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Home » From Obscurity to Stardom: How Yuta Transformed His Career Overnight! 🌟 - inBeat

From Obscurity to Stardom: How Yuta Transformed His Career Overnight! 🌟 - inBeat

📅 May 4, 2026 👤 scraface

May 04, 2026

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But for small $n=8$, $k=3$, we use a constructive method.
Fix one station as selected. By rotational symmetry, fix station 1. Th...
So available: 3, 4, 5, 6, 7, excluding 2 and 8 → valid: 3–7.
We need 2 non-adjacent from {3,4,5,6,7}.
List all 2-element non-adjacent pairs in 5 consecutive positions:
Total: 6 valid pairs with station 1 selected.
But each selection is counted 3 times (once for each selected station)...
\frac{8 \times 6}{3} = 16
Thus, number of non-adjacent triplets is 16.
\frac{16}{56} = \frac{2}{7}

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