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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?

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    \$\begingroup\$ For context, we have a wizard in our current party who is played by a new player. I was helping them out when this question came to mind. It is not immediately relevant to our 4th-level party; our DM does not track time that finely, and (speaking as a sometimes-DM) spending an extra hour in the morning getting ready is probably not worth tracking in most cases anyways. \$\endgroup\$ – Izzy May 4 at 17:56
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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.

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