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In Ingenious, a.k.a. Einfach Genial, players take turns placing colored domino-style tiles on a game board, scoring for each line of colored symbols that they enlarge. The trick, however, is that a player's score is equal to their worst-scoring color, not their best, so they need to score for all colors instead of specializing in only one or two.
Ingenious Extreme features the same gameplay as Ingenious, but with the domino-style tiles consisting of two conjoined octagons instead of two conjoined hexes. Since the pieces in Ingenious had six colors on them, 'Ingenious Extreme features eight colors, giving players more to juggle as they try to score well across the board while shutting out opponents.
In more detail, each player has a rack with six tiles on it, and on a turn a player places one tile from their rack onto two empty octagon spaces of the game board. For each octagon on this tile, they score one point in that color for each octagon of the same color that lies adjacent to it and each octagon in a straight line from it. (In all you must check for scoring in seven directions from each half of the tile; you never look back from one half of the tile through the other half.) If a player brings the score of a color to 13, they immediately take another turn. At the end of their turn, they refill their rack to six tiles. (Before refilling their rack, if they have no tiles on it that contain hexes in their lowest-scoring color, they can discard all of their tiles, then draw six new tiles from the bag.)
When no more tiles can be placed on the game board or when one player scores 13 in each color, the game ends. Players then compare their lowest scores, and whoever has the highest low score wins.