Seven cards, numbered $1,2,3,4,5,6,7$, are distributed randomly among three people: Rand gets one of them, Deusovi gets three of them, and Gareth gets three of them. All three know what the seven cards are and how many each person gets, but the only card(s) they can see are their own.
Deusovi and Gareth each post a statement in the Sphinx's Lair. All three people can see the messages, and they know that each speaker knows his statement to be true.
After this, Deusovi and Gareth each know exactly who holds which cards, but Rand still doesn't know the location of any card apart from his own.
No private communication is allowed either before or after the cards are distributed. Deusovi and Gareth can't use the Puzzling mod room or other private rooms to decide a strategy beforehand and encode more information in their messages.
What could the two public statements be?
Of course, the statements can depend on what cards each person holds, but there should be a strategy for what statements to make regardless of the distribution of cards among the three people.
This is based on a puzzle from the Moscow Mathematical Olympiad. It's interesting because there's a nice mathematical answer but also a 'trick' answer whose validity can be debated according to how rigorously the question is phrased. For extra bonus points, find the 'trick' answer - but note that it's NOT lateral-thinking, and is still based on pure logic.