Thursday, 9 January 2014

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:


example of interior solution


Now try this one:


puzzle for you to try



Answer




My answer :



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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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