I know that in previous editions you could only have one magic ring per hand, is that true in 5th edition (RAW) as well?
[RPG] limit to the number of magic rings a character can wear on one hand
dnd-5emagic-items
Related Solutions
The DM controls treasure…
The Dungeon Master's Guide (1979) on Placement of Monetary Treasure says
All monsters would not and should not possess treasure! The treasure types given in the Monster Manual are the optimums and ore meant to consider the maximum number of creatures guarding them. Many of the monsters shown as possessing some form of wealth are quite unlikely to have any at all. This is not a contradiction in the rules, but an admonition to the DM not to give away too much! Any treasure possessed by weak, low-level monsters will be trifling compared to what numbers of stronger monsters might guard. So in distributing wealth amongst the creatures which inhabit the upper levels of dungeons/dungeon-like areas, as well as for petty monsters dwelling in small numbers in the wilderness, assign it accordingly. The bulk of such treasure will be copper pieces and silver. Perhaps there will be a bit of ivory or a cunningly-crafted item worth a few gold pieces. (91-2)
The section then details how the DM places monetary treasure. This is followed by a section describing the placement of magic items (92-3). Neither section encourages slavish adherence to random treasure table rolls and, on the contrary, recommends the DM place (not roll) monetary and magical treasure based on the creatures encountered and the player characters themselves.
So the DM decides what treasure exists not the dice, and if the DM doesn't like a rolled result, the DM rejects that result and either rolls again or just picks something. Even in AD&D, a DM shouldn't feel as though he's, like, cheating by rerolling or even picking what's best for that campaign instead of inserting something the DM knows is bad for campaign.
Thus, while the dice might've dictated that a ring of three wishes is somewhere in the dungeon, that doesn't mean the DM then must put it there or else the DM's doing it wrong. In fact, I suspect that Gygax would likely put forth that DM is doing his players a favor by excluding from the 2nd-level dungeon a ring of three wishes: a treasure like that at low levels skews players' expectations, giving them less to look forward to at higher levels when such treasures can be rightfully earned instead of accidentally rolled.
The Monster Manual (1978) in its description of treasure type further explains that the monster's treasure type entry means that such
treasures are only found in the lairs of monsters[, and] it must be stated that treasure types are based upon the occurrence of a mean number of monsters as indicated by the number appearing and adjustments detailed in the explanatory material particular to the monster in question. Adjustment downwards should always be made for instances where a few monsters are encountered. Similarly, a minor adjustment upwards might be called for if the actual number of monsters encountered is greatly in excess of the mean. The use of treasure type to determine the treasure guarded by a creature in a dungeon is not generally recommended. (5)
So this means the level 1 PCs upon defeating the 1–4 giant ants (see the DMG's Dungeon Random Monster Tables for Monster Level 1 on 175) should not get all or even the bulk of the giant ants' Q×3 and S treasure types but, instead, only a tiny portion—if any!—of that treasure, the Number Appearing entry of giant ants being 1–100, and even that tiny portion of giant anty treasure assuming the PCs defeat the giant ants in their (probably less than expansive) lair.
(If the DM doesn't mind mixing his dnd-bx material with his AD&D material, this DM recommends the Monster & Treasure Assortment: Sets One–Three: Levels One–Nine (1980) for a multitude of examples of reasonable lower-level treasures suitable for a party that's defeated, for example, some not-in-their-lair, less-than-the-listed-mean wandering monsters. The tables, if so desired, can also be used pretty much as-is, needing hardly any conversion.)
…But I understand wanting to roll dice and stick with the results
So you rolled a ring of three wishes and feel like, because it was rolled, it should be in the dungeon, darn it! That's cool. Make the ring almost inaccessible, nearly impossible to find except through great ingenuity, skill, or luck (maybe the ring's surrounded by puzzles and traps as the dungeon's centerpiece or made of glass and at the bottom of an underground lake). Or, perhaps even better, somewhere in the dungeon there's a clue that leads to another dungeon where the ring can be found. Or you can just give the PCs such a ring and see what happens; remember, these are AD&D wishes, after all.
From the Monster Manual:
A master can only have one homonculus at a time (attempts to create another one always fail), and when its master dies, the homonculus also dies.
So yes, there is a limit - you can only ever have a single homonculus.
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Best Answer
The rules that answer this can be found on page 141 of the DMG, under the heading "Multiple Items of the Same Kind".
Like many parts of the 5th edition rules, this was left up to the DM. The guidelines in that section make it pretty clear that the only real restriction to how many (non-attuned) magic items of a type you can wear is how many you can physically fit on your body.
There are no rules that I can find that say that rings would be an exception to this, and many rings don't require attunement. You can still only attune three items at a time, but you can wear as many non-attuned rings as you can fit on your fingers.