This paper proposes an algorithm for detecting 3-way interactions. As far as the authors know, this is the first proposal ever made for a detection algorithm of 3-way interactions. In this paper, by analyzing examples, the mechanism of 3-way interactions is clarified and a detection algorithm of 3-way interactions is proposed. Namely the proposed detection algorithm is heuristic. To evaluate the algorithm, we implemented a detection system based on the proposed algorithm and applied it to 12 services, and 82 3-way interactions were detected. This shows the proposed algorithm is effective.