6

Part of 1968 Poland - Second Round

Problems(1)

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

Source: Polish MO Second Round 1968 p6

On the plane are chosen

n \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 \ge n

geometrycombinatoricscombinatorial geometry