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Chords in a circle

Source: MEMO 2023 I2

August 24, 2023
combinatoricsMEMO2023geometry

Problem Statement

Find all positive integers n≥3n \geq 3, for which it is possible to draw nn chords on a circle, with their 2n2n endpoints being pairwise distinct, such that each chords intersects exactly kk others for:
(a) k=n−2k=n-2,
(b) k=n−3k=n-3.
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