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You have a white grid of size
a) 9x9
b) 10x10
and you are asked to paint some squares black. Your generous friend has given you a challenge:

Can you paint them so that each white square has only one adjacent black square?

After some puzzling around, you proudly present to your friend a piece of paper showing your answers.
What did you write down?

Good luck!

⬜⬜⬜⬜⬜⬜⬜⬜⬜  
⬜⬛⬛⬜⬜⬜⬛⬛⬜  
⬜⬛⬛⬜⬜⬜⬛⬛⬜  
⬜⬜⬜⬜⬜⬜⬜⬜⬜  
⬜⬜⬜⬜⬛⬜⬜⬜⬜  
⬜⬛⬜⬜⬜⬜⬜⬛⬜  
⬜⬛⬛⬜⬜⬜⬛⬛⬜  
⬜⬜⬛⬛⬛⬛⬛⬜⬜  
⬜⬜⬜⬜⬜⬜⬜⬜⬜

Hint 1:

Observe how many squares are adjacent to a black square around the grid!

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  • 1
    $\begingroup$ Does adjacent mean they share an edge, or can two squares be diagonally adjacent? $\endgroup$
    – SQLnoob
    Commented May 20, 2021 at 16:56
  • $\begingroup$ I take it rot13(Whfg cnvagvat rirelguvat oynpx qbrfa'g pbhag?) $\endgroup$
    – loopy walt
    Commented May 20, 2021 at 16:57

2 Answers 2

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7
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Here's a solution to both problems

Paint all squares black

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Assuming adjacent means they share an edge, then a trivial solution where some white squares exist is

just paint everything except the first and last rows black. Then each white square in the first and last rows is touching exactly one black square.

If adjacency includes squares that touch diagonally, then something simple like these should work:

enter image description here

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