Combinatorics · Games · Winning strategy · Digits · Divisibility rules
Two players play the following game. Taking turns, each player writes down one digit, the digits appearing in a row from left to right in the order in which they are written, and no player is allowed to write a digit that has already been used. The game ends after six moves, when the row of six digits is read as a six-digit number. The first player wins if that number is composite, and the second player wins if it is prime.
Which of the two players has a winning strategy?
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Serbian National Competition (Drzavno takmicenje) 2020, high school grade I, category A, problem 2. Organized by the Mathematical Society of Serbia (DMS). Source