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The description of the Headband of Intellect says:

Your Intelligence score is 19 while you wear this headband. It has no effect on you if your Intelligence is already 19 or higher.

The Feeblemind spell description says that my Intelligence score becomes 1 on a failed save:

[...] On a failed save, the creature's Intelligence and Charisma scores become 1. The creature can't cast spells, activate magic items, understand language, or communicate in any intelligible way. [...]

If I am affected by Feeblemind and I am wearing the Headband of Intellect, would I have an Intelligence score of 19 or 1?

Also, what about the other effects like not being able to cast, activate magic items, understand languages or communicate in any way? Those seem Intelligence-related, but are mentioned additionally to the reduction.

If the Intelligence score becomes 19, are the other effects still active?

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What is your Intelligence score?

I think we can look at this like a program. We are doing so ONLY as a method of thinking about this problem, NOT because this is how the game works. Below I will describe an update loop and the like, but the game does not run on such a thing. This is based on the phrasing.

The headband is not a one time occurrence, it is a continuous loop. It uses the word while.

Your Intelligence score is 19 while you wear this headband.

If we look at it like a program, we're setting the Intelligence to be 19 every "update". Or rather, every moment in time. Is the headband on? if yes, your intelligence is 19.

Feeblemind is a one time effect, meaning one time and one time only, we're setting the creatures Intelligence and Charisma to be 1. It has a duration of "Instantaneous", which implies that the effect is not contingent on the duration of the spell -- It is not 1 "while this spell is active", like the way the headband sets your intelligence to 19 "while you wear this headband". It is just set to 1. Without interference, your intelligence will stay 1.

When the headband is considered, your intelligence becomes 19. You can wear the headband because that is not the same as activating it, which the spell prohibits. If the headband's wording used "when" or "after" you put the headband on, we could conclude that Feeblemind would win out, as it was the latest affect on your intelligence. But because it uses "while", we treat it as a continuous effect.

Can I communicate, understand language, cast spells, and activate magic items?

Because of the wording of the spell, you still cannot speak, cast spells, or anything like that. The spell does not give a condition on the secondary effects' end, other than the spells that can dispell it, so we must conclude that the effects are ongoing as part of the spell itself, not because of the mental scores of the target. It is not because of the intelligence score that you cannot do those things, they are separate from each other.

Furthermore, Intelligence is not described as being important for language. Page 12 of the PHB states that Intelligence is a measure of mental acuity, information recall, and analytical skill. On page 17 of the PHB, you know certain languages "by virtue of your race". You also acquire some from your background. In the DMG page 278 for the language of a created monster, there are no ability score requirements for language. There are some spells that don't work on creatures of poor Intelligence, some of them regarding communication, but other than that there is no other requirement to be able to understand or speak a language. If you want more reasoning, there is a very good answer for a similar question I posed regarding Intelligence and Language

We must treat the inability to understand languages, activate magic items, etc etc, as an effect that the spell is having on your character, not as an effect the low intelligence is having on him/her. Call it "brain fart on steroids" if you want. You're smart, but you just can't do certain things. Your Intelligence is 19, you're very good at recalling information and can make good saving throws, but you cannot cast spells, activate magic items, understand language, or communicate in any intelligible way.

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    \$\begingroup\$ "you're very good at recalling information ..., but you cannot ... understand language, or communicate in any intelligible way." - So, you can recall information, but can neither be prompted to by others, nor communicate what you recall? That isn't super helpful. \$\endgroup\$ – Adeptus Jul 5 '16 at 5:17
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    \$\begingroup\$ Such is the way of feeblemind \$\endgroup\$ – Premier Bromanov Jul 5 '16 at 15:18
  • \$\begingroup\$ +many for lasering in on the importance of "while." Also, you make me blush =) \$\endgroup\$ – nitsua60 Jul 15 '16 at 3:09
  • \$\begingroup\$ @nitsua60 It's something I couldn't answer until now, but turned out to be basically the same. Thanks! \$\endgroup\$ – Premier Bromanov Jul 15 '16 at 3:20
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The Headband keeps it at 19

Feeblemind specifically alters your base ability score:

...the creature's Intelligence and Charisma scores become 1.

This spell is a functional to change to your score itself and can only be undone by greater restoration, heal, wish, or making a save after every 30 days. This spell changes your actual ability score from whatever it was previously to 1.

Items such as the Headband of Intellect override your actual score (emphasis mine).

Your Intelligence score is 19 while you wear this headband.

If you didn't have the Headband, your score would be 1. The text for the Headband is only concerned with what your score currently is (currently 1) and then says"No, when you are wearing me, your score is 19."

