1-In-a-plane-there-are-nt-poins-arranged-such-that-nostraight-line-passesg-throuh-more-than-3-points-h-Wat-is-the-maximume-numbr-of-straight-lines-thatcan-pass-throughy-exactl-3-points2-If-thee-nu

Question Number 212462 by MrGaster last updated on 14/Oct/24

$$1.\mathrm{In}\mathrm{a}\mathrm{plane}\mathrm{there}\mathrm{are}\mathrm{nt}$$$$\mathrm{poins}\mathrm{arranged}\mathrm{such}\mathrm{that}$$$$\mathrm{nostraight}\mathrm{line}\mathrm{passesg}$$$$\mathrm{throuh}\mathrm{more}\mathrm{than}3\mathrm{points}.\mathrm{h}$$$$\mathrm{Wat}\mathrm{is}\mathrm{the}\mathrm{maximume}$$$$\mathrm{numbr}\mathrm{of}\mathrm{straight}\mathrm{lines}$$$$\mathrm{thatcan}\mathrm{pass}\mathrm{throughy}$$$$\mathrm{exactl}3\mathrm{points}2.\mathrm{If}\mathrm{thee}$$$$\mathrm{numbr}3\mathrm{in}\mathrm{the}\mathrm{aboveo}$$$$\mathrm{questin}\mathrm{is}\mathrm{changed}\mathrm{to}\mathrm{anys}$$$$\mathrm{poitive}\mathrm{integer}\mathrm{greater}$$$$\mathrm{than}2\mathrm{denoted}\mathrm{as}\mathrm{x}\mathrm{whatu}$$$$\mathrm{wold}\mathrm{the}\mathrm{answer}\mathrm{be}$$

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?

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