这是一道 GPT-4.5 使用思维链都无法答对的简单的算术题

This paper investigates how different prompting strategies affect large language models (LLMs) when solving a seemingly straightforward puzzle: transporting 7 people across a river in a 2-person boat. We compare "general-purpose" models (GPT-4o, GPT-4.5, Claude 3.5 Sonnet, Gemini 2.0 Flash, DeepSeek V3, Grok 3) and "reasoning-optimized" models (GPT o1, GPT o3-mini-high, Claude 3.7 Sonnet Extended Thinking, Gemini 2.5 Pro, Gemini 2.0 Flash Thinking, DeepSeek R1, Grok 3 Thinking) under three prompt conditions:

We observe that some general-purpose models fail unless given a very explicit prompt—sometimes contradicting expectations of their advanced reasoning abilities—whereas others (including newly updated "general" versions) succeed even without CoT. Notably, GPT-4o, an ostensibly reliable GPT-4 variant, consistently fails under all prompt types. Meanwhile, all tested reasoning-optimized models solve the puzzle correctly in every scenario. We discuss how these findings reveal surprising vulnerabilities in older or baseline models, question whether prompt hints merely trigger existing logic modules, and highlight how "general vs. reasoning" boundaries are increasingly blurred.

Large Language Models (LLMs) have demonstrated remarkable capabilities in tasks requiring knowledge retrieval, text generation, and limited forms of logical reasoning. However, small yet precise logic puzzles—like the classic "boat can carry two, 7 people crossing" problem—can expose unexpected weaknesses. One particularly striking example is the consistent failure of GPT-4o, despite GPT-4 being widely considered "relatively reliable" in logical tasks. This highlights the reality that some older or baseline LLM versions still struggle with seemingly trivial puzzles, even though more advanced or newly fine-tuned models handle them with ease.

To explore why such failures occur, we investigate:

By comparing both “general-purpose" and “reasoning-optimized" models under three prompt conditions (no CoT, simple CoT, and detailed CoT), we shed light on the interplay of prompt specificity and model architecture. In doing so, we illustrate a potentially “shocking" fact: some older or established models can repeatedly fail a basic puzzle—a cautionary reminder that vendor or version labels do not guarantee robust reasoning for every scenario.

Chain-of-Thought prompting (CoT) has been shown to improve multi-step reasoning by prompting the model to "show its work" [1,2]. Meanwhile, commercial LLM deployments often introduce specialized "reasoning" or "extended thinking" variants, further complicating the landscape [3,4]. Although prior research highlights that the same model can perform significantly better or worse under slightly different prompts [1,2], less attention has been paid to consistently failing older or baseline versions that do not respond well to any form of CoT.

Our study contributes by:

We use the puzzle:

Key constraints:

Each model was tested under three prompt conditions:

We group models into:

Table 1 summarizes correctness under no CoT, simple CoT, and detailed CoT prompts.

Table 1. Performance Across Prompts

Given GPT-4’s reputation for advanced reasoning, one might expect GPT-4o—an older or baseline variant—to at least succeed under a detailed CoT prompt. Surprisingly, it repeatedly fails, often providing "9" or "13" as final answers. Possible factors include:

This phenomenon challenges the assumption that "triggering a logic chain" (via CoT) is always enough; if the model’s internal representation or heuristic is off, even explicit step-by-step instructions might not correct it.

The fact that GPT-4.5 and Claude 3.5 remain incorrect under "Think step by step" yet become correct with "Think step by step and write the detail analysis" raises questions:

Such outcomes indicate that prompt engineering is not merely about enabling any chain of thought, but about ensuring the model invests in verifying each step. Meanwhile, updated "general" models like DeepSeek V3 or Grok 3 and all "reasoning-optimized" models appear to do so automatically.

Our findings highlight a broader reality in the LLM ecosystem:

This has major implications:

Many answers included "5," "6," or "9," sometimes referencing the difference between a full round trip and single crossings. The puzzle’s wording "来回几次" can be read as "how many round trips?" or "how many one-way trips total?" Models that enumerated every crossing typically arrived at 11, while others only counted complete back-and-forth cycles. This discrepancy is further complicated by the final crossing not needing a return trip.

Hence, puzzle specification is crucial: If the question clarifies "count each single crossing," or "count only how many times the boat leaves side A," ambiguity is minimized.

We presented a comparative study on a classic 2-person boat puzzle across multiple LLMs and prompt strategies. Key observations:

Future directions include:

We hope our findings serve as a cautionary tale: even "big names" can falter on "simple" tasks, and subtle changes in prompt wording can be the difference between a correct solution and a baffling error.

1 Wei, J. et al. (2022). Chain-of-Thought Prompting Elicits Reasoning in Large Language Models.
2 Kojima, T. et al. (2022). Large Language Models are Zero-Shot Reasoners.
3 Anthropic, OpenAI, DeepMind, etc. (2023–2025). Public model release notes.
4 Nye, M. et al. (2022). Show Your Work: Scratchpads for Intermediate Computation with Language Models.

The screenshots listed in this appendix showcase examples of outputs
from different models under three prompting strategies: No CoT,
Simple CoT, and Detailed CoT. Unless otherwise specified, all
images are taken from actual conversation results.