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You're supposed to communicate with the kids via the card. I see no reason why you can't use the placement of the card as a means of communication. If so, just pick 4 spots in the room to put the card in. Everyone flips the card one time.
If the card is white first, the first visitor flips it to black. The next unique visitor makes it white again and moves it to the second position. When somone sees the card on the black side in the 4th position, he knows that everyone has been there.
If you can't use the placement of the card, I'd go with rsl12's info gatherer approach.
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