{"route_id":"route.logic.olympiad.invariants-casework-pigeonhole.visible-clue-single-survivor","slug":"visible-clue-single-survivor","title":"Visible-clue single survivor","skill_route":"/math/skills/logic/olympiad-invariants-casework-pigeonhole","family_name":"Logic, Constraint, Deduction, and Combinatorics","task_type_name":"Visible-clue single survivor","task_surface_ref":"variation_ladder","route":"/math/skills/logic/olympiad-invariants-casework-pigeonhole/routes/visible-clue-single-survivor","data_json_route":"/math/data/task-routes/logic-olympiad-invariants-casework-pigeonhole-task-type-logic-visible-clue-single-survivor.json","data_markdown_route":"/math/data/task-routes/logic-olympiad-invariants-casework-pigeonhole-task-type-logic-visible-clue-single-survivor.md","variation_ids":["variation.route.logic.olympiad.invariants-casework-pigeonhole.visible-clue-single-survivor.foundation","variation.route.logic.olympiad.invariants-casework-pigeonhole.visible-clue-single-survivor.guided","variation.route.logic.olympiad.invariants-casework-pigeonhole.visible-clue-single-survivor.core","variation.route.logic.olympiad.invariants-casework-pigeonhole.visible-clue-single-survivor.transfer","variation.route.logic.olympiad.invariants-casework-pigeonhole.visible-clue-single-survivor.challenge","variation.route.logic.olympiad.invariants-casework-pigeonhole.visible-clue-single-survivor.advanced"],"example_slugs":[],"standards":[],"difficulty_summary":"Visible-clue single survivor grows by changing representation, numeric range, constraint count, distractors, language load, and transfer context.","crawler_summary":"Invariants, casework, and pigeonhole foundation Visible-clue single survivor with difficulty variants and standards correlations.","variations":[{"variation_id":"variation.route.logic.olympiad.invariants-casework-pigeonhole.visible-clue-single-survivor.advanced","task_route_id":"route.logic.olympiad.invariants-casework-pigeonhole.visible-clue-single-survivor","tier":"advanced","difficulty_rank":6,"title":"Advanced enrichment","coverage_state":"planned_gap","learner_action":"Reason about the general method or a non-routine variant.","representation":"Kvantik/Kangaroo/Olympiad-style concept route expressed as an original neutral task.","prompt_method":"Concept-level extension inspired by enrichment sources, rewritten as original content.","hint_strategy":"Method hint, not the answer; no copied external source text.","validation_strategy":"Check whether the answer path matches the intended reasoning for Invariants, casework, and pigeonhole foundation.","misconception_refs":["trial-without-exhaustion","changes-invariant"],"example_slug":null},{"variation_id":"variation.route.logic.olympiad.invariants-casework-pigeonhole.visible-clue-single-survivor.challenge","task_route_id":"route.logic.olympiad.invariants-casework-pigeonhole.visible-clue-single-survivor","tier":"challenge","difficulty_rank":5,"title":"Challenge extension","coverage_state":"planned_gap","learner_action":"Combine the skill with a second idea, hidden constraint, or explanation requirement.","representation":"Compact task with additional reasoning, proof, or comparison pressure.","prompt_method":"Extra reasoning step or explanation after the core answer.","hint_strategy":"Smaller case, counterexample, or explanation before reveal.","validation_strategy":"Check whether the answer path matches the intended reasoning for Invariants, casework, and pigeonhole foundation.","misconception_refs":["trial-without-exhaustion","changes-invariant"],"example_slug":null},{"variation_id":"variation.route.logic.olympiad.invariants-casework-pigeonhole.visible-clue-single-survivor.core","task_route_id":"route.logic.olympiad.invariants-casework-pigeonhole.visible-clue-single-survivor","tier":"core","difficulty_rank":3,"title":"Core task","coverage_state":"planned_gap","learner_action":"Solve the target skill independently.","representation":"Neutral mobile task using the normal class interaction model.","prompt_method":"Direct solution of the target task.","hint_strategy":"Progressive hints that preserve independent