1. Given a cube, each face of which is a grid of 2015 by 2015

cells. In the center of one of the faces stands a pawn. Danil and Maxim move the pawn across the cells of the cube. Danil can only move to an adjacent cell (it is allowed to move to another face if the cells are adjacent), while Maxim can place the pawn in any cell. The pawn colors the cells it moves over. It is not allowed to move the pawn to a colored cell. The initial cell (the center of the face) is colored. Danil moves first. The player who cannot make a move loses. Who will win with correct play from both?
Solution. Answer: Danil wins.

We will present a winning strategy for Danil.

The number of cells on the surface is even (equal to 2015*2015*6). We will divide the entire surface of the cube into dominoes; the dominoes do not overlap and cover the entire cube. We will not provide an example of the division. It is easy to see that such examples exist. Students who wrote this solution should provide an example.

At the beginning of Danil's turn, the pawn is in one of the dominoes. Danil moves to the second cell of the domino. If Danil has acted according to this strategy up to this point, then the second cell of the domino is not colored and the move can be made. It is obvious that Danil will make the last move - at least because he can always make a move.

## Criteria

+- - a correct strategy is presented without an example of dividing the cube into dominoes.