The purpose of this study is to demonstrate a constraint relaxation which is followed by the transition to an appropriate representation in insight problem solving. The puzzle game “Tangram” was used as a new insight problem, in which problem-solvers were presented a silhouette and asked to make the same configuration by arranging 7 pieces. At the beginning, problem-solvers had a constraint allocating the pieces into a geometric shape, but then relaxed this to reach the correct configuration at a later stage of problem solving. Participants’ subjective assessments of their confidence to reach the solution predicted neither the constraint relaxation nor the successful problem solving. However, eye-tracking data suggested that the successful problem-solvers tended to search the problem space more widely than the unsuccessful-problem solvers.