The small squares of the board in the figure must be filled in such a way that:

- in the small squares of each of the regions in the shape of $\hookleftarrow$ appear the numbers 1, 3, 5, and 7 or the numbers 2, 4, 6, and 8;
- in small squares with a common side, consecutive numbers do not appear.

![](https://cdn.mathpix.com/cropped/2024_05_01_984603b876c0bc28095bg-05.jpg?height=294&width=297&top_left_y=984&top_left_x=979)

What is the sum of the numbers that will appear in the gray squares?
A) 12
B) 14
C) 16
D) 18
E) 20

#
Solution

## ALTERNATIVE E

One way to fill in the table according to the conditions of the statement is given below. In each step, we indicate with gray color the new cells filled; the reader can justify each of the illustrated steps. We note that the final table is unique, regardless of how it is filled.
![](https://cdn.mathpix.com/cropped/2024_05_01_984603b876c0bc28095bg-24.jpg?height=188&width=1002&top_left_y=1804&top_left_x=433)

Referring back to the statement of this question, we see that the sum of the numbers in the gray squares marked in the drawing of this statement is equal to $6+8+5+1=20$.