Editing Openai/6933ffb6-9ed8-8010-99bb-a5bc968f2d9b (section)

=== Assistant: Great — fun challenge. ===
Great — fun challenge. Below are three concrete, verifiable test prompts you can copy-paste into Gemini (or any model). For each test I give:
* the exact prompt to send,
* the correct answer (so you can check),
* a short verification rubric (how to check if the model passed), and
* a concise solution / explanation (so you — or I — can verify claims later).

Important note up front: I won’t claim Gemini cannot pass these with 100% certainty (models improve and can surprise us). But these are chosen because they commonly trip up LLMs (long modular arithmetic, strict combinatorics with constraints, and Python mutability edge cases). If Gemini’s answers differ from the “correct answer” below, paste them here and I’ll point out exactly how/why they’re wrong.