Two players play on a $3 \times 100$ board: they take turns placing dominoes $1 \times 2$ on free cells. The first player places dominoes along the board, the second - in the transverse direction. The player who cannot make a move loses. Which of the players can ensure their victory (regardless of how their opponent plays), and how should they play?
Let's divide the board into 50 rectangles of $3 \times 2$. The first player, on each turn, places a domino in the center of one of the free sections until it is no longer possible. Each domino of the second player is entirely within one of the sections, so the first player will make at least 25 moves according to this strategy. After at least one domino is placed in each section, the first player can still make at least 50 more moves in the sections where their dominoes are placed. The second player, however, can make no more than 25 moves—in the sections where their dominoes are placed (the second player cannot move into sections where the first player's dominoes are placed).

## Answer

The first player

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