<p>This study examined how variation in specific word-problem characteristics is associated with differences in problem difficulty among second-grade students. Prior research has typically compared the difficulty of individual features without controlling for the co-occurrence of other characteristics, limiting the ability to isolate their individual contributions. To address this limitation, the present study employed an orthogonal experimental design that systematically manipulated five characteristics: the position of the unknown, the presence of irrelevant information, the number of solving steps, the number magnitude, and regrouping. A sample of 305&#xa0;s-grade students in China was classified into four groups based on arithmetic and word-problem comprehension performance: Arithmetic Difficulties (AD) (<i>n</i> = 56), Word-Problem-Comprehension Difficulties (WPCD) (<i>n</i> = 41), AD + WPCD (<i>n</i> = 21), and No Mathematics Difficulty (No MD) (<i>n</i> = 187). The results indicated that the position of the unknown, the presence of irrelevant information, and the number of steps were associated with the greatest variation in error rates. Moreover, descriptive patterns of error-rate variation differed across student profiles. Multi-step problems showed comparatively greater error-rate variation among students with arithmetic difficulties, whereas irrelevant information showed comparatively greater variation among students without arithmetic difficulties and those with word-problem comprehension difficulties. Overall, these findings underscore the importance of specific problem characteristics in shaping problem difficulty in the Chinese primary mathematics context and demonstrate the value of orthogonal designs for isolating their individual contributions.</p>