[sirclueless]

There's actually a constraint that no blue circle can be alone, which you can find by reaching an end board with a solitary blue that the game will prompt you about. So X red and Y blue would be well-determined.

However there does appear to be another constraint that is not mentioned explicitly, which is that there are no blue circles that are not in line-of-sight with a numbered circle.

[T-hawk]

That last isn't defined explicitly. It's an emergent property from the constraint that the solution must be unique.

Any blue circle (or any linear group of them) that is not in line-of-sight with a numbered circle would have no constraint preventing it/them from being red instead. Therefore the solution wouldn't be unique, so such blue circles can't exist.