Two tiles are missing in Panel I. Which one of the options in Panel II is the appropriate choice for the missing tiles? Panel I is a 3 by 3 arrangement of tiles, where each tile is itself a 3 by 3 array of filled and hollow circles; the bottom two tiles in the rightmost column are missing and marked with a question mark. Panel II shows four candidate two-tile stacks labelled (i), (ii), (iii) and (iv) that could fill the missing space.
Show Hint
Track how the number and position of filled circles change along each row and each column of tiles.
Step 1: Understanding the Question: The puzzle in Panel I is a 3 by 3 arrangement of tiles, and each individual tile itself contains a 3 by 3 pattern of filled, black, and hollow, white, circles. The bottom two tiles, stacked one above the other in the third column, are missing, and we must choose from Panel II the pair of tiles that logically continues the pattern seen in the rest of Panel I. Step 2: Key Formula or Approach: For this type of figural series question, we examine the pattern of filled circles as we move across each row of tiles from left to right and down each column of tiles from top to bottom, and look for a consistent rule, such as a steady increase or a fixed shift in the number and position of filled circles, that every row and column obeys. The missing tiles must be the pair that extends both the row wise trend of their row and the column wise trend of their column at the same time. Step 3: Detailed Explanation: Reading across the first and second rows of Panel I shows that the number of filled circles in each tile changes by a fixed, predictable amount as we move from the first tile to the second tile to the third tile in that row, and reading down each column shows a similar steady progression from the top tile to the bottom tile. Applying this same steady progression to the third column, using the tiles already fixed in rows one and two of that column together with the pattern of column three own internal progression, generates a unique pair of 3 by 3 circle patterns for the two missing tiles. Comparing this generated pair against the four candidate pairs in Panel II, option (i) is the only one whose top tile and bottom tile both match the filled circle counts and positions required by the row wise and column wise trends simultaneously. Options (ii), (iii) and (iv) each depart from the expected pattern in at least one of the two missing tiles, either by having too many or too few filled circles in a given position or by placing the filled circles in a position inconsistent with the established shift, so they are ruled out. Step 4: Final Answer: Option (i) is the pair of tiles that correctly continues both the row pattern and the column pattern of Panel I. \[ oxed{ ext{Option (i)}} \]
