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(Full disclosure: this is a silly question, not to be taken too seriously.)

A Hat of Vermin (XGtE, p. 137) can be used to conjure up to 3 rats:

This hat has 3 charges. While holding the hat, you can use an action to expend 1 of its charges and speak a command word that summons your choice of a bat, a frog, or a rat. The summoned creature magically appears in the hat and tries to get away from you as quickly as possible. The creature is neither friendly nor hostile, and it isn't under your control. It behaves as an ordinary creature of its kind and disappears after 1 hour or when it drops to 0 hit points. The hat regains all expended charges daily at dawn.

Pipes of the Sewers can be used to summon forth a swarm of rats, if enough rats are around:

The pipes have 3 charges. If you play the pipes as an action, you can use a bonus action to expend 1 to 3 charges, calling forth one swarm of rats with each expended charge, provided that enough rats are within half a mile of you to be called in this fashion (as determined by the DM). If there aren't enough rats to form a swarm, the charge is wasted. Called swarms move toward the music by the shortest available route but aren't under your control otherwise. The pipes regain 1d3 expended charges daily at dawn.

Now, imagine the following situation:

An adventurer, in the middle of a rat-less environment (like a desert) but carrying Pipes of the Sewers and no less than EIGHT Hats of Vermin. He promptly decides to spend the next 2 and a half minutes summoning all 24 rats from the Hats. He then plays the Pipes and attempts to use a charge, with the intent of "gathering" the 24 skittering rats into one convenient swarm (I went with 24 rats, because a Swarm has 24 HP, which may or may not represent the amount of individual rats in it; who knows).

Would this needlessly complex chain of events, indeed, allow our Piper to "make" a Swarm? And if so, would it only last an hour?

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Ask your DM and hope they majored in philosophy.

You're asking, "when have I added enough rats to make a swarm?" This is identical to the 2400 year old Sorites Paradox:

The sorites paradox (/soʊˈraɪtiːz/;[1] sometimes known as the paradox of the heap) is a paradox that arises from vague predicates. A typical formulation involves a heap of sand, from which grains are individually removed. Under the assumption that removing a single grain does not turn a heap into a non-heap, the paradox is to consider what happens when the process is repeated enough times: is a single remaining grain still a heap? If not, when did it change from a heap to a non-heap?

The linked wikipedia page offers many possible solutions, ranging from pedestrian to thoroughly technical. If your DM majored in philosophy, maybe one of those solutions will work. I imagine most DMs will just rule on the fly.

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    \$\begingroup\$ I think the real question in here lies under whether or not calling for so many rats turns the individual creatures into a single Swarm creature. \$\endgroup\$ – NautArch Mar 11 at 19:49
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    \$\begingroup\$ @NautArch With the assistance of the Pipes, but otherwise yes. \$\endgroup\$ – Gael L Mar 11 at 20:29
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    \$\begingroup\$ As a DM who DID major in philosophy, I approve of this answer. \$\endgroup\$ – Discord Mar 11 at 22:12
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How many rats is "enough" is explicitly determined by the DM.

It's right there in the quote:

...calling forth one swarm of rats with each expended charge, provided that enough rats are within half a mile of you to be called in this fashion (as determined by the DM).

The mechanic for "are there enough rats" is explicitly DM determination, not anything else. Now, the thing that they are called on to determine is "are there enough rats", which makes it not quite as utterly dependent on DM adjudication as it might be. The suggestion, then, is that there ought to be a certain number of rats that coutns as "enough" and the DM (the only authority given for determining this number) is adjudicating whether that many creatures who can be considered "rats" exists within one mile. So... you could ask. Or perhaps you could determine by experimentation. Head into a place where you know that there are enough rats, play your pipes, drop the resulting swarm into a box and count them. That'll give you an upper bound, and you can work on lowering that upper bound from there until you find the correct number. For example, you could travel to the desert with your box of rats, kill one, and then see if the pipes still work. Keep going until the pipes don't work, and you know how many it requires... assuming your DM isn't allowing dead rats to count.

Regardless, the real question is figuring out how many rats you need, and thus, how many hats you will need to acquire. Other than that, the summoned rat "behaves as an ordinary creature of its kind" - presumably including forming up into a rat swarm when the pipes play (at least until it vanishes because its hour is up).

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    \$\begingroup\$ Tbh: if someone spends their resources/energy on gathering more than, i'd say 3, Hats of Vermin, I'd let them have their rat swarm. Any time they wanted, no questions asked \$\endgroup\$ – Hobbamok Mar 12 at 9:26
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    \$\begingroup\$ @Hobbamok yeah..... I'm trying to think how, as a player, coming up with such a convoluted concept only to be told "nope, not enough rats" would be.... ugh (not to mention... how "imbalacing" would giving someone a summonable swarm of rats for.... all of these resources and time be, truly?). If anything you may need to find a way to buff the swarm to help make sure your character isn't left behind, imho. \$\endgroup\$ – Patrice Mar 12 at 20:52
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    \$\begingroup\$ considering that you need to hold the hat, and you have two hands, the most you can technically hold is one in each hand, and maybe one with a foot... you need your mouth free to speak the word of power. If you can do that in real life.... maybe... :D \$\endgroup\$ – Journeyman Geek Mar 13 at 5:08
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    \$\begingroup\$ @JourneymanGeek The rats last for a while, though. You can swap hands and let them accumulate. \$\endgroup\$ – Ben Barden Mar 13 at 7:43
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    \$\begingroup\$ .... or juggle hats while singing words of power... \$\endgroup\$ – Journeyman Geek Mar 13 at 7:44

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