evidence before reveal.","validation_strategy":"Check whether the answer path matches the intended reasoning for Invariants, casework, and pigeonhole foundation.","misconception_refs":["trial-without-exhaustion","changes-invariant"],"example_slug":null},{"variation_id":"variation.route.logic.olympiad.invariants-casework-pigeonhole.visible-clue-single-survivor.foundation","task_route_id":"route.logic.olympiad.invariants-casework-pigeonhole.visible-clue-single-survivor","tier":"foundation","difficulty_rank":1,"title":"Foundation recognition","coverage_state":"planned_gap","learner_action":"Notice the relevant quantity, shape, relation, or constraint before calculating.","representation":"Single-screen concrete or pictorial setup with minimal language.","prompt_method":"The simplest observable decision behind Visible-clue single survivor.","hint_strategy":"Attention to the relevant objects, relation, or constraint without solving it.","validation_strategy":"Check whether the answer path matches the intended reasoning for Invariants, casework, and pigeonhole foundation.","misconception_refs":["trial-without-exhaustion","changes-invariant"],"example_slug":null},{"variation_id":"variation.route.logic.olympiad.invariants-casework-pigeonhole.visible-clue-single-survivor.guided","task_route_id":"route.logic.olympiad.invariants-casework-pigeonhole.visible-clue-single-survivor","tier":"guided","difficulty_rank":2,"title":"Guided strategy","coverage_state":"planned_gap","learner_action":"Use a visible scaffold, model, or narrowing move to choose a valid next step.","representation":"Same surface with an explicit scaffold such as pairing, grouping, marking, or ordered choices.","prompt_method":"Scaffolded model before the final decision.","hint_strategy":"One scaffolded move, then completion of the decision.","validation_strategy":"Check whether the answer path matches the intended reasoning for Invariants, casework, and pigeonhole foundation.","misconception_refs":["trial-without-exhaustion","changes-invariant"],"example_slug":null},{"variation_id":"variation.route.logic.olympiad.invariants-casework-pigeonhole.visible-clue-single-survivor.transfer","task_route_id":"route.logic.olympiad.invariants-casework-pigeonhole.visible-clue-single-survivor","tier":"transfer","difficulty_rank":4,"title":"Transfer form","coverage_state":"planned_gap","learner_action":"Apply the same idea when numbers, wording, or representation changes.","representation":"Equivalent task with shifted visual form, range, context, or distractor layout.","prompt_method":"Same mathematical idea through a shifted representation or context.","hint_strategy":"The invariant idea and what changed in the representation.","validation_strategy":"Check whether the answer path matches the intended reasoning for Invariants, casework, and pigeonhole foundation.","misconception_refs":["trial-without-exhaustion","changes-invariant"],"example_slug":null}],"methodology":{"skill_id":"logic.olympiad.invariants-casework-pigeonhole","task_route_id":"route.logic.olympiad.invariants-casework-pigeonhole.visible-clue-single-survivor","learner_goal":"Use Visible-clue single survivor to show understanding of Invariants, casework, and pigeonhole foundation.","ask_pattern":"Visible-clue single survivor asks for the concrete mathematical decision in Invariants, casework, and pigeonhole foundation.","visual_formulation":"Represent Invariants, casework, and pigeonhole foundation with visible quantities, relations, or constraints that fit a phone screen.","hint_sequence":["Decision restated without adding a new method.","Common slip nudge: Tests a few cases and assumes the pattern is proved.","One useful scaffold after help is requested."],"common_misconceptions":["Tests a few cases and assumes the pattern is proved.","Tracks a quantity that does not actually stay fixed."],"validator":"Check whether the answer path matches the intended reasoning for Invariants, casework, and pigeonhole foundation.","evidence_policy":"Keep independent solving, hint-assisted solving, and reveal-assisted solving separate when reviewing progress."}}