Combinatorics · Combinatorial games · Winning strategy · Arrangements of lines · Incidence counting
Maksim and Mina play the following game. Maksim starts by drawing a line in the plane; Mina then draws a line different from it; Maksim then draws a line different from both lines already drawn, and so on, the two players alternating. The game finishes once \(18\) lines have been drawn altogether, so the last one is Mina's.
Maksim wins if the drawn lines have more than \(100\) distinct points of intersection, and Mina wins otherwise, that is, if the number of such points is \(100\) or fewer. Which player has a winning strategy?
Sign in to check answers, open hints, read the full solution, and track your progress. Statements are always free.
Serbian Regional Competition 2018, high school grade I, category A, problem 5. Organized by the Mathematical Society of Serbia (DMS). Source