Scores in Tesseræ are based on the number of tiles remaining on the board and the number of moves you have made to get to that point.
The Best Scores for the mosaics are also based on the number of tiles and the number of moves made. Because of this, you don't have to finish a mosaic to get a Best Score; if the number of tiles left is less than one of scores in a Best Scores list, or the number of tiles is the same and the number of moves is less, then you will have made a Best Score for that mosaic.
(In this demo, Best Scores are disabled. The score you make on a mosaic will not be saved, and the Best Scores list is not available.)
