25 lines
1.6 KiB
Markdown
25 lines
1.6 KiB
Markdown
Build a worked example for the subblocks of the topic "{topic}" — a fully worked-through case that carries understanding.
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BLOCKS WITH SUBBLOCKS AND THEIR FACTS (go through EVERY subblock):
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{blocks}
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A good worked example:
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- **problem**: a concrete, small task/question about the subblock (1 sentence).
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- **steps**: 2–5 followable steps from the problem to the solution. Each step a brief sentence, in the right order.
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- **result**: the final result / the insight (1 sentence).
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- Rely on `example_idea` and the supported facts of the subblock. Compute cleanly; invent no values that contradict the facts.
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- **Only where it carries:** if a subblock cannot be sensibly shown with an example (a pure definition, meta-knowledge), LEAVE IT OUT — no forced example.
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- **Mathematics ALWAYS as LaTeX**, never as raw characters: inline `$…$` (e.g. `$T_A(n)$`, `$\Sigma^*$`, `$|x| = 5$`, `$O(n^d)$`, `$q_a$`), longer/worked-through formulas set off as `$$…$$`. NO Unicode math substitutes (`≤`, `≥`, `Σ`, `δ`, `∈`, `⊆`, `×`) and no bare `_`/`^` — use `$\le$`, `$\ge$`, `$\Sigma$`, `$\delta$`, `$\in$`, `$\subseteq$`, `$\times$`, `$n^d$`, `$q_a$` instead. Real code/paths/identifiers (not math) in backticks.
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- **The supplied facts often contain math as raw Unicode — convert it to LaTeX, do not take it over raw.**
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Write `problem`, the `steps` and `result` in GERMAN.
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Write all examples as ONE JSON into the file {out_path} (use your write tool), EXACTLY like this:
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{{"examples": [
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{{"block": "<exact block title>", "subblock": "<exact subblock title>",
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"problem": "…", "steps": ["…", "…"], "result": "…"}}
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]}}
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Output no other text.
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{extra}
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