headband of intellect "exploit"

I'm not sure if this is widely known already but the extra spells you can prepare with the headband on actually stay prepared (seemingly) forever even if you remove it.

so let's say you take a wizard 1 dip to be able to learn extra spells, you can keep intelligence at 8, use the headband to prepare 4 spells (instead of 1) and then switch to another headpiece like the arcane synergy gear or something else.

this is really interesting because it means that my paladin 2 / monk 6 / cleric 3 / wizard 1 will be able to have shield, mirror image, misty steps and counterspell prepared at all time!

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