combinatorics - Holo-puzzle (1)

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:

Now try this one:

Answer

My answer :

And the number of red cells for each pattern :

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.


Then a few random tries gave me the answer