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One late night on a hill in Innsbruck, Doug struggled to organize his memories. He picked up the “present” which looked like a cross between an IPad and a giant Blackberry (whatever the hell those were). He only had one chance to recollect his memories and figure out the password. Apparently, the prize was astronomical.

That morning while walking back to his friends' place after purchasing a new towel, Doug had run into a group of 6 humanoid or at least mostly sapient tourists and their guide. After repeatedly muttering in confusion about how they shouldn’t be Doug’s problem, the guide introduced the 6 tourists and, for fun, organized a game for them and Doug. He also provided pendants and the password protected prize.

The rules were as follows:

  1. The guide called ahead to buy them food and drinks at 3 different popular establishments where they would meet to play the game.

  2. One of the tourists would be told the password before leaving earth without Doug hearing.

  3. When the red button was pressed on an individuals pendant, it take them to one of the 3 meals or to the final meeting place. The meals were lunch at the Big Bang Burger Bar, dinner at Milliways, and after dinner drinks at some epic floating party. While Doug had to attend all three meals “in order” the others could control where they went.

  4. None of the tourists could go anywhere except to the 3 meals until they went to the final meeting. Every tourist who attends a meal must meet all participants who attend that meal before leaving. They may not come back to a meal after they left it or went to the final meeting but they are not required to go to every meal.

  5. At each meal, the current password holder would randomly select exactly one of the participating tourists at that meal who was not on his list of tourists who had already been told the password. He would then communicate the password to this participant along with his list of all past password holders. That new password holder would then go to a different meal and chose the next password holder unless he already knew this was impossible.

  6. If someone successfully passed on the password, he would then be required to proceed directly from that meal to the last meeting place.

  7. At the last meeting, the tourist who knew the password but had not told anyone would tell Doug the password. Any participating tourist who knew the password but had passed it on, would tell Doug a false password. Anyone who had never been told the password would not be allowed to speak to Doug.

  8. A paradox occurs under one of the following (surprisingly lax) conditions:

    • Something made of matter exists at the same time as another version of itself (without certain safeguards which are not present in this puzzle)

    • Somethings occurs which prevents its own occurrence.

  9. If a paradox occurs the entire universe in which the paradox occurs will cease to exist. This means that since we know Doug survived, anything that could happen that would result in a paradox simply won’t happen (thanks to a silly interpretation of the Copenhagen interpretation and the anthropic principle which should not extend outside of this made up reality).

Before leaving Earth, Doug learned the six tourists’ names: Thor, Zem, Gally, Emjay, Wowbagger, and Lintilla. Zem was used to demonstrate how to send someone off with the pendant. Finally, Doug caught Gally stealing his towel and he failed to get it back.

At the burger bar, Thor, Zem, and Emjay were in attendance. While Emjay was trying to ignore Zem gurgling constantly at him, Thor got violent about the lack of alcoholic beverages. Probably because Zem has fluff for brains and can’t remember the password on his own, Doug saw a scribbled up Janx Spirit napkin be put in a satchel made of Doug’s tied-up towel. When Doug tried to get the towel back, Emjay reprimanded him for trying to cheat. Emjay then sent Zem and the satchel off.

At Milliways, Thor, Gally, Lintilla, and Wowbagger were in attendance. Thor spent most of the night trying to get the attention of a cute raven haired girl he knew. She, however, did not seem to recognize or notice him. In order: they ate their meal; Thor left in a huff; Doug realized the table cloth Lintilla kept fiddling with was his towel; the tourists left; and Doug followed after them.

At the party all tourists arrived except Wowbagger. In order the following events occurred. Doug failed to get the satchel back from Zem as he couldn’t get through the crowd fast enough. Doug saw Thor meeting the girl from earlier; this somehow resulted in Thor walking out the door into midair. Killer robots destroyed the flying building. Doug witnessed Gally teleport away with his towel after failing to use it as a parachute. Doug finally remembered to use the pendant rather than go splat.

Doug only remembered 2 things from the final meeting.

  • Everyone told him a password.
  • Just before he passed out from the nausea (which he of course blamed on the shapeshifting room and time travel), Lintilla put Doug’s head on a pillow made from his folded up towel.

When Doug awoke, still ihebriated, he found the list of tourists and the passwords they said tucked into his towel pillow. Unfortunately the above events are all he can remember. Who was the person who told Doug the correct password?

