Menu Close

There-are-2016-straight-lines-drawn-on-a-board-such-that-1-2-of-the-lines-are-parallel-to-one-another-3-8-of-them-meet-at-a-point-and-each-of-the-remaining-ones-intersect-with-all-other-lines-on-




Question Number 112812 by Aina Samuel Temidayo last updated on 09/Sep/20
There are 2016 straight lines drawn on  a board such that (1/2) of the lines are  parallel to one another. (3/8) of them  meet at a point and each of the  remaining ones intersect with all  other lines on the board. Determine  the total number of intersections  possible.
$$\mathrm{There}\:\mathrm{are}\:\mathrm{2016}\:\mathrm{straight}\:\mathrm{lines}\:\mathrm{drawn}\:\mathrm{on} \\ $$$$\mathrm{a}\:\mathrm{board}\:\mathrm{such}\:\mathrm{that}\:\frac{\mathrm{1}}{\mathrm{2}}\:\mathrm{of}\:\mathrm{the}\:\mathrm{lines}\:\mathrm{are} \\ $$$$\mathrm{parallel}\:\mathrm{to}\:\mathrm{one}\:\mathrm{another}.\:\frac{\mathrm{3}}{\mathrm{8}}\:\mathrm{of}\:\mathrm{them} \\ $$$$\mathrm{meet}\:\mathrm{at}\:\mathrm{a}\:\mathrm{point}\:\mathrm{and}\:\mathrm{each}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{remaining}\:\mathrm{ones}\:\mathrm{intersect}\:\mathrm{with}\:\mathrm{all} \\ $$$$\mathrm{other}\:\mathrm{lines}\:\mathrm{on}\:\mathrm{the}\:\mathrm{board}.\:\mathrm{Determine} \\ $$$$\mathrm{the}\:\mathrm{total}\:\mathrm{number}\:\mathrm{of}\:\mathrm{intersections} \\ $$$$\mathrm{possible}. \\ $$
Commented by ahmediname last updated on 10/Sep/20
-241.31
Commented by Aina Samuel Temidayo last updated on 10/Sep/20
What do you mean?
$$\mathrm{What}\:\mathrm{do}\:\mathrm{you}\:\mathrm{mean}? \\ $$

Leave a Reply

Your email address will not be published. Required fields are marked *