Select the alternative which represents three out of the five alternative…

2025

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.

    134

  2. B.

    124

  3. C.

    234

  4. D.

    345

Attempted by 2 students.

Show answer & explanation

Correct answer: A

In a 'complete the square' figure-fitting puzzle, exactly three of the five given pieces have boundaries that are pairwise congruent in length and angle, so that when each piece is only rotated (never mirrored) and placed edge-to-edge, together they retrace the target outline exactly, with no gaps, no overlaps, and no unwanted bend or step breaking a border that must run straight.

The target square is crossed by one straight diagonal running from a corner to an interior point, which then turns into a short pointed notch before reaching the base, dividing the square into three regions.

  1. The piece with a full-height straight edge and a single unbroken diagonal ending in a point supplies the square's left region together with that diagonal spine.

  2. The piece with a short top edge and one clean diagonal down to a long base closes the remaining rectangular region at the top.

  3. The bookmark-shaped piece, with a flat top and a V-notch cut into its lower edge, rotates so its notch locks exactly onto the pointed projection, closing the base with a flush edge.

Fitted together, these three pieces retrace the square's four straight outer sides and the internal diagonal-and-notch line exactly, with no gaps or overlaps.

The other two pieces cannot substitute for any of these three:

  • The piece whose long edge bends partway down, rather than running as one straight diagonal, cannot lie flush against a straight border; it leaves either a gap or an overlap wherever it is placed.

  • The piece with a small stepped ledge cut into its base near one corner would place that ledge on what must be a perfectly straight outer edge, leaving a visible notch instead of a flush square border.

Hence, the combination of the full-height pointed piece, the short-top trapezoid piece, and the bookmark-shaped notched piece is correct, i.e. the alternative reading "1 3 4".

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