Parity invariance
Parity invariance means that the number of times a position is flipped determines its final value. If a position is flipped an odd number of times, its value changes, but if it is flipped an even number of times, it stays the same.
Consider the array [1, 0, 0, 1, 0, 1, 1]. We start by flipping three consecutive elements to try and transform all 0s into 1s. First, flipping the subarray [0, 0, 1] at indices 1..3 changes the array to [1, 1, 1, 0, 0, 1, 1]. Then, flipping [0, 0, 1] at indices [3..5] gives [1, 1, 1, 1, 1, 0, 1]. Finally, flipping [1, 0, 1] at indices [1, 0, 1] at indices 4..6 results in [1, 1, 1, 1, 1, 1, 0, 1, 0].
At this point, we see that the 0s at positions 4 and 6 remain, and there is no way to flip them without also flipping the other elements. Since we can only flip three elements at a time, we cannot isolate these 0s in a way that allow us to change them to 1s. This happens because these positions were flipped an even number of times, so they retain their original value. Because of this parity constraint, the transformation is impossible.