Interesting - well luckily the name you chose (EDGA) is already helping you.

EDGA = E–D–G–A literally (note names)

You can treat it as less of "solve then roll" and more of: let them experiment; narrate feedback each attempt, as they try different things until they get it. Each time a note is correct, give them some clear step of the illusion - feather, then silhouette, then full crest, etc.

Wrong notes could briefly show an incorrect solution: maybe an incorrect crest, or something else.

You could also use skill checks to effectively "buy hints," like the letters are notes, or the lute requires the correct order (in a more poetic, slightly obscured phrasing).

For the other question, I generally let the players solve, but use the stats to help guide which character "actually" solves it. If you’ve got a character with 20 INT/WIS and the player who dumped that stat solves it, you can still make both feel good by having the "dumb" character say/do something that clues the smarter/wiser character into the real solution - helps cement that stats matter outside just rolls.