There is a token in one of the nodes of a hexagon with side n, divided into regular triangles (see figure). Two players take turns moving it to one of the neighboring nodes, and it is forbidden to go to a node that the token has already visited. The one who loses who can't make a move. Who wins with the right game?
https://cdn.artofproblemsolving.com/attachments/2/f/18314fe7f9f4cd8e783037a8e5642e17f4e1be.png combinatoricscombinatorial geometrygame