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Q: How do the inhabitants of my city-wide death trap figure out that nobody will be let out until only 100 people are left alive?

Jason ClydeSo, in my story, there is a city that gets cut off from the rest of the world. Golden translucent walls rise up on all four sides, going all the way up into the atmosphere and all the way down to the earth's core. And while most matter can pass through these walls, it swiftly becomes apparent tha...

This seems really difficult, if not impossible. If you start out with more than 100 people, then none of them can leave until there is only 100 remaining (which renders the battle royale moot). If it's not said anywhere (as you don't want), then the only way is via wild-mass-guessing, or some kind of clues. The guessing part might not be all that bad since you plant doubt in the characters' minds, but I'm guessing you don't want that to be the ultimate reason. It could be a start, though.
@HenryShao Correct. I want this to be a situation where people feel forced to kill. Obviously there will have to he some aspect of the square that indirectly conveys what needs to happen, but the key word is "indirectly". I don't want it to feel like whoever or whatever made the square is explicitly telling the inhabitants the rules.
How can the walls be golden and invisible?
@L.Dutch-ReinstateMonica I just searched the page and I never used the word invisible to describe it. In fact nobody did, you're the first person to use the word. If you mean transparent, I'm pretty sure that word still applies to things like, say, colored glass that you can still see through.
@JasonClyde in your previous posting about 2x2 squares, worldbuilding.stackexchange.com/questions/200254/… , you did indeed quite explicitly state "It has invisible walls on all four sides of the square" . It is a very reasonable assumption that this square would be similar.
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@PcMan Ah. Well my concept of how squares work has changed and evolved since then.
Wait till the smart ones communicate with the outside world, electrocute someone near the barrier, shove the dead human body through it and on the other side start CPR to bring them back to live ...
Do you also have some narrative reason why the rest of the world is no longer interested in the welfare of the people inside the square? Otherwise, people outside the square can send food and water through the wall to postpone the "all starve" event indefinitely. And unless you practically have the 100-person limit communicated explicitly somehow, I think it will take a lot less time to figure out how to keep everyone alive than to figure out that if all but 100 were killed then the 100 would be released.
@DavidK Yes, I do, that being that the rest of the world is also dealing with supernatural gimmicks like this and is in a poor position to help them.
What's the point of getting out, then, if everywhere else is just as bad?
"Most matter can pass through these walls" and "all starve to death" are substantially incompatible, unless, as you mention above, "the rest of the world is…in a poor position to help them". Then, the issue, while it's different, isn't all that far from a normal city in a apocalyptic society crash. All cities rely nearly completely on food and water transported from outside. If that transport stops, then a large portion of those people are going to die, even with migration outward. If transport would have continued, there's not that much to solve if "most matter can pass through these walls".
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This is the plot of the famous Star trek TNG episode: en.m.wikipedia.org/wiki/…
Vote to Close: This one seems to walk the murky line between WB and plot because it is asking for a mechanic, but it is also asking how people figure out that the mechanic exists which is plot. Despite its WB characteristics, it can't really be wholly answered as WB though.
#1 "in addition to electricity not working properly" Where did you state that electricity doesn't work properly, and what does that mean? #2 "most matter can pass through these walls .. the golden walls of the square stop letting living humans pass through them (neither in nor out)" If atmosphere can circulate, and drone trucks ca drive through (after all, "matter can pass through these walls") there's no reason to start fighting. Connections to the outside are reestablished (because -- remember "matter can pass through these walls") and life goes on.
Bottom line: this isn't even a half-baked scenario: it's "let me splatter something on WB and have them figure it out".
If the rest of the world is as busy as this patch dealing with supernatural gimmicks, why is it not at least equally reasonable, useful or interesting for the poor victims to stumble on or invent another gimmick? What other limitations are there on the golden walls, that stop people largely ignoring the whole set-up and simply passing most matter through the walls, living humans remaining in their own little enclaves just as most people have throughout history?
the people inside should figure it out pretty quick since there there can never be more than at most 101 people inside , so they can leave as soon as anyone dies. this pattern will not be hard not to notice.
This sounds quite similar to a novel called Under the Dome by Stehpen King (en.wikipedia.org/wiki/Under_the_Dome_(novel)). You could get some ideas from there.
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You could add some creepy countdown, that is displayed in random places (like some numbers that should normally be random, but end up all displaying the same number, and it is the number of people left alive)
I guess the upshot is that this will settle the question whether an unborn fetus is a live human or not, assuming at least one pregnant woman survives.
Problem here is that you don't let people in at 100 so there can never be greater than 100. Even then it is doubtful people will battle-royale as only a couple people need to die. Given a choice people would eventually leave for a different area. Eventually people would figure it out, and pass laws to prevent this from ever resulting in battle-royale. They would be 90 person limit (for safety margin), and if you have a child you have leave town. No battle-royale.

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