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China Grove is a game using 63 of the 64 hexagonal tiles of a two-groups transcendental solution of the China Labyrinth as a board.

 Material On the left you can see such a solution. It was generated by the China Grove app. For completeness the one tile that is always disconnected in a transcendental solution has been added to the picture, but it plays no role in the game. Both players have a sufficient number of checkers, one player having white, the other black. Definitions The China Labyrinth has hexagons with every possible number and pattern of exits, in all possible rotations and reflections, without identical doubles. China Grove's main variant is played pattern based but there's an additional option to play it number based, as explained below. A group consists of one or more like coloured checkers that are connected via unbroken paths of like coloured checkers. A group is maximal, meaning that part of a group is not a group.

Rules
• The game starts on an empty board, White plays first, Black is entitled to a swap.
• If a player on his turn puts one checker on a vacant cell, then all vacant cells that are open to further placements in the same turn are highlighted. In pattern mode these are cells with the same pattern of exits as the cell of the first checker that is placed, including all possible rotations and reflections.
• A player must always place the maximum number of checkers that is possible, which is 7 minus the number of neighbour cells of the cell on which the first checker is placed.

Obviously only one checker can be placed on the one cell with six neighbour cells. But place the first checker on a cell with one neighbour cell, then you must place six checkers.

Goal
The game ends when the board is full, or earlier if a player resigns. On a full board the players' respective numbers of stones and groups are compared. A player gets one point for every stone of his colour and loses 'P' points for every separate group, where 'P' is the agreed penalty for the game, which is 2 or 4 points. Because the playing area has an odd number of cells the count leads to an inevitable decision.

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Number mode
In number mode the app will every turn highlight all vacant cells with the same number of exits as the cell on which the first checker is placed, regardless of patterns, as possible follow up placement options in the same turn. All else is the same.
Note that for cells with one neighbour cell or with five, there is no difference between number mode and pattern mode.

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How I invented ... China Grove

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