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Home » x_2 = \frac12 - 66 = \frac66 = 1 - Nelissen Grade advocaten

x_2 = \frac12 - 66 = \frac66 = 1 - Nelissen Grade advocaten

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 Let the 3 close pairs form a path: \( A - B - C \). Then the pairs are \( AB, BC, AC \), with only \( AB \) and \( BC \) close â so 2 close pairs, 1 non-close (namely \( AC \)). This trio counts.

📌 Any other configuration of 3 close pairs that does not form such a path?

📌 Try a star: \( AB, AC, BC \) â but thatâs 3 edges all connected to B â actually forms a triangle. Then every pair is close: 3 close pairs â violates our "exactly 2" condition.

📌 Can we have a non-path configuration with exactly 2 close pairs?

📌 Example: close pairs: \( AB, CD, DE \). Then the trio \( B,C,D \): pairs \( BC \) (not close), \( CD, DE \) â only 2 close: \( CD, DE \). So this trio has exactly 2 close pairs and 1 non-close.

📌 But this is not a path of length 2 â itâs a chain of 3.

📌 So we must count all triples where exactly two of the three internal pairs are close.

📌 Letâs count how many such triples exist.

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