Each square adds and removes surrounding dividers. Squares 4 and 10 are the only ones that do not add dividers, while 16 is the only one that only adds dividers. Try pressing squares that are touching the most dividers… upon press, if they don’t do the desired effect, take note.
Squares on the left remove dividers; Squares in the middle left shift dividers to the left; Squares in the middle right shift dividers to the right; Squares on the right add dividers;
The corner squares remove two dividers (or shift a divider) in counter clock-wise rotation; The 4 middle squares remove dividers if all 4 dividers are present. Otherwise, the dividers rotate around counter clock-wise; Squares 2, 8, 15, 9, upon press, will shift their dividers to the nearest middle square if that square has no dividers; Squares 3, 12, 14, 5, upon press, will add dividers if they are missing any – otherwise they will shift their dividers to the nearest middle square if that square has no dividers;