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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 the 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 shows their ball to a fourth person, Zog. Zog then says, “One of the lottery balls is a number that is the sum of the numbers on the other two lottery 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?

This puzzle was taken from a post written by Alex Bellos @alexbellos which first appeared in the Guardian newspaper on Mon 13 Aug 2018 07.10 BST. Last modified on Mon 13 Aug 2018 18.52 BST.

If you are interested in problem-solving and would like to find out if you are smarter than a Singaporean 10-year-old, then you may be interested in Can You Solve My Problems? : A casebook of ingenious, perplexing, and totally satisfying puzzles by Alex Bellos and available at the Book Depository.

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