1. On the board, there is a table containing 100 columns and 2 rows. Sasha and Zhenya take turns filling in one cell of the table, writing either -1 or 1. Sasha makes the first move. After the table is completely filled, the products of all 100 numbers in each row are calculated. Similarly, for each column, the products of the two numbers in that column are calculated. Can Zhenya make her moves in such a way that in the filled table, the sum of the products of the numbers in the rows equals -2, and the sum of the products of the numbers in the columns equals 0?
Solution. Consider pairs of cells in each row of the table, where each pair will consist of a cell with an odd and an even number. The winning strategy for Zhenya is to give Sasha the opportunity to make the first move in each such pair. Let Sasha fill one (any) of the two cells. In response, Zhenya needs to fill the second cell of the pair according to the following rule. In the first pair of the top row, Zhenya should place the same number that Sasha places. In the table below, this is indicated as the pair $|y| y \mid$. In all pairs of the top row, except the first, Zhenya should write the number opposite to the one placed by Sasha. In the table below, this is indicated as the pair $|x|-x \mid$. In the bottom row, pairs will be filled in the opposite way - the first pair after filling should contain two opposite numbers $|x|-x \mid$, all other pairs, except the first, should contain the same numbers $|y| y \mid$. Obviously, Zhenya will always be able to make the necessary move in each pair. After placing -1 and 1 according to this strategy, in each row there will be an odd number of minus ones, the product of the numbers in the row will be -1. The sum of the products in the rows will be -2. In adjacent odd and even columns, the products of the numbers will be opposite, and the sum of these products will be zero.

| $y$ | $y$ | $x$ | $-x$ | $x$ | $-x$ | $\ldots$ | $x$ | $-x$ | $x$ | $-x$ |
| :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: |
| $x$ | $-x$ | $y$ | $y$ | $y$ | $y$ | $\ldots$ | $y$ | $y$ | $y$ | $y$ |

Answer. Can.