Step 1: Recognize the layout as a magic square in disguise.
Replace each 3x3 dot tile by the number of black dots it contains. Reading off the 7 visible tiles of Panel I gives the grid: 8, 1, 6 on top; 3, 5 and a question mark in the middle; 4, 9 and a question mark at the bottom.
Step 2: Recall the property of this square.
This is the well known Lo Shu magic square, built from the digits 1 to 9 with every row, column and both diagonals summing to $15$.
The completed square reads $8, 1, 6$ on top, $3, 5, 7$ in the middle, and $4, 9, 2$ at the bottom.
Step 3: Read off the two missing values.
The middle-right tile must show $7$ filled dots and the bottom-right tile must show $2$ filled dots, since these are the only values that keep every row and column at $15$.
Step 4: Check each option's dot counts.
Option (i) shows 7 filled dots on top and 2 filled dots below, matching the required pair exactly. Options (ii) and (iv) show only 6 dots in the upper tile, and option (iii) shows 3 dots in the lower tile instead of 2.
Final Answer:
The tile pair with counts 7 and 2 belongs to option (i), so that is the correct completion of Panel I.
\[ \boxed{\text{Answer} = \text{(i)}} \]
