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If a breadth-first search in Prolog executes by looking for paths of length 0, then paths of length 1, then paths of length 2... How

If a breadth-first search in Prolog executes by looking for paths of length 0, then paths of length 1, then paths of length 2... How many paths, in the worst case, would be checked before a path of length n was found when "steps" were defined as rolls of a 6-sided die?

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