Question Number 212462 by MrGaster last updated on 14/Oct/24
$$\mathrm{1}.\:\mathrm{In}\:\mathrm{a}\:\mathrm{plane}\:\mathrm{there}\:\mathrm{are}\:\mathrm{nt} \\ $$$$\mathrm{poins}\:\mathrm{arranged}\:\mathrm{such}\:\mathrm{that}\: \\ $$$$\mathrm{nostraight}\:\mathrm{line}\:\mathrm{passesg} \\ $$$$\mathrm{throuh}\:\mathrm{more}\:\mathrm{than}\:\mathrm{3}\:\mathrm{points}.\mathrm{h} \\ $$$$\mathrm{Wat}\:\mathrm{is}\:\mathrm{the}\:\mathrm{maximume} \\ $$$$\mathrm{numbr}\:\mathrm{of}\:\mathrm{straight}\:\mathrm{lines}\: \\ $$$$\mathrm{thatcan}\:\mathrm{pass}\:\mathrm{throughy} \\ $$$$\mathrm{exactl}\:\mathrm{3}\:\mathrm{points2}.\:\mathrm{If}\:\mathrm{thee} \\ $$$$\mathrm{numbr}\:\mathrm{3}\:\mathrm{in}\:\mathrm{the}\:\mathrm{aboveo} \\ $$$$\mathrm{questin}\:\mathrm{is}\:\mathrm{changed}\:\mathrm{to}\:\mathrm{anys} \\ $$$$\mathrm{poitive}\:\mathrm{integer}\:\mathrm{greater}\: \\ $$$$\mathrm{than2}\:\mathrm{denoted}\:\mathrm{as}\:\mathrm{x}\:\mathrm{whatu} \\ $$$$\mathrm{wold}\:\mathrm{the}\:\mathrm{answer}\:\mathrm{be} \\ $$
Commented by MrGaster last updated on 14/Oct/24
The original title is from China, and the poster said this:
A question that comes to mind when I am a little bit:
If n points are arranged in a plane, so that any straight line in the plane passes no more than 3 points, how many straight lines can pass through 3 points at most?
If the above "3" is changed into an arbitrary positive integer x greater than 2, what is the answer?