Combinatorics · Arrangements of lines · Counting intersections · Case analysis · Parallel classes
Jure drew four distinct lines in the plane, one arrangement after another, and for each arrangement he wrote down the number \(n\) of points at which at least two of his lines cross. Which of the sets below contains exactly the values that \(n\) can take?
- A \(\{0, 2, 3, 4, 5, 6\}\)
- B \(\{0, 1, 3, 4, 5, 6\}\)
- C \(\{0, 1, 3, 4, 6\}\)
- D \(\{1, 3, 4, 5, 6\}\)
- E \(\{0, 1, 2, 3, 4, 6\}\)
Sign in to check answers, open hints, read the full solution, and track your progress. Statements are always free.
Slovenian High School Mathematics Competition for Vega Awards (MaSSA), drzavno (national) round 2016, 1. letnik, category A, problem A1. Organized by DMFA Slovenije (Society of Mathematicians, Physicists and Astronomers of Slovenia). Source