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There is a mall with 4 entrances, in each entrance is standing a doorman with a counter who counts the amount of people who entered through that entrance. If the counter reaches 200, the doorman closes the specific entrance, if one person exits through this entrance the counter is down to 199 and the entrance is open again.

How can more than 800 people enter the mall?

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    $\begingroup$ What if the counter is at 0 and somebody exits? Does it go to -1? $\endgroup$ – hexomino Sep 26 at 13:26
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    $\begingroup$ Is this an open ended puzzle or is there a specific answer you have in mind? $\endgroup$ – Ambo100 Sep 26 at 17:12
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    $\begingroup$ "If the counter reaches 200, the doorman closes the specific entrance, if one person exits through this entrance the counter is down to 199": how can someone leave if the entrance is closed? $\endgroup$ – msh210 Sep 26 at 20:02
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To answer the literal question:

Many more than 800 people can enter, as long as during that time some people leave. Eg 800 people enter, 100 leave, 50 more enter, now 850 people have entered the mall.

It's possible you wanted us to try to answer:

How can more than 800 people be in the mall?

But you didn't ask that. Right?

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Firstly I don't know if the spelling mistakes are deliberate.

One way is for parents to smuggle their kids by putting them in suitcases.

Or because there are 4 door men who have entered the mall beforehand there can be 804.

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    $\begingroup$ 🤣 This made me laugh a lot. Indeed a "Deep Thinker"!!! $\endgroup$ – Ak19 Sep 26 at 12:13
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It's possible if the mall contains by any chance a

birthing clinic (or a woman otherwise gives birth while inside the mall)

Here's how:

800 people enter normally through the four doors, including a pregnant woman. The pregnant woman happens to give birth. If you count the newborn as "having entered the mall" (by extension of just having entered the world), the condition is already fulfilled. Otherwise, the woman can just leave through any door with her newborn, allowing 2 more people to enter.

Of course, this depends on exactly where you might define someone starts being a "person". But as long as the definition allows for the creation of a new persion inside the mall, the same should still work.

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Seems a bit simple, so I'm probably wrong, but

Some of the people simply came in through the exits. You said there were four entrances with doormen, but you didn't say there were no exits. So the extra people simply walked in through the unguarded exit doors.

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A military solution to the question:

the 800-people crowd (who are already in) attacks the doormen and drives them out from the entrances. Even if the doormen are heavily armed, 4 people can do little while fighting against 800.

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