Question 53
Ats and Pets take turns to write representations of the number $15$ as the sum of three distinct single-digit positive integers. On every move, each player must write a sum that has exactly one common addend with the previous sum, no common addends with the second previous sum, and less than three common addends with any sum written earlier. Ats starts and can choose the first sum arbitrarily. The player who cannot write a sum loses. Which player can win regardless of his opponent's play?