| """
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| Problem Generator - Generates diverse reasoning problems from concepts.
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| Takes a concept text and generates 5-8 different reasoning problems across
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| types: explain, compare, apply, critique, extend, analogize, decompose, synthesize.
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| Each problem type has 10+ templates.
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| """
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| import random
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| import re
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| class ProblemGenerator:
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| """Generates multi-type reasoning problems from concept text."""
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| _problem_templates: dict[str, list[str]] = {
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| "explain": [
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| "Explain the underlying mechanisms of {concept} as if teaching a graduate student who is brilliant but unfamiliar with this domain.",
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| "Provide a first-principles explanation of {concept}, starting from the most fundamental assumptions and building up to the full picture.",
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| "Explain why {concept} matters, tracing the chain of consequences from the immediate to the long-term.",
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| "Explain {concept} by identifying the three most important things someone must understand and why each matters.",
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| "Explain the causal structure of {concept}: what drives it, what it drives, and what mediates the relationship.",
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| "Give an explanation of {concept} that a thoughtful 15-year-old would find both accessible and intellectually satisfying.",
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| "Explain what makes {concept} difficult to understand and how that difficulty can be resolved.",
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| "Explain {concept} by contrasting what most people think it means with what it actually means upon closer examination.",
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| "Explain the boundary conditions of {concept}: under what circumstances does it hold, and when does it break down?",
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| "Explain {concept} using only concrete examples and observable phenomena, avoiding abstract terminology.",
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| "Explain how {concept} changes depending on the scale at which you examine it.",
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| "Explain the history of how our understanding of {concept} has evolved and what drove each major shift.",
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| ],
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| "compare": [
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| "Compare {concept} with its closest alternative or rival, highlighting where they agree, where they diverge, and why the differences matter.",
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| "Compare how {concept} would be understood by an engineer versus a philosopher, and explain what each perspective captures that the other misses.",
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| "Compare the short-term and long-term implications of {concept}, noting where they align and where they conflict.",
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| "Compare {concept} as it appears in theory versus how it manifests in practice, explaining the gap.",
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| "Compare the strongest argument for {concept} with the strongest argument against it, steelmanning both sides.",
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| "Compare how {concept} is understood in two different cultural or disciplinary contexts.",
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| "Compare the naive understanding of {concept} with the expert understanding, identifying exactly where they diverge.",
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| "Compare {concept} with a superficially similar but fundamentally different concept, explaining the crucial distinction.",
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| "Compare the risks of overestimating versus underestimating the importance of {concept}.",
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| "Compare how {concept} would be analyzed using quantitative methods versus qualitative methods, and what each approach reveals.",
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| "Compare the state of {concept} ten years ago with its current state, identifying the key drivers of change.",
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| ],
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| "apply": [
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| "Apply the principles underlying {concept} to solve a concrete real-world problem that you specify.",
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| "Describe how you would apply {concept} in a professional context, including specific steps and expected outcomes.",
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| "Apply {concept} to a domain where it is not typically used and explain what new insights emerge.",
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| "Design an experiment or test that would apply {concept} to generate actionable data.",
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| "Apply {concept} to evaluate a current real-world controversy or decision, showing how it clarifies the issues.",
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| "Show how {concept} could be applied to improve an existing system or process, specifying the mechanism of improvement.",
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| "Apply {concept} to predict what will happen in a specified scenario and explain your reasoning.",
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| "Demonstrate how {concept} applies to everyday decision-making by walking through a common choice people face.",
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| "Apply {concept} to diagnose why a particular system or approach is failing and propose a remedy.",
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| "Show how {concept} could be applied at three different scales (individual, organizational, societal) with different implications at each.",
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| "Apply {concept} to a field where it has been underutilized and argue for its relevance.",
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| ],
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| "critique": [
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| "Identify the three most significant weaknesses or limitations of {concept} and assess how seriously they undermine it.",
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| "Construct the strongest possible objection to {concept} and then evaluate whether the objection succeeds.",
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| "Critique the hidden assumptions underlying {concept}, assessing which are well-founded and which are questionable.",
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| "Evaluate whether {concept} confuses correlation with causation, and if so, what the actual causal story might be.",
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| "Critique the evidence base for {concept}: is it sufficient, and what kinds of evidence are missing?",
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| "Identify who benefits from the current framing of {concept} and whether that framing may be self-serving.",
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| "Assess whether {concept} commits any logical fallacies and, if so, whether the core insight survives the correction.",
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| "Critique the scalability of {concept}: does it work at small scale but fail at large scale, or vice versa?",
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| "Evaluate whether {concept} is genuinely novel or whether it is a repackaging of older ideas under new terminology.",
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| "Critique the precision of {concept}: is it defined clearly enough to be testable, or is it vague enough to be unfalsifiable?",
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| "Assess whether {concept} adequately accounts for the perspectives and experiences of marginalized groups.",
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| ],
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| "extend": [
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| "Extend {concept} to its logical conclusion: if we take it seriously and follow it consistently, where does it lead?",
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| "Propose a novel extension of {concept} that addresses one of its current limitations.",
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| "Extend {concept} into the future: how might it evolve over the next decade given current trends?",
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| "Identify a domain where {concept} has not yet been applied and develop the extension, including what modifications would be needed.",
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| "Extend {concept} by combining it with an insight from a different field, creating something neither field has alone.",
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| "Propose how {concept} could be extended to address a problem it was not originally designed for.",
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| "Extend {concept} by asking what happens at its extreme: what if it were applied maximally or universally?",
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| "Develop an extension of {concept} that makes it more robust against its known failure modes.",
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| "Extend {concept} by integrating quantitative measurement where it currently relies on qualitative judgment.",
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| "Propose a version of {concept} adapted for a context where resources are extremely limited.",
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| "Extend {concept} by identifying the next logical question it raises and sketching how to answer it.",
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| ],
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| "analogize": [
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| "Construct an analogy between {concept} and a biological system, mapping each component to its biological counterpart.",
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| "Create an analogy between {concept} and a well-known everyday experience that makes the abstract concrete.",
