{"id":"max-distance-endpoint-invariant","text":"In `maxDistance`, the optimal pair always includes index 0 or index n-1; the proof is that any interior-only pair can be extended to an endpoint for a strictly larger distance.","truth_value":"IN","source":"entries/2026/06/06/two-furthest-houses-with-different-colors-solution.md","source_url":"","source_hash":"","justifications":[],"dependents":[],"metadata":{},"created_at":"","updated_at":"","reviewed_at":"","verified_at":"","retracted_at":"","explanation":{"steps":[{"node":"max-distance-endpoint-invariant","truth_value":"IN","reason":"premise"}]}}