Reading this maze
Paired doorways starts at row 2, column 1. 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.
Diamond A at row 3, column 5 toggles both barred cells marked A. Diamond B at row 3, column 6 toggles the gate marked B. Start right and stop at row 2, column 5. Both A gates share one state, while B stays independent; plan the closed bars as stopping points. The first slide covers 5 of 28 target tiles.
The verified opening crosses 4 tiles before stopping. A breadth-first search proves a 24-slide finish from this exact starting board; that is a reference target, not a move limit. You may revisit any painted tile.
A and B keep separate states. The A diamond toggles both A gates together, while the B diamond toggles only B. Every barred cell must be painted. Undo restores all gate states, and Hint searches your current trail.