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| "Develop an analogy between {concept} and a historical event or period, drawing specific parallels.",
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| "Build an analogy between {concept} and a mechanical or engineering system, identifying the load-bearing correspondences.",
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| "Construct an analogy between {concept} and a game or sport, mapping rules, strategies, and winning conditions.",
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| "Create an analogy between {concept} and a musical composition, identifying rhythm, harmony, dissonance, and resolution.",
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| "Develop an analogy between {concept} and an ecosystem, mapping the roles of producers, consumers, decomposers, and energy flow.",
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| "Build an analogy between {concept} and the process of cooking a complex meal, mapping ingredients, techniques, and timing.",
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| "Construct an analogy between {concept} and a journey, identifying the starting point, obstacles, milestones, and destination.",
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| "Create an analogy between {concept} and a language, mapping grammar, vocabulary, syntax, and meaning.",
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| "After constructing your best analogy for {concept}, identify exactly where the analogy breaks down and what the breakdown reveals.",
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| ],
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| "decompose": [
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| "Decompose {concept} into its fundamental components and explain how each contributes to the whole.",
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| "Break {concept} into its necessary and sufficient conditions: what must be present for it to hold?",
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| "Decompose {concept} into layers of abstraction, from the most concrete to the most abstract.",
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| "Identify the independent variables within {concept} and explain how each can be varied independently.",
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| "Decompose {concept} into its temporal phases: what happens first, second, third, and how do the phases connect?",
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| "Break {concept} into its stakeholder dimensions: how does each affected party experience it differently?",
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| "Decompose {concept} into its inputs, processes, and outputs, tracing the transformation at each stage.",
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| "Identify the key tensions or trade-offs within {concept} and explain how they create its characteristic behavior.",
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| "Decompose {concept} into what is known with confidence, what is suspected but unconfirmed, and what remains entirely unknown.",
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| "Break {concept} into its structural elements (what it is) and its dynamic elements (how it changes).",
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| "Decompose the causal graph of {concept}: which factors cause which, and which are merely correlated?",
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| ],
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| "synthesize": [
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| "Synthesize a unified understanding of {concept} that integrates scientific, philosophical, and practical perspectives.",
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| "Synthesize the arguments for and against {concept} into a balanced position that acknowledges the valid points on both sides.",
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| "Create a synthesis that resolves the apparent contradiction between two competing interpretations of {concept}.",
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| "Synthesize insights about {concept} from at least three different disciplines into a coherent framework.",
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| "Synthesize a practical guide for engaging with {concept} that draws on both theoretical understanding and real-world experience.",
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| "Synthesize the historical evolution and current state of {concept} into a narrative that explains both where we are and how we got here.",
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| "Create a synthesis of {concept} that a diverse audience (technical and non-technical, young and old) would find valuable.",
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| "Synthesize the local and global dimensions of {concept} into an understanding that operates at both scales.",
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| "Synthesize the quantitative and qualitative aspects of {concept} into an integrated assessment.",
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| "Create a synthesis of {concept} that explicitly addresses and resolves the top three objections to it.",
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| "Synthesize a forward-looking vision of {concept} that builds on current understanding to anticipate future development.",
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| ],
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| }
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|
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| def generate_problems(
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| self, concept: str, count: int | None = None
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| ) -> list[tuple[str, str]]:
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| """Generate reasoning problems from a concept.
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| Args:
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| concept: The concept text to generate problems for.
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| count: Number of problems to generate (5-8 if None).
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| Returns:
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| List of (problem_type, problem_text) tuples.
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| """
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| if count is None:
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| count = random.randint(5, 8)
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| count = max(1, min(count, len(self._problem_templates)))
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| all_types = list(self._problem_templates.keys())
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| required = ["explain", "synthesize"]
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| optional = [t for t in all_types if t not in required]
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| random.shuffle(optional)
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| selected_types = required + optional[: max(0, count - len(required))]
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| random.shuffle(selected_types)
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| problems = []
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| for ptype in selected_types:
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| templates = self._problem_templates[ptype]
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| template = self._select_relevant_template(concept, templates)
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| problem_text = template.replace("{concept}", concept)
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| problems.append((ptype, problem_text))
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| return problems
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|
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| def generate_all_types(self, concept: str) -> list[tuple[str, str]]:
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| """Generate one problem of each type for a concept.
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| Args:
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| concept: The concept text.
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| Returns:
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| List of (problem_type, problem_text) tuples, one per type.
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| """
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| problems = []
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| for ptype, templates in self._problem_templates.items():
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| template = self._select_relevant_template(concept, templates)
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| problem_text = template.replace("{concept}", concept)
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| problems.append((ptype, problem_text))
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| return problems
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|
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| def _select_relevant_template(
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| self, concept: str, templates: list[str]
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| ) -> str:
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| """Select the template most relevant to the concept keywords.
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|
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| Falls back to random selection if no strong match.
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| """
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| concept_words = set(re.findall(r'\b[a-z]{4,}\b', concept.lower()))
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| if not concept_words:
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| return random.choice(templates)
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|
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| scored = []
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| for template in templates:
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| template_lower = template.lower()
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| score = sum(1 for w in concept_words if w in template_lower)
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| scored.append((score, template))
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| max_score = max(s for s, _ in scored)
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| if max_score > 0:
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| best = [t for s, t in scored if s == max_score]
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| return random.choice(best)
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|
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| return random.choice(templates)
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|
