Zhendarov P.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 a single 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_f36000480089c1ccffcbg-08.jpg?height=354&width=323&top_left_y=0&top_left_x=865)

## Answer

6.