From the four alternatives given below, choose the one figure that fits…
2023
From the four alternatives given below, choose the one figure that fits exactly into Figure-X, completing it into a full square.
- A.
1
- B.
2
- C.
3
- D.
4
Show answer & explanation
Correct answer: D
Concept: In a figure-completion puzzle, Figure-X is a square with a stepped (staircase) boundary missing on one side. The correct piece is the one whose own boundary is the exact complementary staircase - each of its steps must match, in reverse, the width and depth of every step missing from Figure-X, so the two outlines interlock with no gap and no overlap and together enclose one solid square.
Application: Tracing Figure-X's outline, the top and left edges are solid, but a staircase of several steps of different widths and depths is cut away toward the bottom-right. The matching piece must begin its own boundary at the same point Figure-X's cut begins, and its steps must step inward/outward by exactly the same amounts, in the same order, before closing off at the outer edge - only then does placing it against Figure-X leave a straight, complete square boundary with no jagged edge left over.
Checking each alternative against this requirement:
Figure (1): its notch sits at a different position than Figure-X's cut, and the lower part of the figure stays a uniform width instead of stepping in further, so its edge does not continue Figure-X's staircase - a gap is left near the base.
Figure (2): it narrows into one centred column rather than continuing Figure-X's offset staircase, so its two side edges do not land on Figure-X's step edges and the boundary cannot close into a straight square edge.
Figure (3): it keeps a tall flat edge on one side and places its steps only on the other side, in different proportions than Figure-X's cut, so aligning it against Figure-X leaves an irregular notch rather than a straight edge.
Figure (4)'s steps decrease in width and depth in exactly the sequence needed to continue Figure-X's missing boundary. Placed against Figure-X, the two outlines interlock exactly along every step, closing the shape into one complete square with no gap or overlap.
Cross-check: adding the area enclosed by Figure-X to the area enclosed by Figure (4) accounts for the full area of the square, and every step-edge of Figure-X's cut has a matching complementary edge of the same length in Figure (4) - confirming the fit.
