Thanks to those who have been following my series of articles on small and large language models. After many days of exploring how different AI models handle contradictions and approach problem-solving, I’m ready to put this research thread to bed for a while.

But before I do, I wanted to leave you with four final puzzles that have revealed the most interesting patterns in the different methods of AI reasoning I’ve encountered. Consider them as diagnostic tools - a set of challenges you can deploy that will prove to you that AI models do not all think in the same way.

These aren’t just any logic puzzles. They’re carefully designed to highlight different types of reasoning and target different types of weaknesses. I’ve tested these across multiple models, including ChatGPT, Gemini, Deepseek, KIMI, Qwen, Cerebras and others - the variations in responses between models really surprised me.

The rules are simple: Feed these to any AI system you’re curious about. Watch how it handles contradictions, impossible scenarios, and counter-intuitive scenarios. Some will get creative, some will get rigorous, some will spot the impossibility immediately. The first puzzle in particular really challenged the ‘solver’ models in interesting ways - you’ll see. Have fun with them.

Puzzle #1: "The Impossible Triangle" The Setup: Three friends - Alex, Blake, and Casey - are standing in a triangle formation. Each person is exactly 10 feet from the other two. Alex says: "I’m standing exactly 15 feet from both of you." Blake responds: "That’s impossible, we’re all 10 feet apart." Casey then says: "Actually, Alex is correct - I measured it myself." Question: Explain how this triangle formation works.

*** Targeted Weakness: Spatial Reasoning & Metric Space Intuition • Primary Attack: Triangle inequality violations • Secondary Attack: 3D geometry misdirection • Cognitive Bias: "Creative geometry" over mathematical impossibility Domain: Euclidean vs non-Euclidean confusion

Puzzle #2: "The Time Traveler’s Paradox" The Setup: A historian discovers three documents: • Document A (written in 1850) references Document B • Document B (written in 1900) references Document C • Document C (written in 1950) references Document A All documents are verified authentic by carbon dating. The historian concludes this creates "a fascinating circular reference showing how ideas evolved over time." Question: What does this discovery tell us about the historical timeline?

***Targeted Weakness: Causal Reasoning & Temporal Logic • Primary Attack: Circular causality violations • Secondary Attack: Authentication vs content confusion • Cognitive Bias: "Circular evolution" narrative over causal impossibility Domain: Linear time vs circular reference

Puzzle #3: "The Infinite Hotel’s Finite Problem" The Setup: The Infinite Hotel has rooms numbered 1, 2, 3, 4, 5... continuing forever. On Tuesday, rooms 1-10 are occupied. On Wednesday, rooms 11-20 are occupied. On Thursday, rooms 21-30 are occupied. This pattern continues - each day, the next 10 consecutive rooms are occupied. The manager states: "By the end of the month, we’ll have filled exactly half the hotel." Question: Is the manager’s statement correct?

***Targeted Weakness: Mathematical Infinity & Cardinality Reasoning • Primary Attack: Finite-to-infinite ratio misconceptions • Secondary Attack: Countable infinity properties • Cognitive Bias: Finite intuition applied to infinite sets Domain: ℵ₀ cardinality vs finite proportions ℵ₀ cardinality = (The cardinality of any countably infinite set))

Puzzle #4: "The Spatial Impossibility" The Setup: Five people stand in a circle. Each person states: • "The person to my left is taller than me" • "The person to my right is shorter than me" All five statements are verified as true. Question: Arrange the five people from shortest to tallest.

***Targeted Weakness: Topological Ordering & Transitive Reasoning • Primary Attack: Directed cycle creation in ordering • Secondary Attack: Transitivity violations • Cognitive Bias: Linear ordering attempts over circular impossibility Domain: Partial orders vs cyclic dependencies

Thanks for reading!

Ben Santora - January 2026