Find the minimum number of straight lines required to make the given figure.

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Find the minimum number of straight lines required to make the given figure.

  1. A.

    9

  2. B.

    11

  3. C.

    15

  4. D.

    16

Attempted by 2 students.

Show answer & explanation

Correct answer: B

Concept: When counting the straight lines in a subdivided figure, do not treat every small edge as its own line — segments that lie on the same continuous straight line must be merged and counted once. Do this separately for each distinct direction present in the figure (here: horizontal, and the two diagonal directions), then add the counts across directions.

Label the figure's intersection points as shown below.

  • Horizontal lines: DE, FH, IL and BC — 4 lines.

  • Lines slanting the same way as edge AC: AC, DO, FN and IM — 4 lines.

  • Lines slanting the same way as edge AB: AB, EM and HN — only 3 lines here, because unlike the corner cell near B, the small cell in the corner near C is not cut by a further line parallel to AB.

Total straight lines = 4 + 4 + 3 = 11.

Cross-check: every one of the 15 labelled points (A–O) is used by exactly one line from each of the three directions it lies on, and no segment is counted twice, confirming the count of 11.

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