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  • $\begingroup$ Is the assumption here that the tourists can travel through time (e.g. to the after-dinner party, and then to the lunch) while Doug has to traverse time linearly (lunch, dinner, after-dinner)? $\endgroup$ – GentlePurpleRain Apr 20 '15 at 20:48
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    $\begingroup$ @BenAaronson yes but not twice by the same person or by a person who learned it there. If Aaron told Bob it at breakfast, neither can tell anyone else at breakfast. Bob could tell Charlie at lunch. Under normal circumstances, that means no one could tell it to anyone else at breakfast. As time travel is involved, however, Charlie who missed breakfast could go back in time and tell Dave at breakfast. (rule 5) $\endgroup$ – kaine Apr 20 '15 at 21:28
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    $\begingroup$ @BenAaronson As via rule 7 they can only say a password if they knew the real one (sort with Zem) and they all say a password, and there are only 3 meals at which to pass it on. The password must be passed on multiple times a meal. $\endgroup$ – kaine Apr 20 '15 at 21:34
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    $\begingroup$ I'm taking Thor's complaints about alcohol in the lunch to mean he either just came from the party or goes to it next. Are those both (either?) supposed to be valid interpretations? $\endgroup$ – Ben Aaronson Apr 20 '15 at 22:12
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    $\begingroup$ @RobWatts anything made of matter does.... you have to know where your towel is to be able to solve the puzzle....Gally stealing his towel doeant mean she left with it. $\endgroup$ – kaine Apr 20 '15 at 23:02
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Whoever started with the password would have to give it up at the first event they attended and then go to the meeting directly.

Everyone except Wowbagger went to at least two events.

So Wowbagger started with the password.

So nobody else was given the password on Earth.

Zem left the burger bar with the towel.

Gally left the party with the towel.

Gally did not show up at the burger bar.

Thor did not leave Milliway's or the party with the towel.

Neither Zem nor Emjay was at Milliway's.

So the towel must have come to the burger bar directly from Earth.

The towel did not go from the burger bar directly to the final meeting.

The towel did not go from the burger bar directly to Milliway's.

So Zem brought the towel from the burger bar to the party.

So Gally brought the towel from the party to Milliway's.

So Gally did not arrive at the party with the password.

Zem was given the password at the burger bar.

The password could only have been exchanged once at the burger bar.

So neither Thor nor Emjay received the password at the burger bar.

So Emjay did not arrive at the party with the password.

Thor went to the party some time before he went to Milliway's.

So Thor did not arrive at the party with the password.

The password must have been exchanged twice at the party.

So two tourists must have arrived at the party with the password.

So Zem and Lintilla must have arrived at the party with the password.

So Lintilla received the password at Milliway's.

The napkin could not have come to the burger bar from Earth.

The napkin could not have come from the party, because Zem went there with the napkin.

So the napkin came from Milliway's.

So Thor brought the napkin from Milliway's to the burger bar.

Zem did not leave Earth with the towel.

So Emjay brought the towel from Earth to the burger bar.

So Emjay did not have the password at the burger bar.

So Thor brought the password to the burger bar.

So Thor went from the burger bar directly to the meeting.

So Thor went from Earth to the party, then to Milliway's, where he received the password.

Thor and Lintella both received the password at Milliway's.

So Gally passed on the password at Milliway's.

Thor gave up the password to Zem at the burger bar. Gally and Wowbagger both gave up the password at Milliway's. Zem and Lintella both arrived at the party with the password, and gave it to someone else.

So only Emjay never gave the password to any of the other tourists. So Emjay's password was correct.

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  • $\begingroup$ This solution is 100% the one I expected/intended. It is worth nothing that it does not establish the entire path of who told who; that is impossible. There are 2 possible paths the password could have taken and both lead to Emjay knowing. $\endgroup$ – kaine Apr 21 '15 at 20:05
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The person with the correct password is

Emjay

I feel like the reasoning ended up being fairly simple once I found the right path to follow. Based on rules 5, 6, and 7 and the results of the final meeting:

Because everyone tells Doug a password, everyone heard the password. That means that everyone participated in an exchange of the password at their last meal. In every case except for one, the exchange consisted of someone at their last meal giving the password to someone who was at their next-to-last meal. The exception is when the last person received the password - having nobody else to give it to, they would have needed to go straight to the final meeting.

Keeping this in mind, let's trace the path of the towel and the napkin:

Zem was given the password on the napkin at lunch and put it in the towel-satchel, then took them both to the party. From there, Gally took the towel to dinner, where Lintilla got it. The napkin, since it went to the party and didn't originate from the burger bar, must have come from the dinner. The only person who could have taken it to lunch from dinner is Thor.

Towel - lunch with Zem -> party with Zem -> party with Gally -> dinner with Gally -> dinner with Lintilla

Napkin - dinner with Thor -> lunch with Thor -> lunch with Zem -> party with Zem

Let's take a closer look at lunch now:

With three people at lunch, only one exchange of the password can happen, so someone is left out. It's clear that Zem was given the password, so either Emjay or Thor must have told it to him. Thanks to the napkin, we know that Thor must have just come from dinner. Also, look at Thor's interaction with the raven-haired girl - she didn't know him at the dinner, but did at the party. So they must have gone in opposite directions - she from the dinner to the party, and he from the party to the dinner. This means that Thor's schedule was party first, then dinner, then lunch.

Putting all the parts together:

Because lunch was Thor's last meal, he must have either received or given the password there. Because we know Zem received the password there and only one exchange happened at lunch, Thor must have given the password to Zem. This means Emjay did not give or receive the password at lunch. Emjay did not go to dinner, so he must have received the password at the party. Because he cannot both receive and give the password at the same place, Emjay did not give the password to anyone else.

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