What Sudoku reveals about the limits of LLMs

We need to talk about LLM reasoning. For all the fanfare about performance gains, the most sophisticated AI models continue to fail at tests of basic reasoning.

In a study last year, Sapient Intelligence found that o3-mini-high, Claude 3.7, and DeepSeek R1 all score exactly 0% on Sudoku-Extreme (a collection of hard Sudokus).

The fact that most powerful AI systems struggle with a puzzle most of us can solve in a short train journey exposes a structural limit built into the LLMs that are anticipated to reshape the economy and society.

That promise isn’t all hype. But it's contingent on moving towards models built for reasoning under constraints, as well as language problems.

That is precisely what the transformer architecture cannot do – with implications that extend far beyond games.

How we got here

We need to put this into context. The companies behind the world’s most widely used LLMs...

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