Which one of the following sets of pieces can be assembled to form a square with a single round hole near the center? Pieces cannot overlap. A. [Four irregular interlocking pieces with a circular cutout among them] B. [Four irregular pieces that do not combine into a complete square] C. [Four irregular interlocking pieces that fit together to form a perfect square with a round hole at center] D. [Four pieces with mismatched edges that leave gaps when assembled]

GATE 2022 · General Aptitude · Assembling Pieces · medium

Answer: Option C is the correct answer. The pieces in set C can be assembled to form a square with a single round hole near the center.

1. Identify the target outline: The target is a square. Count the total area covered by the pieces in each option. The piece set whose total area equals the square area minus the circular hole area is a candidate.
2. Test options A, B, D by edge matching: Options A, B, and D each contain pieces whose concave and convex edges do not complement each other when arranged inside a square. Attempting assembly reveals either gaps along the boundary or interior voids that are not the required circular hole.
3. Verify option C assembles correctly: In option C, the four pieces have complementary step-cuts and curved edges. Placing the piece containing the semicircular notch adjacent to its matching piece creates the full round hole. The remaining two pieces fill the outer corners. The assembled outline is a complete square with the hole near center.