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Omni-MATH / A moth starts at vertex A of a certain cube and is trying to get to vertex B, which is opposite A, in five or fewer "steps," where a step consists in traveling along an edge from o…

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problem

A moth starts at vertex AA of a certain cube and is trying to get to vertex BB, which is opposite AA, in five or fewer "steps," where a step consists in traveling along an edge from one vertex to another. The moth will stop as soon as it reaches BB. How many ways can the moth achieve its objective?
Plain-text mathematical notation (without MathML)
A moth starts at vertex A of a certain cube and is trying to get to vertex B, which is opposite A, in five or fewer "steps," where a step consists in traveling along an edge from one vertex to another. The moth will stop as soon as it reaches B. How many ways can the moth achieve its objective?
Original LaTeX notation
A moth starts at vertex $A$ of a certain cube and is trying to get to vertex $B$, which is opposite $A$, in five or fewer "steps," where a step consists in traveling along an edge from one vertex to another. The moth will stop as soon as it reaches $B$. How many ways can the moth achieve its objective?

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