough interpretation that people can have fun with it even if the "official" solution is revealed.

If you keep dragging it out, don't say I didn't warn you.