Long story short, if the tile below the initial blue tile is blue, we ALWAYS come to a game state in which we must guess to complete the puzzle, so we can deduce that "wait, that tile can't be blue, otherwise I'd have to guess later on!" But the puzzle says that the puzzle has to be solvable without guessing. This means that we now MUST guess for the above "V" formation. And since the tile directly above the initial blue is gray in our hypothetical situation, it can't give us any info about the tiles above. No matter if the bottommost tile is blue or gray, we will have at least one blue left on the board. However, even after solving the bottom of the puzzle, we still have three tiles above the middle section, that "V" formation, so to speak. Assuming this blue that we just uncovered has a number in the middle, it would give us information about the state of the bottom-most tile. That would leave 2 blues left on the board. Let's do a thought experiment: let's just imagine what would happen if the tile below the initial blue was another blue. We have a blue tile in the middle, which indicates that there is one blue tile in its vicinity, either directly above or below it. The board has three blue tiles left to find Let's see if I can explain my thought process through this. Holy crap! After looking at this puzzle time and time again over the past six months, I think I finally understand it. Remember that all levels are solvable without guessing.
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