I just used ms paint to map out every viable arrangement of the colors and the given symbols, and while there are a total of 5 arrangements that would validate, only 1 of the arrangements leaves nothing to guesswork: 3-color bar on the right, 2 hearts row on the bottom, 2 stars row in the middle. This arrangement gives 2 shapes for each color and 3 unique open colors. The other 2 arrangements each leave 2 pink squares with no definite given solution.