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MathNet 2010 — Part 01 Question 158

Math Olympiad Vault · MathNet 2010 — Part 01

Question 158

The vertices of a cube are numbered from 1 to 8, such that one of the faces has the vertices $\{1,2,6,7\}$ and the other five have the vertices $\{1,4,6,8\}$, $\{1,2,5,8\}$, $\{2,3,5,7\}$, $\{3,4,6,7\}$ and $\{3,4,5,8\}$. What is the number of the vertex that is farthest from vertex number 6?
(a) 1
(b) 3
(c) 4
(d) 5
(e) 7