In Chains (Cooperation Games IV)

We continue with translucent trominoes, add an I-tromino, and select those that have two translucent squares (gray with red border). There are just three of them, shown below to the left. To the right are how they can be attached to each other, overlapping in exactly one translucent square:

Linkages 01

What we don’t allow today is that two trominoes overlap in both of their translucent squares, as below.

Nono 01

This has the interesting consequence that the gray squares will necessarily form chains or loops, which adds useful structure. A tiling is complete if all translucent squares are covered twice. We will then have twice as many translucent squares visible than colored squared.

Chains 01

Below is an example of a complete tiling of a 6×6 board.

6x6 01

And here is our game: Each player gets the same number of tiles. For two players, is a good choice, say three of each kind. The players take turns placing one tile on the table so that 

  1. each new tile links with a previous tile
  2. two linked tiles are of different color

Alternatively, a player can also remove the last played tile and replace it by another one.

The goal is to create a complete closed chain when all tiles are used up. 

Below is an example of a successfully closed loop of length 8.

Loop 01

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