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.

  1. A.

    123

  2. B.

    124

  3. C.

    125

  4. D.

    235

Attempted by 4 students.

Show answer & explanation

Correct answer: A

Concept: In a figure-dissection puzzle like this, one square is cut by two straight internal lines into three genuine pieces. When the three genuine pieces are placed edge to edge, their matching straight edges and angles reproduce the square's four straight sides and four right-angle corners exactly, with no gap and no overlap. The other figures offered are drawn with a wrong edge length, a wrong angle, or an extra bend that can never occur in a straight-line dissection of a square, so they can never complete the figure.

Application: Placing figures 1, 2 and 3 edge to edge (as shown in the figure alongside) reconstructs the square exactly: figure 1 forms the wedge running along the full top side, figure 2 forms the broad lower-left portion using the left side and part of the bottom side, and figure 3 forms the narrow remaining wedge on the right using the right side. Together the three pieces cover the square with no gap and no overlap.

Cross-check: Figures 4 and 5 cannot take figure 3's place: figure 4 has an extra concave notch that never appears in a straight-line square dissection, and figure 5's sharp point does not match the angle where the two internal cuts meet — either substitution would leave a gap or an overlap. So the set that completes the square is figures 1, 2 and 3.

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