Build a worked example for the subblocks of the topic "{topic}" — a fully worked-through case that carries understanding.

BLOCKS WITH SUBBLOCKS AND THEIR FACTS (go through EVERY subblock):
{blocks}

A good worked example:
- **problem**: a concrete, small task/question about the subblock (1 sentence).
- **steps**: 2–5 followable steps from the problem to the solution. Each step a brief sentence, in the right order.
- **result**: the final result / the insight (1 sentence).
- Rely on `example_idea` and the supported facts of the subblock. Compute cleanly; invent no values that contradict the facts.
- **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.
- **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.
- **The supplied facts often contain math as raw Unicode — convert it to LaTeX, do not take it over raw.**

Write `problem`, the `steps` and `result` in GERMAN.

Write all examples as ONE JSON into the file {out_path} (use your write tool), EXACTLY like this:
{{"examples": [
  {{"block": "<exact block title>", "subblock": "<exact subblock title>",
    "problem": "…", "steps": ["…", "…"], "result": "…"}}
]}}

Output no other text.
{extra}
