## 1 Introduction  
Problem solving has become a research hotspot with the rapid advancement of artificial intelligence, in which solving Arithmetic Word Problems (AWPs) is one of the most active and challenging tasks [1]. An AWP typically describes a series of quantitative relations and one or more unknown quantities related to these relations in natural language [2]. Solvers for AWPs usually need to possess language comprehension, logical reasoning, and world knowledge, among other skills [3]. In recent years, with the rapid advancement of Natural Language Processing (NLP) and deep learning technologies [4, 5], significant progress has been made in the research of AWP solving [6, 7]. Nevertheless, the performance of existing solving algorithms still falls short of practical requirements [8, 9]. Developing algorithms for solving AWPs focuses on two main tasks: first, improving the solving accuracy of the algorithm, as this directly determines its performance and application range; second, enhancing the reliability of the algorithm's output, as this affects users' willingness and experience in using machine solvers. Large Language Models (LLMs) are natural language generation models achieved through unsupervised pre-training and reinforcement learning [5, 10]. They have gainedwidespread popularity across various industries due to their strong adaptability to different tasks [4]. Recently, many studies have focused on the usage of LLMs in solving AWPs [11; 12]. One of the most notable areas of research is Chain-Of-Thought (COT), which enhances the reasoning capabilities of an LLM by prompting it to process complex tasks step by step [6]. Language models employing COT-like methods achieve considerable progress in solving problems because they can continually leverage the extensive knowledge acquired during pre-training to analyze and understand the problem during the step generation [13; 14]. However, the main issues with COT-like methods are twofold. First, as AWPs become more complex, LLMs employing COT may generate useless and incorrect steps in the chain (e.g., listing invalid equations) [15], leading to the incorrect solution; second, the precise reasoning for equations relies on the correct invocation of external code interpreters by LLMs [7]. The COT method, when generating long content containing multiple steps, requires repeated calls to the interpreter, which leads to an increase in errors. Therefore, although LLMs excel at leveraging pre-trained knowledge to understand natural language representations of AWPs, they are better suited for solving AWPs when combined with other precise and reliable methods. The relation-flow approach developed in the past decade is a branch of problem-solving algorithms aiming at providing reliable, accurate, and interpretable solutions [16; 17]. The commonality among these algorithms is that they all acquire relations from the problem text through patterns and derive solutions by reasoning about these relations. This characteristic makes the relation-flow approach suitable for educational applications because both the relations involved and the actions to manipulate these relations are aligned with user cognition [18]. Although recent studies have shown good performance on AWPs [17], these algorithms still lag behind State-Of-The-Art (SOTA) algorithms [14; 19] in terms of solving accuracy. This is because extracting relations from complex AWPs requires rich external linguistic knowledge (e.g., co-reference resolution) and world knowledge (e.g., common sense), which are difficult to formalize into patterns or rules in relation-flow algorithms. Fortunately, the rapid development of LLMs in recent years has enabled access to extensive linguistic and world knowledge through pre-training [4; 20; 21], further providing new potential for the development of relation-flow approaches. Based on these findings, this paper suggests that combining LLMs with the relation-flow approach can offer complementary advantages in solving AWPs.