China Tangle 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 tangle initial position Material
On the left you can see such a solution. It was generated by the China Tangle 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. The game 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.
  • On his turn a player puts one checker on a vacant cell. Therewith 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.
  • The maximum number of checkers a player may place, if possible, equals 7 minus the number of exits of the cell on which the first checker is placed.

So obviously only one checker can be placed on the one cell with six exits. But place the first checker on a cell with one exit, then you can place six checkers, provided all six cells with one exit are vacant. It will not always be possible to place checkers up to the theoretical limit. This holds especially in pattern mode.
Note that for cells with one exit 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' groups are compared, and the player with the largest group is te winner. If the players' largest groups are of equal size, then these two groups are out of competition and the next largest groups are compared (which may be the same size for one or both colours), and so on. Because the playing area has an odd number of cells the count is cascading down to an inevitable decision.


How I invented ... China Tangle

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