# 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:

• If you didn't give the exterior I would have mad one all gree. Mar 27, 2016 at 14:40
• 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.
– Deusovi
Mar 27, 2016 at 16:16
• @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. Mar 27, 2016 at 17:08
• @Johannes: Just approved the edit - that's a lot better.
– Deusovi
Mar 27, 2016 at 17:09
• @ruakh has been so kind to change the colors. Thanks Ruakh! Mar 27, 2016 at 17:12

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

• You found the unique answer (unique as the boundary colors fully specify the interior). However, a more elegant solution strategy is feasible. Mar 27, 2016 at 13:44
• Try the next level: puzzling.stackexchange.com/questions/29732/holo-puzzle-2 :-) Mar 27, 2016 at 15:42