Feeblemind changes your ability score to 1, but wearing the headband overrides that as it would any ability sore and your ability score will be 19. The headband is functionally covering up your intelligence flaws, no matter how you got that intelligence. There is nothing in the spell feeblemind that states the score is unalterable - just that it is turned into a 1 and that certain spells can end the spell effect doing that.

The headband isn't changing your INT from, it's just giving you a 19 while your score is still 1.

Another argument: Instantaneous duration is equivalent to permanence

Big thanks to Carcer for this :)

The change wrought by feeblemind is instantaneous and can't be dispelled. Because of that, it's effect is near permanent with the exceptions provided in the spell for removing it. With that permanent-style change, items that artificially alter scores are still applicable.

I do think this argument is secondary to primary argument that the headband only cares what your score is and states that if it's less than 19 it changes it to 19.

The additional effects persist

The effects of feeblemind appear to be unconnected:

On a failed save, the creature's Intelligence and Charisma scores become 1. The creature can't cast spells, activate magic items, understand language, or communicate in any intelligible way.

While it seems like the effects of "can't cast spells, activate magic items, etc." are tied to having an Intelligence/Charisma of 1 - it doesn't specifically state that. In fact, you could be a Wisdom-focused caster and still be unable to cast as well.

Unfortunately, even if the headband brings your Int back to 19, you will still be under the effects that prevent you from casting spells, activating magic items, understanding language, or communicating in any intelligible way.

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Feeblemind will win

But it's really the dice that decide

Just reading the rules and not trying to get too clever, Feeblemind seems to win the day.

Here's how it progresses: The target is wearing his headband, and his intelligence is 19. He fails his Intelligence save, and his "intelligence becomes 1." (There's no mechanic on the headband that says otherwise, we're just doing what the rules tell us.)

The benighted target taps his headband and wonders why he doesn't feel smart anymore, but he "can't activate magic items." So the effect of Feeblemind isn't then overridden in turn by the "while worn" effect of the magic item.

Don't sever the effects of Feeblemind

The sentence in Feeblemind's spell description (PH p. 239) should not be understood as a list of separate effects. It's an apositive clause, defining what you can do when your intelligence is 1. This description continues in the next sentence:

...The creature can, however, identify its friends, follow them, and even protect them.

Spells don't include lists of effects they do not have, so these two sentences should be understood as elaboration, not separable effects.

This roughly jibes with language in the SRD:

An animal has an Intelligence score of 1 or 2. A creature of humanlike intelligence has a score of at least 3.

The saving throw is a sort of contest between the spell and the item

Since Feeblemind requires an Intelligence save, the headband's effect would give a measure of protection against the spell. If the target still failed their saving throw, you might thus understand the headband's magic to be overcome by the spell. That's not to say the headband would be destroyed or damaged, just overcome in this particular instance.

In this way, the dice decide the whether the spell or magic item wins. And rolling dice is what we came to do, right?

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    \$\begingroup\$ -1, as much for technical/mechanical disagreement with the as for the last sentence. Rollplaying is not roleplaying; for many people, there's a whole lot more to gaming than throwing dice. \$\endgroup\$ – T.J.L. May 31 '17 at 14:38
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All effects in D&D 5e stack unless they are from the same spell. Therefore, "the creature" has its intelligence and charisma reduced to 1 and can't do all the things that it says they can't do. The headband then gives it an intelligence of 19, however, it doesn't allow it to do any of the things feeblemind prevents.

Think about it like this: if the feeblemind happened first and then you put on the headband, this would be the obvious outcome. Applying the effects in reverse order cannot give a different result.

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    \$\begingroup\$ I don't think your argument in the second paragraph holds water. \$\endgroup\$ – Nickmagus Jul 1 '16 at 19:15
  • \$\begingroup\$ @Nickmagus in what way? Are you saying its non obvious or that applying the effects in the opposite order gives a different outcome? \$\endgroup\$ – Dale M Jul 2 '16 at 13:38
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    \$\begingroup\$ applying the effects in reverse order can actually give a different result, in many situations. Why should it not be possible for those to give a different result? \$\endgroup\$ – Patta Jul 2 '16 at 15:33
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    \$\begingroup\$ It is both non obvious and not the case that reversing the order of effects can't give a different result \$\endgroup\$ – Nickmagus Jul 2 '16 at 17:43
  • \$\begingroup\$ In the second paragraph, are you suggesting the headband's effect takes precedence because it "layers overtop" the spell effect? \$\endgroup\$ – Tim Grant Jul 2 '16 at 18:22

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