Zhendarov R.G.

In the cells of a $4 \times 4$ table, numbers are written such that the sum of the neighbors of each number is 1 (cells are considered neighbors if they share a side).

Find the sum of all the numbers in the table.

#
Let's divide all cells into 6 groups (in the figure, cells of each group are marked with their own symbol). Each group consists of all neighbors of some one cell, so the sum of the numbers in it is 1. Therefore, the sum of all numbers is 6.

![](https://cdn.mathpix.com/cropped/2024_05_06_b3d98ec29b07c8345931g-16.jpg?height=334&width=326&top_left_y=948&top_left_x=866)

## Answer

6.