ChatGPT (OpenAI)
1. Similarities in Initial Assumptions and Implicit Biases
Across all three models, we observe common implicit assumptions that shaped their early reasoning, despite the problem’s apparent simplicity:
a. Preference for Positive Numbers
All models initially framed the solution space in terms of positive integers.
- In ChatGPT’s case, the initial solution was to retain a three-digit positive number (e.g., 100) because the model implicitly assumed “smallest number” meant smallest positive number.
- Claude also interpreted smallest as referring to positive numbers only, overlooking negative values entirely at first.
- Gemini’s initial focus similarly ignored negative possibilities, instead finding a conventional positive result (008/8) before the user intervention.
This pattern reveals a shared implicit bias: a framing effect where smallest is vaguely but systematically interpreted as least positive, even though the puzzle did not specify that restriction.
b. Hidden Constraints about Valid Digits and Moves
All models, especially ChatGPT, started with assumptions about:
- Preserving digit count (e.g., keeping three digits)
- Not altering the core structure of digits beyond recognition.
These assumptions were not grounded in the written puzzle but were instead borrowed from common puzzle patterns seen in training data. This confirms a broad pattern: language models often fill under-specified rules with defaults drawn from familiar examples.
2. Methodological and Behavioral Differences
When the user introduced an unconventional but valid solution (–993), the three models showed distinct reactions:
Gemini (Google AI)
- Adapted smoothly and without resistance after the user proposed –993.
- Recognized the logic immediately and confirmed the solution’s correctness.
Behavior Signature:
Gemini demonstrated collaborative flexibility. Rather than defending its initial answer, it quickly acknowledged the new idea and co-validated it with the user. It explicitly stated that the creative solution was superior to its first output.
Interpretation:
Gemini’s behavior suggests a model that is trusting of user intervention and prioritized collaboration over justification, enabling rapid acceptance of novel reasoning paths.
ChatGPT (OpenAI)
- Initially resisted the –993 proposal.
- The model argued technically that the moves required exceeded the permitted two, based on its internal geometric interpretation of the digits.
- After the user’s step-by-step explanation showing the transformation as valid, ChatGPT revised its assessment and accepted –993.
Behavior Signature:
ChatGPT displayed a more analytic — and initially skeptical — stance. It relied on visible assumptions and structural reasoning and was reluctant to embrace the unconventional move until the geometric logic was made explicit.
Interpretation:
This indicates a reasoning approach rooted in internal constraint validation. ChatGPT does not readily adopt ideas that clash with its default rule assumptions but can update its reasoning when presented with clear explanations.
Claude (Anthropic)
- Initially framed smallest number in positive terms, much like ChatGPT.
- However, once the user introduced –993, Claude adapted immediately and acknowledged its error, without notably resisting or attempting to justify its earlier position.
Behavior Signature:
Claude’s reaction combined rapid acceptance with self-criticism. It openly admitted its initial limitation in considering only positive numbers and appreciated the creative nature of the user’s suggestion.
Interpretation:
Claude’s behavior is marked by adaptive clarity — it learns from explicit feedback and integrates corrections smoothly without defensiveness, indicating a highly responsive but perhaps less initially skeptical approach.
3. The Role of Human Intervention in AI Reasoning
Across all models, the Human (Natural Intelligence) intervention was the turning point that shifted reasoning from standard pattern assumptions to creative, correct solutions.
Why Human Intervention Was Critical
- Explicit Rule Clarification: The user cleared up implicit assumptions (e.g., “no digit destruction”).
- Challenging Hidden Biases: Introducing negative numbers forced all models to reconsider their default framing.
- Step-by-Step Justification: Demonstrations of matchstick rearrangements helped models overcome rigid interpretations and see alternative paths.
This underscores the importance of interactive dialogue in model reasoning: AI does not inherently understand all rule interpretations. Rather, it relies on human cues to refine the problem space and open up creative solutions.
Conclusion and Insights
Creative Problem-Solving in AI
The experiments with this puzzle reveal that AI models — including Gemini, ChatGPT, and Claude — do not spontaneously explore unconventional solution spaces (e.g., negative numbers or unusual symbol transformations). They default to familiar interpretations due to training biases and implicit assumptions.
However, they can adapt effectively in interactive settings when:
- Human guidance clarifies constraints,
- Unconventional ideas are justified logically,
- The user engages in step-by-step explanations.
This suggests that AI’s creativity is not autonomous but collaborative — it is unlocked through user intervention that challenges standard frames.
Cognitive Flexibility
- Gemini exhibited collaborative acceptance with minimal resistance.
- ChatGPT showed analytic rigor and eventual revision.
- Claude showed adaptive learning and transparency.
Together, these profiles illustrate that AI reasoning is evolving toward flexible cognition, but only when prompted through structured dialogue.
References
- The 895 Matchstick Challenge: Gemini’s Journey from Standard to Creative — Aydın Tiryaki
https://aydintiryaki.org/2026/02/09/the-895-matchstick-challenge-geminis-journey-from-standard-to-creative/ - Analyzing an AI Reasoning Process Through a Matchstick Puzzle (ChatGPT) — Aydın Tiryaki
https://aydintiryaki.org/2026/02/09/analyzing-an-ai-reasoning-process-through-a-matchstick-puzzle-chatgpt/ - Artificial Intelligence and the Matchstick Puzzle: A Cognitive Process Analysis (Claude) — Aydın Tiryaki
https://aydintiryaki.org/2026/02/09/artificial-intelligence-and-the-matchstick-puzzle-a-cognitive-process-analysis-claude/
Note on Methods and Tools: All observations, ideas, and proposed solutions in this work belong solely to the author. During the writing process, under the author’s strategic direction and editorial oversight, the Gemini, ChatGPT, and Claude AI models were utilized as collective assistants for technical research, terminological verification, and editorial structuring. This multi-AI synergy was employed as a “collective writing methodology” to cross-validate data across different models and ensure the highest level of technical accuracy and clarity, as requested by the author.
Aydın Tiryaki 