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Home » So the number of valid configurations is \(\boxed20\) - Baxtercollege

So the number of valid configurations is \(\boxed20\) - Baxtercollege

📅 March 11, 2026 👤 scraface

Mar 11, 2026

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📌 However, in a **scaled hexagonal lattice** used for energy grid modeling, nodes may be placed at **integer-coordinate projections** using vectors $\vec{v}_1 = (1, 0)$, $\vec{v}_2 = \left(\frac{1}{2}, \frac{\sqrt{3}}}{2}\right)$, but these are not integer.

📌 But the problem says "assuming integer coordinates are used in a scaled grid". So perhaps the hexagon is scaled by 2 to clear denominators:

📌 Vertices become:

📌 $A = (2, 0)$

📌 $B = (1, \sqrt{3})$ → not integer

📌 But to have integer-coordinate nodes in a hexagonal grid, we consider a **hexagonal lattice embedded in $\mathbb{Z}^2

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