Reading this maze
Alternating returns starts at row 6, column 4. Of the 42 grid positions, 28 are paintable and 14 are walls. The start is already painted; the other 27 tiles remain to be reached.
Diamonds A at row 1, column 5 and row 3, column 1 toggle the gate marked A. Diamonds B at row 3, column 6 and row 1, column 2 toggle the gate marked B. Start left and stop at row 6, column 2. Either matching diamond flips its letter; both A diamonds share A, and both B diamonds share B. The first slide covers 3 of 28 target tiles.
The verified opening crosses 2 tiles before stopping. A breadth-first search proves a 27-slide finish from this exact starting board; that is a reference target, not a move limit. You may revisit any painted tile.
Diamonds A and B control separate gate groups. Each letter toggles only its matching barred gate; the other group keeps its current state. Changes take effect during the same slide. Undo restores both groups, and Hint searches from both gate states and the painted floor.