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Home » Let’s compute how many ways to place 3 non-adjacent G’s in 5 positions. - American Beagle Club

Let’s compute how many ways to place 3 non-adjacent G’s in 5 positions. - American Beagle Club

📅 February 27, 2026 👤 scraface

Feb 27, 2026

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ho\sin\phi
Recall in spherical coordinates:
ho^2 = x^2 + y^2 + z^2, \quad
ho\sin\phi = \sqrt{x^2 + y^2}
x^2 + y^2 + z^2 = 4\sqrt{x^2 + y^2}
Let $r = \sqrt{x^2 + y^2}$. Then:
r^2 + z^2 = 4r \Rightarrow r^2 - 4r + z^2 = 0 \Rightarrow (r - 2)^2 +...
This is a sphere of radius 2 centered at $(2, 0, 0)$ in cylindrical co...
oxed{(x - 2)^2 + y^2 + z^2 = 4}
Question: A regular tetrahedron has three of its vertices at $A = (1,...

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