feat: add plugin framework with UI contributions and suite selection
- Implemented PluginBlocks component to render various plugin UI elements. - Created SuitePicker for selecting test suites and questions. - Introduced usePluginUI hook for managing plugin UI state and manifest. - Developed DocsPage for comprehensive plugin framework documentation. - Added PluginPage to render pages declared by plugins based on the current path.
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Solve the following deduction problem. Show every inference step.
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Four researchers — Alvarez, Brandt, Chen, and Dube — each work in exactly one of four buildings (North, South, East, West) and each studies exactly one topic (algae, basalt, comets, dialects). No two share a building or a topic.
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Clues:
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1. The person in North studies neither algae nor comets.
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2. Chen works in neither South nor West.
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3. The basalt researcher works directly east of the algae researcher. Among these four buildings, only East is directly east of West; North and South are neither east nor west of anything.
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4. Brandt studies dialects.
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5. Alvarez does not work in East.
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6. Dube does not study comets.
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Produce:
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(a) The complete assignment of person, building, and topic.
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(b) A numbered chain of deductions in which every step cites the clue number it uses. Each step must follow from clues and prior steps only.
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(c) A statement of whether the solution is unique, with the reasoning that establishes uniqueness.
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(d) Identify any clue that is logically redundant — one whose removal would not change the solution — and prove it is redundant.
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If the constraints turn out to be contradictory, say so and name the minimal set of clues that conflict. Do not invent an assignment that satisfies only some of them.
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