From the "Combining Magical Effects" section of the Player's Handbook (p. 205) and the Basic Rules (p. 85):
The effects of different spells add together while the durations of those spells overlap. The effects of the same spell cast multiple times don't combine, however. Instead, the most potent effect — such as the highest bonus — from those castings applies while their durations overlap, or the most recent effect applies if the castings are equally potent and their durations overlap.
This rule can lead to one of two different rulings:
- The DM could rule that, since Enlarge/Reduce is a single spell, the more recent casting of it (Reducto's) would take precedence, and Inflatoman would not only return to normal size but actually become Small.
- The DM could rule that Enlarge and Reduce — while the same spell — are considered separate for the purpose of combining effects, and rule that the two effects cancel out, resulting in a Medium-sized Reducto.
If Engorgo were to stop concentrating, then Inflatoman would either remain Small (option 1) or become Small (option 2). If Reducto were to stop concentrating, then Inflatoman would become Large in either case.
Thank you to @V2Blast for notifying me of the 2018 PHB errata on this!
All effects with a fixed duration measurable in rounds end just before the beginning of one of your turns. (Otherwise, their duration would be too short to be a full round, or a full 2 rounds, etc.)
We can see this by looking at a duration of 1 round, and applying the same logic to the case of 10 rounds.
A duration of 1 round, measured in turns, is “each participant in a battle takes a turn” (PHB, p. 189) — or put another way, one turn each for you and everyone else. Since you enjoy the benefits of an effect like Rage on the turn you activate it, that's one turn of effect for you; everyone afterward also “enjoys” the effect for their turn after you, until the end of the turn of the creature just before your next turn. When your next turn begins, you would be enjoying the effect for a second turn, therefore the 2nd round of the effect begins as your 2nd turn begins.
Thus the dividing line between the rounds, for an effect you enjoy on its first turn of activation, is just as/before one of your turns begins.
(There are a few exceptions, but these explicitly say when they end in relation to your turn. Most are single-round spells that alter your next action, which explicitly extend to the end of you next round so that they're not useless — you can think of effects like that as beginning to be “enjoyed” by you and everyone else only after the end of your 1st turn.)
Now we can extend this out to 10 turns, to see that Rage ends just before your 11th turn begins. For simplicity, we'll call the turn an effect starts “your 1st turn”, no matter how long combat has been.
A duration of 1 round begins on your 1st turn and ends just before the beginning of your 2nd (next) turn. Otherwise, it would not be a full round long.
A duration of 2 rounds begins on your 1st turn and ends just before the beginning of your 3rd turn. Otherwise, it would not be a full 2 rounds long.
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A duration of 10 rounds begins on your 1st turn and ends just before the beginning of your 11th turn. Otherwise, it would not be a full 10 rounds long.
So in the case of rage, it ends just before you take your 11th turn, preventing you from enjoying 11 rounds of rage but allowing you to enjoy the full 10th round of your rage, including during everyone else's turns.
Best Answer
Yes, it will last the full minute*
*Unless the effect is removed by some other mechanic.
There is a difference between Casting a Spell (see Chapter 11 of PHB) and gaining the effects of a spell as if you had cast it. In this case, the effect is external.
The wand is providing the effects of the Reduce/Enlarge spell but doing so without having you cast it. Since you aren't casting it, you also have no control over how long it lasts.
Can you turn it off at will?
It's not a concentration spell that you have control over so RAW it doesn't seem like you can turn it off. This is similar to ending a non-concentration spell early and that RAW it doesn't seem possible but I think many tables allow it. In this case, you are controlling the wand and it wouldn't be unreasonable for a DM to allow you to turn the effect off at will. However, that would be on a DM decision and not purely within the mechanics.
Removable via other mechanics/abilities
This is still a magical effect and a spell effect. Mechanics such as dispel magic or even a Paladin's cleansing touch could remove the spell effect early if a DM didn't permit the wand owner to do so (or if someone else wanted to end it.)