Question

Which option will replace the question mark?

• A. Fig A
• B. Fig B
• C. Fig C
• D. Fig D

Hint:

To solve multi-component grid puzzles, isolate the simplest tile (like the 3-cell Green tile) and track its rotation. This single-point analysis usually helps eliminate most incorrect options instantly.

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
This question belongs to the topic of

2D Matrix Puzzle and Geometric Transformations.
We are presented with a series of \(4 \times 4\) grids containing four distinct colored interlocking L-shaped tiles: Green, Pink, Orange, and Blue. We must identify the correct pattern that replaces the question mark by analyzing the rotation and translation of each tile.

Step 2: Key Formula or Approach:
We track the coordinates of each color tile from Grid 1 to Grid 3 to determine the direction and degree of rotation and translation:

• The Green tile is an L-shape consisting of 3 cells.

• The Pink, Orange, and Blue tiles are L-shapes consisting of 4 cells each.

• We observe the movement of each block's centroid or bounding box across successive frames.


Step 3: Detailed Explanation:

• Let us analyze the movement of each colored tile step-by-step:
-

Green Tile: In Grid 1, it is positioned at the top-left, occupying cells (1,1), (2,1), and (2,2). In Grid 2, it is rotated 90 degrees clockwise to occupy (1,1), (1,2), and (2,2). In Grid 3, it rotates another 90 degrees to occupy (1,2), (2,2), and (2,1). For the fourth step (the question mark), it must rotate another 90 degrees to occupy (1,1), (1,2), and (2,1).
-

Pink Tile: In Grid 1, it occupies the bottom-left region. In Grid 2, it shifts and rotates slightly. By tracing this sequence, we can see that in the final frame (C), the Pink tile must settle at the bottom-left corner, occupying (3,1), (3,2), and (4,1).
-

Orange Tile: This tile occupies the top-right in Grid 1, shifts downwards along the right edge in Grid 2, and continues this cyclic motion in Grid 3. In the final grid, it must occupy the top-right \(2 \times 2\) area.
-

Blue Tile: It enters from the bottom-right in Grid 2, and in Grid 3, it occupies the bottom-right. In the final grid (C), it settles into the bottom-right corner.

• Comparing these mapped positions with the options, we find that Fig C satisfies the exact positions and orientations of all four colored tiles.


Step 4: Final Answer:
Option (C) correctly replaces the question mark.