12
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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?

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9
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I think the answer for $14 \times 14$ is

$112$

Achieved as follows

enter image description here

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

$50$

Achieved as follows

enter image description here

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  • $\begingroup$ At least you can blank out your boards' corners. $\endgroup$ – msh210 Jul 3 at 13:29
  • $\begingroup$ @msh10 If we blank out the board's corners, the ones adjacent two those now only have one red square. $\endgroup$ – hexomino Jul 3 at 13:30
5
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For $14$x$14$ I got...

$112$

With this ...

enter image description here

Or with this...

enter image description here

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3
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I assume

the boards are independent

Then one solution would be

171 red squares.

As shown below

enter image description here
for 51 squares

And

enter image description here
for 120 squares

No idea if this is minimal though

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  • $\begingroup$ I think that for example cell x=9,y=14 doesn't have to be red $\endgroup$ – Matti Jul 3 at 13:34
-1
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9*9 solution:

45 reds

Looks like:

enter image description here

14*14 solution:

110 reds

Looks like:

enter image description here

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  • $\begingroup$ 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, $\endgroup$ – hexomino Jul 3 at 16:16
  • $\begingroup$ Oh crap, apologies, I thought that the rule was that all white squares needed to be adjacent to two red squares $\endgroup$ – kanoo Jul 3 at 16:17

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