This is a solution for the 7 x 7 game, and is submitted by Angelmorph. You only need to flip all the pieces marked with a star below:



The solution is quite easy to remember, first, you flip the 1st, 2nd, 4th, 6th, 7th pieces on the first row, then you scan the pieces row by row, if a piece is black, then you flip the piece directly below it.

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