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The question is different from this one.

Disclaimer: I want to clarify something. My question is not meant to find a way of breaking the class or whatnot. My question is because I am curious of if it is possible.

I see that it is possible for Keen Mind to bypass the Wizard limitation on number of spell prepared per day. The reason would be (PHB 114):

Preparing a new list of wizard spells requires time spent studying your spellbook and memorizing the incantations and gestures you must make to cast the spell: at least 1 minute per spell level for each spell on your list.

Emphasis mine. From the mechanical point of view, the Keen Mind feat allows you to completely memorize something that you have seen. Since you have to study and memorize your spells, that would mean that the Keen Mind feat might be used to memorize all your spells.

Keen Mind:

You have a mind that can track time, direction, and detail with uncanny precision. You gain the following benefits.

  • Increase your Intelligence score by 1, to a maximum of 20.
  • You always know which way is north.
  • You always know the number of hours left before the next sunrise or sunset.
  • You can accurately recall anything you have seen or heard within the past month.

Emphasis mine. Since studying and memorizing is, well, much more focused than just seen and hearing, there is not limitation on that side. Also, from the perspective of that a specific rule overrides a general rule (PHB, page 7), the specific rule of the feat might invalidate the general rule of the wizard.

Remember this: If a specific rule contradicts a general rule, the specific rule wins.

That is from the mechanical stand point. But from the RP point the wizard memorize his spells easily from "years" of practice, reading and a high intelligence to boost. Little has to do with magic or a magical mind. Just plain and crude practice.

You prepare the list of wizard spells that are available for you to cast. To do so, choose a number of wizard spells from your spellbook equal to your Intelligence modifier + your wizard level (PHB, 114)

The feat would imply that the wizard has an unusual sharp mind to remember and recall details quickly over a specific time. Once that time is passed, if there is not feedback the memory become foggy and unreliable (the spell just might kaboom in his face).

So, it seems that is possible, but, is it really possible (regardless of how OP that might be)?

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Looks like that use of the feat was not part of the designers's intent(Source: Jeremy Crawford twitter):

Question: Does a wizard with the Keen Mind feat have unrestricted prepared spells?

Answer: The Keen Mind feat isn't meant to change how a wizard's spell preparation works.

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Let's take your position at face value.

Specifically where and how does Keen Mind override the specific limit on the number of spell's you can prepare? Yes, you can accurately recall every page of your spell book. Arguably, this means you could prepare your spells without having a spell book (although this depends on how you resolve the conflict between two specific rules). It doesn't give you the ability to prepare more than your Int bonus + level. Prepare ≠ remember.

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No.

By a strict RAW reading, the most this feat would do is remove the time requirement of memorizing the newly prepared spells, but not the long rest requirement to change the list in the first place. If the feat did modify the long rest requirement, it would say so.

Why? Because even when changing something as menial as a level 1 magic missile, you still need a long rest even without the feat despite a level 1 spell requiring only 1 minute to replace.

My extrapolation:

This is primarily an opinion based answer derived from reading the PHB with respect to Wizard spellcasting, preparation and and requires the use of inductive reasoning.

Preparation of a spell is not simple memorization, if it was Keen Mind would include a statement which indicates that you could prepare all of your spells as a Wizard. Preparation includes memorization, but also includes rituals, somatic and material component costs associated with the spells. I'll cover a house rule I use for this last, but I'll get into preparation first.

A wizard preparing spells for the day takes the time to memorize them. You've already done this with Keen Mind. Consider that somatic components of a spell may be something extremely complicated that is time intensive. Which means spending part of your long rest performing the somatic portion, but leaving the final part off of the spell to be completed later, kind of a hang-fire situation. The spell slot could be the power containing the prepared spell, with the trigger releasing it being the final part of your casting. The long rest in this situation would be required in order to prepare things like this.

Plainly put though, 5e doesn't provide specific incantations and gestures required, so we have to extrapolate. Based on the description of spell casting and how wizards prepare their spells, the requirement of a long rest to change spells seems to be intrinsic to the extreme amount of time and effort required to prepare the spells.

Lastly, as a side note and house rule:

I would allow a player with Keen Mind the ability to swap spells at a short rest. Why? Because a major, time consuming portion of spell casting, the memorization of the incantations, has been effectively removed. However I would personally rule that a short rest would need a minimum of 1 hour for the Wizard to alter spells. Although that's a completely arbitrary ruling I would use.

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Preparing and casting spells (PHB p.114):

"Preparing a new list of wizard spells requires time spent studying your spellbook and memorizing the incantations and gestures you must make to cast the spell: at least 1 minute per spell level for each spell on your list."

So NO, Keen Mind feat does NOT allow a Wizard to have prepared all his spells.

It takes study and memorisation, not just memorisation. You have to actually actively study your book to prepare spells, it is not merely an act of memory. Casting magic is a tricky thing and defies explanation sometimes. That's why it is magic.

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