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.

one possible china grove initial position 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, without identical doubles. China Grove may be played number based or pattern based.

  • In number mode the app will every turn highlight all vacant cells with the same number of exits as the first checker that is placed, as possible follow up placement options in the same turn.
  • In pattern mode the app will every turn highlight all vacant cells with the same pattern of exits as the first checker, all in different rotations, as possible follow up placement options in the same turn.
  • 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 is played in number mode or in pattern mode, after the players' choice.
  • 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 number mode these are cells with the same number of exits as the first checker.
    • In pattern mode these are cells with the same pattern of exits as the first checker.
  • 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. The only exception is the very first placement, which is the swap offer. Here the player may place less stones if he so chooses.

So 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.
Note that for cells with one neighbour cell or with five, there is no difference between number mode and pattern mode.

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, 4. 6 or 8 points. Because the playing area has an odd number of cells the count leads to an inevitable decision.


How I invented ... China Grove

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