Perfect Path

In the 18th century, the inhabitants of Królewiec (today's Kaliningrad) had a similar problem (and also for fun), namely the Pregoła River flows through their city, through which at that time there were seven bridges. They wondered if it was possible to cross each of these bridges once and only once and go back to the point where this walk started. Euler answered this question, and by the way he created a new mathematical theory called the graph theory. He introduced the basic concepts of the edges and vertices of the graph, and then presented the plan of the Konigsberg fragment also as a graph. It made it easier for him to answer the question, but also gave a general answer, with different numbers of edges and vertices. Today we refer to the Euler graph as such a graph in which starting from any vertex it is possible to "pass" along each edge to each vertex, but "to pass" through a given edge only once. Perfect Path game is based on random generation of Euler graphs, i.e. such graphs that you can go through the whole board every time. In this game, each field has an assigned weight, i.e. how many times the hero can stand on a given field. The protagonist here is a blue square slightly inverted. The board fields, on the other hand, have different colors, and a given color tells how many times you can stand on this field. Residents and tourists who wanted to walk around Königsberg and its bridges had to cross at least one bridge at least twice - this is not Euler's graph. In Perfect Path, there is always a solution and thus a move to the next random board.