Question

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.

• A. (i)
• B. (ii)
• C. (iii)
• D. (iv)

Hint:

Track how the number and position of filled circles change along each row and each column of tiles.

Answer 1

The Correct Option is A

Step 1: Set Up an Elimination Method:
Instead of predicting the missing tiles from scratch, compare each of the four candidate answer pairs in Panel II directly against the tiles that are already fixed in the same row and the same column of Panel I, and eliminate any candidate that breaks the pattern in either direction.
Step 2: Check Against the Row Pattern:
Look at the top tile of each candidate pair and compare it with the first two tiles already present in that same row of Panel I. Candidates whose top tile does not carry forward the same left to right change in filled circles seen between the first and second tiles of that row can be eliminated immediately, since the missing top tile must continue that row established trend.
Step 3: Check Against the Column Pattern:
Now look at the bottom tile of each remaining candidate pair and compare it with the tile directly above it, which is the top tile of the same candidate. The relationship between the top and bottom tile of the correct candidate must match the same top to bottom change in filled circles seen in the first two columns of Panel I. Any candidate whose internal top to bottom change does not match this established column pattern is eliminated at this stage.
Step 4: Cross-Check and Final Answer:
After applying both checks, only option (i) survives, since its top tile correctly extends the row trend and its bottom tile correctly extends the column trend, while options (ii), (iii) and (iv) each fail at least one of the two checks. This double confirmation, from both the row direction and the column direction, gives the same answer as the direct pattern construction method.
\[ oxed{ ext{Option (i)}} \]