This chapter presents the results of a few investigations carried out with uses of matchstick puzzles. George Katona (1901–1981) explored experimentally how two different pedagogies influence the performances of matchstick solvers involved. The first pedagogy consists in showing the one solution to the puzzle, fostering memorization of the solution. The second pedagogy is to help solvers grasp the principle that leads to the solution, fostering solving process understanding and skills. Katona’s results show that the second pedagogy is better in solving new matchstick puzzles. In addition, these results contradict beliefs that there aren’t general rules for solving matchstick puzzles or that they can be solved only by a trial-and-error approach. Joy Paul Guilford (1897–1987) used various types of matchstick puzzles to explore divergent thinking as an important part of creativity. He also mentioned cognitive bias “sought squares must be equal” that makes solving some puzzles impossible. Various investigations demonstrated existence of a theoretical base for predicting difficulty levels of different arithmetic matchstick puzzles with Roman numerals. These predictions were verified experimentally observing the number of correct solutions and time needed to find them.