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k different lines passing through n points, not all on the same line.

Source: Polish MO Second Round 1968 p6

August 22, 2024
geometrycombinatoricscombinatorial geometry

Problem Statement

On the plane are chosen n≥3n \ge 3 points, not all on the same line. Drawing all lines passing through two of these points one obtains k different lines. Prove that k≥nk \ge n.
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