It is not possible to use all of the remaining 181 paths, however, because many of them lead into the edge of the game board or the central hexagon, and connecting to such a path immediately ends the game. 35 of those paths will be used up by our first 35 moves. Well, each hexagon that we lay has six paths on it, for a total of 6*36 = 216 paths on the board. Thus, we want to just extend our path by a length of one on each of our first 35 moves, and then score big on the 36th move. In order to maximize our score, we want to maximize how much we increase the length of our path on our final move. The standard Entanglement game board is made up of a hexagonal ring of 6 hexagons, surrounded by a hexagonal ring of 12 hexagons, surrounded by a hexagonal ring of 18 hexagons, for a total of 36 hexagons. The question that I am going to answer today is what the maximum score in Entanglement is under this scoring system (inspired by this reddit thread). This encourages clever moves that significantly extend the length of the path all at once. To make things a bit more interesting, the game was updated in November 2010 to include a new scoring system that gives you 1 + 2 + 3 + … + n (the nth triangular number) points on a turn if you extend the length of your path by n on that turn. The goal of the game is to create the longest path possible without running into either the centre hexagon or the outer edge of the game board.Once you have selected an orientation of the hexagon, a path is traced along that hexagon, and you are provided a new hexagon that you may rotate at the end of your current path.You may rotate, but not move the hexagon that has been provided to you.You are given a hexagonal tile with six paths printed on it, with two path ends touching each side of the hexagon.The way the game works is probably best understood by actually playing it, but here is my brief attempt: Entanglement is a browser-based game that has gained a fair bit of popularity lately due to its recent inclusion in Google’s Chrome Web Store and Chrome 9.
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