Question 63
Richard and Kaarel are taking turns to choose numbers from the set $\{1, \dots, p-1\}$ where $p \gt 3$ is a prime. Richard is the first one to choose. Any number which has been chosen by one of the players can be chosen again be neither of the players. Every number chosen by Richard is multiplied with the very next number chosen by Kaarel. Kaarel wins the game if at some moment during the game the sum of all the found products is divisible by $p$. Richard wins if this does not happen i.e. the players run out of numbers before any of the sums is divisible by $p$. Can either of the players guarantee their victory regardless of their opponent's moves and if so, which one?