I'm not following.
The only hiding they would need to do is back in time.
Replacing the sleeping Dumbledore at the foot of the tower would have
happened before and during the events at the top of the tower.
He would already be there, on the ground, when the original starts to fall.
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Wait.....I don't see what you're saying either. Because in any case of what you're saying, one Dumbledore will die, right?

P.S. lol, good one, ginevra, but you know JK would never make it that easy!