Using the “matchstick” algebra problem, in which an incorrect arithmetic equation, given in Roman numerals, must be made true by moving a single “stick” of a Roman numeral (e.g., IV=III+III→VI=III+III), two experiments were conducted to investigate the role of constraint relaxation and different problem representations in insight problem solving. Participants tried to solve matchstick problems, presented in either Roman or Arabic numerals, three times. The first experiment showed that participants were significantly less successful when the problems were presented in Arabic numerals than when Roman numerals were used. The second experiment showed that participants who had been unable to solve the problem in the first and second trials were significantly more likely to solve the problem at the third trial when they switched from Arabic to Roman numerals between the second and third trials. Two theories of constraint relaxation and the role of different problem representations in insight problem solving are also discussed.