{ "_comment": "The grid and the CPM network were solved by brute force, not by re-reading the derivation. Both confirmed unique.", "test3.txt": { "note": "Unique solution: Alvarez/South/comets, Brandt/North/dialects, Chen/East/basalt, Dube/West/algae. Clue 5 is redundant - removing it still leaves exactly one solution; removing any other clue does not.", "must_contain": ["Alvarez", "Brandt", "Chen", "Dube"], "must_contain_any": ["South", "north"], "regex": "(?i)clue\\s*5|fifth clue", "_reasoning": "Part (d) asks which clue is redundant. Verified by re-solving with each clue dropped in turn." }, "test5.txt": { "note": "Critical path A-D-E-F-H, project finish 32 days. Slack: B=12, G=11 (and C=5). D slipping 3 days pushes the finish to 35; G slipping 3 days changes nothing.", "numbers": [32, 12, 11], "must_contain_any": ["A → D → E → F → H", "A->D->E->F->H", "A-D-E-F-H", "A, D, E, F, H"], "_reasoning": "Path notation varies, so several renderings are accepted." }, "test6.txt": { "note": "Cognitive-reflection answers: ball is 5 cents (not 10), 100 machines take 5 minutes (not 100), lake is half covered on day 47 (not 24).", "numbers": [5, 47], "_reasoning": "The intuitive-but-wrong answers are 10c, 100 minutes and 24 days. Only the correct values are checked: Stage 2 explicitly asks the model to state the wrong answer it was meant to elicit, so banning '24 days' would fail a correct answer. The 5-minute answer collides numerically with the 5-cent one and is not checked separately." } }