5
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A boundary of red and blue squares is given. Can you fill in the interior such that each 5-square pattern consisting of an interior cell plus its four nearest neighbours always contains an even number of red squares?

Example:

example of interior solution

Now try this one:

puzzle for you to try

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  • $\begingroup$ If you didn't give the exterior I would have mad one all gree. $\endgroup$ – tox123 Mar 27 '16 at 14:40
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    $\begingroup$ Could you change the colors? I'm red-green colorblind, and it's impossible to tell them apart - currently your puzzle is inaccessible to 10% of the male population. $\endgroup$ – Deusovi Mar 27 '16 at 16:16
  • $\begingroup$ @Deusovi - would red/blue work better than red/green? Awaiting the edit of the figures: the example as well as the puzzle itself have all green boundary squares, with the exception of the four double squares at the points of the figures, which are all red. $\endgroup$ – Johannes Mar 27 '16 at 17:08
  • $\begingroup$ @Johannes: Just approved the edit - that's a lot better. $\endgroup$ – Deusovi Mar 27 '16 at 17:09
  • $\begingroup$ @ruakh has been so kind to change the colors. Thanks Ruakh! $\endgroup$ – Johannes Mar 27 '16 at 17:12
5
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My answer :

enter image description here
And the number of red cells for each pattern :
enter image description here
every interior pattern has an even number of red cells.

How to find it :

I hoped there were a lot of symmetry so I had only a few cells to choose ! All the yellow cells are deduced from the blue cells by symmetry.
enter image description here
Then a few random tries gave me the answer

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