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Some aspects of a special multimodality and adaptivity in a two-person game, renju (a Japanese alignment game on a board) are presented. It is argued that such a renju multimodality will surely be a new basis of ideas and understanding of adaptive processes in artificial inttelligence requiring multimodal optimum search. The necessary concepts are developed, such as distance between any two points, four directions, string, jumstring, costring, dead (jum)string, and criterion function of a placed stone (piece or chip) on a renju board. The essential aspects of renju multimodality and adaptivity studied here are as follows: possible values of the criterion function, realized number of the highest peak (lowest valley) formed by the criterion function within a game, height of maximum peak versus the issue of the game, possible number of the highest peak (lowest valley), illustration of the criterion function, developing processes of peak and valley, adaptive mobility of the optimum point, and practical appearance of the multimodality of renju problems.