OSN 2015 Problem 1
Albert, Bernard, and Cheryl are playing marbles. At the beginning, each of them brings 5 red marbles, 7 green marbles and 13 blue marbles and in the middle of the table, there is a box of infinitely many red, blue and green marbles. In each turn, each player may choose 2 marbles of different color and replace them with 2 marbles of the third color. After a finite number of steps, this conversation happens.
Albert : " I have only red marbles" Bernard : "I have only blue marbles" Cheryl: "I have only green marbles"
Which of the three are lying?
Dataset text AI-MO AoPS. Quoted with source.
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