1. Sasha, Zhenya, and Valya are sitting at a triangular table, which is divided into small triangles, as shown in the figure.

![](https://cdn.mathpix.com/cropped/2024_05_06_d6515d439ee8348f4294g-1.jpg?height=588&width=651&top_left_y=523&top_left_x=725)

They fill all the small triangles with the numbers -1 and 1. After filling all the triangles, they calculate the products of the numbers in their respective horizontal rows and sum the resulting products. (Each person sitting at the table has their own corresponding horizontal direction - parallel to the side of the table facing them). Can it happen that with some arrangement of -1 and 1, Sasha gets a sum of 4, Zhenya gets a sum of -4, and Valya gets a sum of 0?
Solution. One of the possible arrangements is shown in the figure. It is necessary

![](https://cdn.mathpix.com/cropped/2024_05_06_d6515d439ee8348f4294g-1.jpg?height=585&width=645&top_left_y=1649&top_left_x=728)

to place -1 so that in each row in one direction they appear an even number of times, in each row in the second direction -1 appears an odd number of times, in two rows in the third direction -1 appears an even number of times, and in two rows - an odd number of times.

Answer. It is possible.