Cherry’s lottery ball: There are nine shiny new lottery balls in a lottery machine. They are numbered 1, 2, 3, 4, 5, 6, 7, 8 and 9. The machine dispenses one lottery ball to each of three people. Apple, Bean and Cherry. Each person knows only the number of their own ball. They do not know the numbers of the balls that the others were given. Nor do they know which numbers were left in the machine.
Before the game begins, each of them show their ball to a fourth person, Zog. Zog then says, “One of the balls is a number that is the sum of the numbers on the other two balls.”
At which point the following conversation ensues….
Apple: “There are 8 possibilities for Bean’s lottery ball.”
Bean: “There are 8 possibilities for Cherry’s lottery ball.”
Cherry: “There are 4 possibilities for Apple’s lottery ball.”
Apple: “I know Bean’s lottery ball!”
Bean: “I know Cherry’s lottery ball!”
Question: What is Cherry’s lottery ball?