Abstract: As a new insight problem, matchstick arithmetic problems have been used to investigate insight problem solving. However, it is unclear how difficult the different types of matchstick arithmetic problems are and to what extent they exhibit characteristics of insight. In the present study, 68 undergraduates attempted to solve 8 two-move matchstick arithmetic problems either silently or while providing concurrent verbal protocols. The results showed that: 1)Verbal protocols could be used to examine the cognitive processes during the two-move matchstick arithmetic problems solving;2) the difficulty did not depend entirely on the levels of constraint relaxation and chunk decomposition;3) there were three types of cognitive components in the 5 types of problems, such as failure, impasse and restructuring, and the restructuring also included the top-down and bottom-up restructuring. Overall, the cognitive process of problem solving may be viewed as a continuum between the insight and analysis, and the greater difficult tautology and operator types belonged more to the end of insight, the CD type tended to be in the middle, while the lower difficult hybrid and value types belonged to the end of analysis. Additionally, the closer to the end of insight the problem was, the more bottom-up restructuring it had.