I got stuck right at the end of my game, and got the following hint:
What am I missing? What logic dictates that only one combination is possible?
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The rules of the game state that a full row or column must have as many red tiles as it has blue ones.
The row has 2 open spaces, which one needs to be red and the other blue.
The right column can be either blue or red and still be able to fulfill the same number of each color requirement.
The left column has 5 blue and 3 red with only 2 open spaces. This means...
the left square must be red and the right blue
The third column already has 5 blues, and only 3 reds. Since you must have an equal number of tiles of each color in each column/row, both remaining squares in the third column (including the leftmost of the two highlighted) must be red. Then, the other highlighted square, being in the same row, must be blue so that row has an equal number of reds and blues.