Initial failures in solving insight problems commonly cause the solver relax his problem constraints. However, such initial trials also produce usable constraints that can facilitate further solutions. We used a tangram puzzle (constructing a “T” shape from four pieces) to prepare three conditions: a constraint discovery condition wherein our confederate (acting as a member of paired participants) regularly provided two combined pieces as a hint, a constraint relaxation condition wherein the confederate regularly violated the participant’s constraints on how to place pieces, and a control (natural collaboration) condition. Twenty four participants were divided to one of three conditions. We found no significant difference in the number or average time of successful solutions among the conditions. However, the constraint discovery condition outperformed the other conditions in correctly recalling the solution, indicating that, when people discover usable constraints, they retain them as basic knowledge pieces.