Seven cards exist, numbered 0 through 6.

Alice is dealt 3 cards
Bob is dealt 3 cards
Eve is dealt 1 card

All three know the distribution (3, 3, 1) but not each other's hands. Eve can hear everything Alice and Bob say.
Alice and Bob must exchange public announcements — statements Eve fully hears, such that:
- Alice and Bob both learn each other's complete hands
- Eve gains zero information about any card she doesn't hold — meaning for every card in Eve's hand's absence, she cannot determine with any certainty whether Alice or Bob holds it

Can Alice and Bob do this? If so, how?


IMPORTANT NOTE: "zero information" is strict. It's not enough that Eve can't be certain — after all announcements, Eve must have no probabilistic advantage whatsoever on any card. She must be in a 50/50 state on every card she doesn't hold, as if no announcements had been made at all.

Good Luck solving, it took me around an hour of deep focus