# Count Carefully! Abalone Openings

The board game Abalone is played with black and white spheres on a hexagonal board. The spheres can be moved individually one unit in (up to) 6 directions, but spheres can also be moved in pairs or as straight lines of 3; again, this would be one unit in (up to) 6 directions. When moving a pair or line of three, the line of the pieces must point in the same direction after the move as they were before.

Below we can see the 6 possible moves for A. If A moved to the right it would end up on the circle highlighted in red.

The pair of spheres at B are shown moving to the left, but they could also move down-left, down-right or right. They are unable to move up-left or up-right because the other (in this case white) sphere blocks them. Pieces can only move into empty spaces.

The pair of spheres at C are shown moving "in parallel" to the left, but they could also move up-left or down-left. They are unable to move in the other directions because they are at the edge of the board.

The line of 3 spheres at D are shown moving "in parallel" up-right, but they could also move in all six directions.

The next image shows the position at the beginning of a normal game. How many opening moves are there altogether for Black?

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