Combinatorics · Combinatorial games · Winning strategy · Pairing · Arithmetic progressions
Two players alternately write one of the numbers
into a free cell of a \(3 \times 3\) table, where each number may be used only once. On his first move the first player is not allowed to write into the central cell.
The game ends as soon as one of the players obtains the sum \(2019\) in some row, column or diagonal all three of whose cells are filled; that player is then the winner. If the whole table is filled and nobody has obtained such a sum, the winner is the second player.
Which player has a winning strategy?
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Serbian Regional Competition (Okruzno takmicenje) 2019, high school grade I, category A, problem 5. Organized by the Mathematical Society of Serbia (DMS). Source