I met a guy who was a pilot in Vietnam. They had (and still have) a system where everyone carries a card with a grid of numbers and letters on it, and you can authenticate someone over the radio by picking a couple spots on the grid and they respond with, for example, the character adjacent to them. Well, he forgot his card one day and was queried by a controlling agency using the authentication card. He told them to stand by, switched frequencies, and issued the same challenge to another agency. They responded, and he switched back and passed it along to successfully authenticate himself.
In my case I just wrote out the possible combinations, and saw the 1/3 right away. I had fallen for the same problem as the 100 coin tosses: by the time I have identified a child enough to refer to the "other child," I have already beaten some of the odds!
But please clarify the "one is a girl" and "one is named Mary."