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Problem 105
Let be disjoint sets of size and respectively, with not all of contained on a single line. Is there a line which contains at least two points from and no points from ?
Source: erdosproblems.com/105
- Geometry
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Solved, DisprovedAn accepted solution exists. The statement is false.
DISPROVED (LEAN): the site credits three explicit counterexamples posted in its comments by Xichuan in October 2025, one of which (twelve points against nine) was later formalized in Lean in Boris Alexeev's repository; see the claim page (Xichuan, 2025).