Question 197
A $1 \times n$ board is given, where $n \gt 10$ is a natural number. The fields of the board are numbered in order from left to right with the natural numbers from $1$ to $n$. Field number $10$ is black and a token is placed on it; all other fields of the board are white. Two players alternately play the following game. The player who moves first moves the token to an arbitrary white field of the board and colours that field black. In every subsequent move, the player whose turn it is moves the token to one of the white fields of the board, but the token must jump over at least one black field of the board. The player then colours the field on which the token is placed black. The player who first cannot make a move loses the game. Depending on the number $n$, determine which player has a winning strategy: the one who moves first, or the one who moves second.