3. Given a rectangular table $14 \times n$. In its top-left cell, there is a chip. Sasha and Olya take turns (Sasha starts) moving the chip one cell to the right or down. We will say that a turn has occurred if the direction of the player's move differs from the direction of the move made by the opponent before that. If, by the time the chip reaches the bottom-right corner, an even number of turns have occurred, Sasha wins; otherwise, Olya wins. For which values of $n$ can Olya ensure her victory regardless of Sasha's actions?
Answer: 13, 14, 15. The presence of an even number of turns is equivalent to the directions of the first and last moves coinciding. If $n>15$, then Sasha can make the first move down, and then always move right. Similarly, in the case of $n<13$: Sasha can make the first move right, and then move down. It is easy to see that in this case, he will win.

In all other cases, Olya will, as long as possible, repeat Sasha's first move. Suppose Sasha moved, for example, down. Then, since the number of rows is not greater than the number of columns plus one, when the chip is moved to the bottom row, it will not yet be in the first column. Therefore, the direction of the last move will be different from the direction of the first, and Olya will win.