Amazingly enough, a very different new board game was still possible. Symmetries includes 2 options or sub games. The program places at random checkers of few different types in the cells of a grided board. The shape of the board may be chosen from three types: a square, a triangle or an hexagon. The density of the grid can also be chosen. In the case of a square, four axes that start at the center of the board have to be lengthened. The player only needs to lengthen one of them. The other three draw themselves automatically in a centrally symmetric way. The path they follow will hardly ever be a straight line but a winding polygonal trajectory. Once the axes reach the edge, the square is divided into four symmetric zones. The goal of the game is to draw the axes in a way that, either all the checkers of the same color are put into the same zone (sub game 1) , or, contrarily, the same type of checkers are separated into different zones (sub game 2). Symmetries is a very complete mental training instrument because it involves several different types of skills or reasoning: - Positive inferences orienting on how a solution could be. - Negative inferences orienting on how it might not be. - Analysis of different possibilities. - Visual skills to recognize spatial patterns of complete or partial developments. The player himself will discover some other kind of skills involved which are intrinsic to the game itself. Complex configurations will require deep thinking or intuition. As it has a complete set of difficulty regulators, the game is suitable for all ages. It may be used as entertainment but also for educational purposes or even to help medical therapy of mental injuries or to help slow down mental decay due to aging or disease.