# Red and White Squares

There are two grid boards with the dimension of 9x9 and 14x14, consist of all white squares. You are supposed to color some squares with a red color on the conditions below:

• In a board, if two square has a common edge, they are neighbor squares.
• Every square needs to have at least 2 colored neighbor squares (excluding itself)

so

What is the least number of red squares you can have with the condition above?

I think the answer for $$14 \times 14$$ is

$$112$$

Achieved as follows

While the best I've achieved for $$9 \times 9$$ is

$$50$$

Achieved as follows

• you seemed to have reached the answer using brute force. Could you have solved this question using logic ? And if yes, then can you please explain your logic. Nov 21, 2020 at 11:36

For $$14$$x$$14$$ I got...

$$112$$

With this ...

Or with this...

• you seemed to have reached this answer using brute force . Could you have solved it using logic ? Nov 28, 2020 at 16:47

I assume

the boards are independent

Then one solution would be

171 red squares.

As shown below

for 51 squares

And

for 120 squares

No idea if this is minimal though

• I think that for example cell x=9,y=14 doesn't have to be red Jul 3, 2019 at 13:34

9*9 solution:

45 reds

Looks like:

14*14 solution:

110 reds

Looks like:

• In your 9x9, there are eight red squares only adjacent to one red square and the one in the centre is adjacent to none. In your 14 x 14, the two red squares in the centre are adjacent to no red squares, Jul 3, 2019 at 16:16
• Oh crap, apologies, I thought that the rule was that all white squares needed to be adjacent to two red squares Jul 3, 2019 at 16:17