Select the alternative which represents three out of the five alternative…
2024
Select the alternative which represents three out of the five alternative figures which when fitted into each other would form a complete square.

- A.
123
- B.
234
- C.
134
- D.
345
Show answer & explanation
Correct answer: D
Concept: In a figure-fitting series, the printed square already shows the exact boundary lines that the correct pieces must trace; a valid combination of three pieces must together reproduce every printed division line with matching edge lengths and vertex angles, leaving no gap and no overlap anywhere inside the square.
Application: The square's own outline is broken by one large stepped boundary running from the top edge across to a side, plus two thin triangular corners left open. Among the loose pieces, only the shape with a step of exactly that size and angle (piece 3) reproduces the large stepped boundary; the two remaining narrow slivers (pieces 4 and 5), each a slim triangle with a long diagonal edge, exactly match the two triangular corners still uncovered.

Cross-check: Swapping piece 3 for the similarly shaped stepped piece 2 shifts the step off the square's printed line and opens a visible gap along one edge, so 2 cannot substitute for 3; and the remaining pointed piece (piece 1) has a vertex angle that does not match either uncovered triangular corner, confirming the corners can only be closed by pieces 4 and 5.
Result: Fitting pieces 3, 4 and 5 edge-to-edge therefore reconstructs the complete square with no gap or overlap -- the combination 3-4-5.
Why the other combinations fail:
123 -- piece 1's blunt, rounded vertex meets piece 2's differently-angled step at mismatched edges, so 1, 2 and 3 leave a gap where 1 and 2 meet.
234 -- pieces 2 and 3 are both stepped shapes cut at different positions, so together they misalign the stepped region rather than tracing it once; adding piece 4 does not fix this, so 2, 3 and 4 cannot form the square.
134 -- piece 1's blunt vertex cannot align with piece 4's sharply-angled diagonal edge, so 1, 3 and 4 leave a mismatched edge and cannot form the square.
345 -- pieces 3, 4 and 5 fit together edge-to-edge with matching lengths and angles, exactly reconstructing the square with no gap or overlap.