A black square PQRS has been cut into two parts. One part of it is shown in Panel I. Which one of the shapes labelled (i), (ii), (iii), and (iv) in Panel II is the other part of the same square?
Show Hint
The missing piece must be the exact mirror complement of Panel I along the cut line, so the two pieces rejoin into the full square PQRS.
Step 1: Understanding the Concept: A solid black square is split into two jigsaw-like pieces by one irregular cut. Panel I shows one piece, and we must pick from Panel II the one piece that is its perfect match.
Step 2: Key Formula or Approach: Instead of imagining the whole square, focus only on the cut edge, the zigzag boundary where the two pieces meet. The matching piece must have a cut edge that is the mirror image of Panel I's cut edge, so the two edges lock together like puzzle pieces with no gap and no overlap.
Step 3: Detailed Explanation: Trace the steps and notches along the cut edge of Panel I from one corner of the square to the other. For each inward notch in Panel I, the matching piece needs an outward tooth of the same size at the same position, and for each outward tooth in Panel I, the match needs an inward notch. Checking shapes (i), (ii), and (iv) against this rule, at least one notch or tooth fails to line up with Panel I's cut edge, so the two pieces would either overlap or leave a gap if joined. Shape (iii) is the only one whose zigzag pattern is the mirror complement of Panel I all along the cut, so joining it to Panel I reproduces the original square PQRS with straight, unbroken outer sides.
Step 4: Final Answer: Shape (iii) is the missing piece, so the correct option is (C).
