01
Mark the three occupied cells
Number rows from top to bottom and columns from left to right. Mark cells (1,1), (2,2) and (3,3) as occupied; leave the other six empty. This fixes both the coordinates and the orientation of the diagram. Under edge-only adjacency, a cell can connect to the position directly above, below, left or right. None of the three occupied cells shares an edge with another occupied cell. Each therefore forms its own connected group, producing three groups of one cell while the number of occupied cells remains three.
02
Allow corner contact as well
Under edge-or-corner adjacency, the centre cell touches each of the other occupied cells at a corner. The upper-left and lower-right cells do not touch one another directly, but they are connected through the centre. The three occupied cells therefore form one connected group. This is a transitive relationship: a chain of allowed contacts is sufficient. The result is not a claim that the cells have merged physically. It says that the chosen rule treats the path through their corner contacts as a connection.
03
Record both outcomes in a worksheet
Use fields for grid size, occupied coordinates, adjacency rule and resulting groups. For edge-only contact, list {(1,1)}, {(2,2)} and {(3,3)}. For edge-or-corner contact, list all three coordinates in one group. Verify that every occupied coordinate appears exactly once in each result and that no empty cell has been included. A later exercise can add another cell and repeat the comparison. Preserve the rule name with the answer so the difference between three groups and one group remains explainable after the original picture is separated from its notes.