The Marauder's Map was able to detect & display everyone in Hogwarts. I am just curious if it could detect inside Harry's Invisibility Cloak, which was used successfully against even death. As function of both magical objects are opposite, I can re-frame the question as follows: Marauder's Map vs. Invisibility Cloak - which will win?
Well, Lupin addresses that very issue:
“The number of times I saw James disappearing under it…” said Lupin, waving an impatient hand again. “The point is, even if you’re wearing an Invisibility Cloak, you still show up on the Marauder’s Map. I watched you cross the grounds and enter Hagrid’s hut. Twenty minutes later, you left Hagrid, and set off back toward the castle. But you were now accompanied by somebody else.”
See the Harry Potter Wiki on the The Marauder's Map for more details.
We learn in Harry Potter and the Cursed Child that not only can the cloak's user/s be seen on the map, they can even be seen when the person is in the room with the map itself!
PROFESSOR McGONAGALL (from off — trying to give them every chance): I am about to enter.
PROFESSOR McGONAGALL comes into the room, the Marauder’s Map in her hands. The boys disappear beneath the Cloak. She looks around, exasperated.
PROFESSOR McGONAGALL [continued] Well, where have they — I never wanted this thing and now it’s playing tricks on me.
She thinks. She looks back at the map. She identifies where they should be. She looks around the room. Objects move as the boys invisibly move past them. She sees where they’re heading, she makes to block them. But they skirt around her.
PROFESSOR McGONAGALL [continued] Unless. Unless . . . Your father’s Cloak.
She looks back at the map, she looks at the boys. She smiles to herself.
PROFESSOR McGONAGALL [continued] Well, if I didn’t see you, I didn’t see you.
This is a key element of Harry's nighttime adventure with the egg in chapter 25 of Goblet of Fire (my emphasis):
Any moment now, Filch was going to pull aside the tapestry, expecting to see Peeves... and there would be no Peeves... but if he came up the stairs, he would spot the Marauder's Map... and Invisibility Cloak or not, the map would show "Harry Potter" standing exactly where he was.
Yes. In the Goblet of Fire, Moody sees Harry on the map, under the cloak.
protected by Valorum Apr 1 '14 at 13:01
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