Make a square grid with an even side.
Make a continuous trail which passes through all small squares; the trail ends where it started.
Where there is an angle you can put a red or a blue tile.
On the small squares with no tiles place connectors to ensure the continuity of the trail remains intact.
The connectors can be bicolor or tricolor. If we connect two red tiles then the connector has a blue color. If we connect two blue tiles, the connector has a red color. And if we connect a red and a blue tile the connector has a green color (tricolor).
The number of red tiles has to be equal to the number of blue tiles.
The challenge of the puzzle is, when an even side square grid is given, to place the maximum number of tiles with the least number of tricolor connectors. All conditions given above are mandatory.
If the given grid is 14x14, find the maximum number of tiles with the least tricolor connectors. Your answer must contain a grid with a continuous trail, as well as a grid with red and blue tiles and with the appropriate connectors.