How long does it take a wizard to change just one of their prepared spells?

Question

Suppose my 10th-level wizard wakes up from a good night's rest and, using all 20 points of his Intelligence, he realizes that he needs to change his spell list a little. It's time to retire Magic Missile, and prepare Fireball instead. The other 14 spells (with a combined spell level total of, say, 35) are not changed.

That is, he is changing one of his 15 prepared spells; the new spell is a 3rd-level spell. He is not changing any of his other spells.

How long does this take?

The rules in PHB are a little vague. The description in the Spellcasting feature on PHB page 114 says (emphasis mine):

You can change your list of prepared spells when you finish a long rest. 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.

Is the wizard required to spend the full 38 minutes as if he were preparing an entirely new spell list? Or does it require only 3 minutes for the new 3rd-level spell?

Answer 1

Changing one spell changes the list.

Changing a single element on a list makes it a new list. There aren't provisions for modifying a list in the wizard class features just memorizing a new one, as you cited.

Narrative explanation

If a narrative explanation is desired by the table, it could be left to the player for saying why this is so with their character. Perhaps they create mnemonics that are excellent but are ruined by even a small change to the list.

Answer 2

You can change one spell at a time without needing to prepare the whole list again.

The PHB is unclear in its terminology and, Rules As Written, it is written to say that you'd need to entirely prepare a new list of spells even if you only changed one spell in that list.

However, Jeremy Crawford confirmed on Twitter that this was unintentional. Rules As Intended, you can change spells one at a time without needing to prepare your spell list all over again.

Source: https://mobile.twitter.com/TadenRif/status/910551808275357696

@TadenRif @JeremyECrawford
Hi Jeremy. If a wizard changes 1 spell, does she also need to prepare > again all other already prepared, unchanged spells?
12:10 PM · Sep 20, 2017

Jeremy Crawford @JeremyECrawford Sep 20, 2017
Replying to @TadenRif
No.