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Reference card reads : No player may successfully conquer the same Maze/Labyrinth twice, and each path may be conquered only once.
If I conquered one path, entering another path is possible?
For example, I paid 4 move to enter the path and conquered that path. And on my next turn, can I enter another path of that Maze/Labyrinth again?(2 or 6 path)
If you already conquered one path, YOU cannot enter another path, but other players can.
The text seems pretty clear to me.