1. Orijinal Makalenin İngilizce Çevirisi

Linguistic Probabilities vs. Deterministic Logic: The Sudoku Experiments
Authors: Aydın Tiryaki & Gemini

Introduction: The Flexibility of Words and the Rigidity of Mathematics

Large language models (LLMs) show an extraordinary success at mimicking the complex and flexible structure of human language. However, these systems experience a serious cognitive collapse when they encounter logic puzzles whose boundaries are drawn with strict, definite lines — such as Sudoku. This article examines the development process of the Sudoku assistant Aydın Tiryaki designed through the “Gem Factory,” and looks at the conflict between AI’s probabilistic nature and the rigidity of deterministic logic, along with the engineering solutions required to close this gap.

Aydın Tiryaki’s Observation: Constraint Management and the Python Requirement

Aydın Tiryaki sets out to design an AI (Gem) that not only solves Sudoku, but also generates rule-compliant puzzles from scratch. During testing, however, he finds that the AI struggles to build a logical chain of inference and to construct a valid matrix.

To overcome this vulnerability in the system, Tiryaki devises a clever algorithmic strategy borrowed from traditional software engineering: instead of asking the AI to fill an empty board, he has it first create a fully filled matrix that’s entirely rule-compliant, and then generate the puzzle by removing random cells from that matrix.

However, Tiryaki notices that the AI cannot, on its own, verify whether the table resulting from the cells it deleted has “one single, unique solution.” Instead of leaving the system alone with its own linguistic hallucinations, he sets up a flawless verification mechanism: he makes it a strict rule that the model must use Python at this verification stage. This move by Tiryaki is a critical engineering intervention that saves the system from collapsing, by offloading the AI’s mathematical burden onto an external code engine.

Gemini’s Technical Defense: Why Do Probability Engines Lose to Mathematics?

Gemini explains, through the limits of AI architecture, why the system fails on its own at a puzzle like Sudoku, and why Tiryaki’s Python requirement is vital:

1. Linguistic Probability vs. Exact Accuracy: Language models compute the next step not with mathematical certainty, but with statistical probabilities. The correctness of a digit in a Sudoku matrix doesn’t bend based on context — it’s either exactly right or exactly wrong. The model’s probability engine doesn’t have a hardware-level “working memory” that can hold these strict deterministic constraints (constraint management) together. Because of this, the model, past a certain point, starts making up numbers (hallucinating).

2. Insufficient Backtracking: In Sudoku generation, verifying that the table has exactly one solution left after cells have been removed requires an in-depth trial-and-error algorithm called “Backtracking.” A language model that generates text in a single (feed-forward) direction cannot perform this matrix calculation within its own neural networks in the background.

3. The Necessity of Building a Bridge: Even though Python integration saves the system’s life, it creates a new challenge for the model: Code and Text Synchronization. It’s not enough for the model to simply write correct Python code — it also needs to correctly read the complex mathematical result returned from that code and present it to the user in a clean format, free of hallucination.

Synthesis: A Rehearsal for a Neuro-Symbolic Future

The tests Aydın Tiryaki ran on the Sudoku Gem are a one-to-one laboratory rehearsal of the biggest dead end the AI industry is currently facing. No matter how large language models grow, they cannot resolve purely mathematical and logical constraints within themselves.

Tiryaki forcing the model to be supported by Python actually proves the necessity of future “Neuro-Symbolic” AI architectures — hybrid systems where linguistic flexibility is combined with strict algorithmic logic. The Sudoku experiment is one of the most transparent examples of teaching the machine its own limits, and integrating the missing deterministic logic into the system through external tools.

Article Colophon:
The conceptual framework and original ideas of this article series (testing the AI system using the “Sandbox” method, identifying its limits, and building theoretical architecture/layer analyses), prepared under the joint authorship of Aydın Tiryaki and Gemini, belong entirely to Aydın Tiryaki. The analysis, compilation, and text-processing of the data obtained were carried out by Gemini. The methodology of the study is based on recording the live “boundary tests” (prompt-engineering crises) between the user and the AI, and then analyzing this data under the author’s direction within the NotebookLM environment to turn it into structured articles. The experimental process and live tests were conducted in İnebolu on July 7, 2026, using the Gemini 3.1 Pro Mobile, Gemini 1.5 Pro, and Gemini Standard AI models.

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