In each of the following questions, a set of five alternative figures 1, 2, 3,…
2023
In each of the following questions, a set of five alternative figures 1, 2, 3, 4 and 5 followed by a set of four alternatives (A), (B), (C) and (D) is provided. It is required to select the alternative which represents three out of the five alternative figures which when fitted into each other would form a complete square.
Select three figures from the five given alternative figures which when fitted into each other would form a complete square.
- A.
123
- B.
134
- C.
135
- D.
145
Show answer & explanation
Correct answer: B
Concept
In figure-fitting / shape-construction puzzles, three of the five given irregular pieces are complementary jigsaw pieces: each piece's boundary edges (straight edges, notches, and zig-zag cuts) must interlock exactly with the boundary edges of the other two pieces so that, laid together, they trace the plain outline of the target shape (here, a square) with no gap and no overlap. Any leftover figure has at least one edge that cannot match the boundary needed to close that outline.
Application
The target outline is a plain square: four straight sides meeting at right angles, so every internal cut shared between two neighbouring pieces must be a single line that both pieces reproduce identically on their touching edge.
Figure (1) is a concave, arrow-shaped piece. Placed at the top-left, its slanted straight edge runs from a point on the top side down to a central point, filling the top-left region, while its notch sits against the piece below it.
Figure (3) has a two-peak, zig-zag lower edge. Placed at the bottom, this zig-zag boundary interlocks exactly with figure (1)'s notch and runs on to the same central point.
Figure (4) is a quadrilateral piece. Placed at the right, its straight slanted edge runs from that same central point up to the right side, closing the remaining region.
Fitted together this way, figures (1), (3), and (4) trace exactly the four straight outer sides of a square with no gap or overlap, matching the assembled figure shown below.
Cross-check: why the other figures don't fit
Figure (2) is a near-mirror-image concave shape to figure (1); its notch angle does not sit flush against figure (1)'s or figure (3)'s touching edges, so a group containing it leaves a step in the boundary instead of a straight square edge.
Figure (5) is a plain triangle with three straight, unnotched edges. It has no zig-zag or notch to interlock with the other pieces' touching edges, so any group containing it leaves an open gap along the square's outline.
Hence figures (1), (3), and (4) is the only trio (among the ones offered) that assembles into a complete square.
