This study aims to determine the explanatory and discriminative powers of non-routine problem solving strategies used by fourth graders. Six problems were asked to 240 pupils. After scoring answers between 0 and 10, bottom and top segments of 27% were determined based on total scores. Lastly, all scripts of students in these segments were re-scored with regard to strategy use. Multiple regression and discriminant analysis were utilized to evaluate data. Results showed that strategies explain 84% of the problem solving success, and their importance order is as follows: look for a pattern, work backward, make a systematic list, make a drawing, guess and check and simplify the problem. Strategies which play a significant role in distinguishing students are look for a pattern, make a systematic list, work backward, simplify the problem, make a drawing, respectively. Further researches using more problems, and examining students of different grades are suggested. An example of a problem-solving test is appended.