google-deepmind / google-deepmind/formal-conjectures

Green's Open Problems #75

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green-problems new conjecture
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Description

### What is the conjecture
https://people.maths.ox.ac.uk/greenbj/papers/open-problems.pdf#problem.75

Let $X \subset \mathbb{R}^2$ be a set of $n$ points. Does there exist a line $l$ through at least two points of $X$ such that the numbers of points on either side of $l$ differ by at most 100?

### [AMS categories](https://github.com/google-deepmind/formal-conjectures/labels?q=ams-)

* ams-05
* ams-52

### Choose either option
- [ ] I plan on adding this conjecture to the repository
- [x] This issue is up for grabs: I would like to see this conjecture added by somebody else

Contributor guide

Open the contributing guide

Research direction

Read problem 75 in the linked Green's Open Problems PDF, then inspect existing formalized conjectures in the repository to learn its Lean structure and conventions. Done means adding a faithful formal statement of the conjecture, including its point-set and line conditions, in the repository's established format.

Written by the indexing model from the issue text.

Assessment

Domain
tooling
Issue type
Feature
Difficulty
5/5
Estimated time
Over a week
Activity status
Stale
Clarity
Mostly clear
Newbie friendliness
35/100

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