Puzzle: When everything goes wrong


During war, two spies (Jack and Arnold) are being parachuted in a hostile country. But during their landing, their plane gets intercepted by the special forces. Things started to go out of control: they both lose all their equipment, and Ann, the person that is waiting for them on the ground, is killed. They both land far from the original location (and far from each other) in a completely unknown area. Eventually, each of them reaches a pay phone, but when they call Ann’s phone number they obviously get no response.


The first thing that they have to do is get in touch with each other. They obviously can’t call 911 or any random number, or do anything that will draw attention (like putting announcements in a newspaper), because all special forces are looking for them. In fact there is no TV, radio or newspapers in that area that would allow one of them to get information about another. Of course, they have no cell phones, walkie-talkies or anything that would allow them to communicate.


What would be their strategy to get in touch?

Comments (10)

  1. Every minute on the minute Jack can choose to call Ann’s number. If Jack calls, it signals a 1. If Jack doesn’t call, it signals a 0. Right after the minute, Arnold calls Ann’s number. If the line is busy, Arnold know that Jack sent a 1. If the line is not busy, Arnold knows that Jack either sent a 0 or has not arrived. Jack will use a distinctive bit pattern to signal the start of the message. Jack will continually repeat sending the message. Once Arnold has heard a full message from one start pattern to the next, Arnold calls Ann’s number just before the minute. When the line is busy for Jack he knows the message has been received.

  2. Doug says:

    Paratroopers always land away from the designated drop point, so they arranged to meet at a rendevous point at a pre-arranged time.

  3. AdiOltean says:

    >> Paratroopers always land away from the designated drop point, so they arranged to meet at a rendevous point at a pre-arranged time.

    Well, they lost the map! :-)

    Anyway, the solution posted by Nicolas is definitely in the right direction. The only remaining problem to be solved is that the spies don’t have a predetermined communication plan/algorithm at the time of forced landing.

  4. Snorrk says:

    If one of them goes straight to a payphone and starts calling Ann, chances are that the other one will too. Since Ann doesn’t answer, the spies are likely to hover around the payphone to try again. Therefore it might make sense to simply get a list of payphones in the area and call them in the hope that the other spy will pick up..

    I’m guessing that the simple option of going to Ann’s house and simply answering the telephone is not available because the special forces are watching her house.

    >S

  5. Well, it’s your puzzle and you get to make the rules, but it’s a little contrived to say that they lost the map and didn’t memorize enough landmarks to find their way to the rendezvous point, but they did both memorize Ann’s phone number, AND are both absolutely sure that the other also memorized Ann’s phone number.

    (Since we don’t have the full answer yet, the puzzle may not rely on them knowing that the other has it memorized, but it seems likely.)

    Personally, if I were going to be dropping into enemy territory, I’d be more inclined to memorize the map than anything else :)

  6. mikeb says:

    > Well, it’s your puzzle and you get to make the rules, but it’s a little contrived <<

    A puzzle that’s a little contrived???

    Well, I guess that my prison compadres and I can stop wasting our time with this and go back to flipping the light switches that aren’t hooked up to anything in that room down the hall…

    Damn, have I counted up to 23 or 24?

  7. BradC says:

    It seems to me that the only common thread they have is Ann’s phone number, and since they don’t know where the other person is, the only way to interact in any way is to both call ann’s number at the same time, one of them finding it busy.

    A key question: Do they both KNOW that Ann has been killed? If one person calls and finds it busy, will they KNOW it is the other spy? And not Ann or somebody else on the line?

    Depends also on what you mean by "get in touch". If one calls while the other is ringing Ann, they should know its the other spy on the line. Is this "getting in touch"? Or are we talking about designing a communication method consisting of nothing but frequency and pattern of busy signals??

    Nicholas Allen’s method is one way to do this, but I have a hard time thinking that each spy will simultaneously "choose" the same pattern.

    Only other thing I can think of is for both of them to interpret Ann’s seven-digit phone number in some other way to give coordinates and time for a meeting place. This assumes, of course, that both spies think of this and interpret the seven digits in the same way. (or is it 10 digits?)

  8. AdiOltean says:

    >> Do they both KNOW that Ann has been killed?

    I initially assumed yes, but this is not necessarily.

    >>> If one person calls and finds it busy, will they KNOW it is the other spy?

    After both of them are calling for days, both will eventually figure out that the phone is either busy or not answering – so they can reliable assume that Ann is not there, and it is either the other person who is calling, or there is a periodic defect on the line that cause the "busy" signal to appear.

    Then, the question is: how can each of them reliably tell that these "busy" signals are caused by the other spy, and not by some defections in the phone network, or by a third person calling?

    Well – the beatuy of this is that there is only one way to know. One of them can start ringing for a really long time – let’s say 5 hours. The other spy has only one choice left – she can repeatedly call for a few seconds and get a "busy" signal for those 5 hours. Then, the other spy can assume that either the first spy rang for 5 hours, or there was a defection that lasted for approx. 5 hours. Now, the first spy (or the second, whoever goes first) can repeat the same 5 hours calling technique again and again, until both of them will eventually figure out that there is "someone" on the other line that tries to communicate.

    After they figured out that they are trying to communicate, the next step would be for them to establish some sort of communication channel using the same technique. One of them can start transmitting a message using the Morse alphabet, by picking for example the dot = 5 minutes and the line = 30 min. He will just hope that the other will "read" the message. Then he will wait some arbitrary idle time and do probing, and then try again. The other one will do the same. At some point, the other will receive the message (or parts of the message) and after decryption they will start communicating more efficiently from that point on. For example – one spy can just attempt to send his pay phone number, or his current address.

  9. Dave says:

    Something tells me these guys didn’t parachute in with 50 lbs of quarters and dimes. And since they lost ALL their equipment, they would both have to con some willing operator into making an obscene amount of collect calls and then convince that operator to allow the phone to ring for certain amounts of time??

    If I were Jack (he’s the smart one) I’d find/steal myself a few dollars in coins, call Ann’s number and leave the phone off the hook. Then I’d make rounds to as many payphones I could find hoping that Arnold is continuously calling from another payphone.

  10. AdiOltean says:

    >> Something tells me these guys didn’t parachute in with 50 lbs of quarters and dimes.

    Good point – although a reasonably designed pay phone will not consume coins unless the person on the other end is picking up the phone… :-)