Each of four friends (Andy, Beth, Cici, Dave) ate 1 candy out of 11 leaving 7 in the bowl. A sudden blackout made the room completely dark, and when the light came back on, all of the 7 candies were eaten.
Andy first asked Beth, "Did you eat more than I did?"
Beth answered, "I don't know."
Then Beth asked Cici, "Did you eat more than I did?"
Cici answered, "I don't know."
Upon hearing these, Dave said he knew the exact distribution of the 11 candies.
If everyone is telling the truth, and is smart enough to catch the implications of the conversations, what is the distribution of the 11 candies that Dave figured out?