{"id": "r2-001-buses", "expect": "solved", "text": "A school rents 6 buses for a trip. Each large bus holds 50 students and each small bus holds 30 students. The buses carry 260 students in total. How many large buses are there?", "unknowns": [{"symbol": "large_bus", "entity": "large bus", "unit": "bus", "domain": "nonnegative_integer"}, {"symbol": "small_bus", "entity": "small bus", "unit": "bus", "domain": "nonnegative_integer"}], "facts": [{"category": "large_bus", "measured_unit": "student", "value": 50}, {"category": "small_bus", "measured_unit": "student", "value": 30}], "constraints": [{"terms": [["large_bus", 1], ["small_bus", 1]], "relation": "eq", "rhs": 6}, {"terms": [["large_bus", 50], ["small_bus", 30]], "relation": "eq", "rhs": 260}], "query": {"symbol": "large_bus", "unit": "bus"}, "gold": 4, "options": {"A": 2, "B": 3, "C": 4, "D": 5}, "answer": "C", "notes": "Canonical two-category count/weight system: large+small=6, 50*large+30*small=260 -> large=4, small=2."}
{"id": "r2-002-chickens", "expect": "solved", "text": "A farm has 18 animals, all chickens and cows. Altogether the animals have 50 legs. Each chicken has 2 legs and each cow has 4 legs. How many chickens are there?", "unknowns": [{"symbol": "chicken", "entity": "chicken", "unit": "animal", "domain": "nonnegative_integer"}, {"symbol": "cow", "entity": "cow", "unit": "animal", "domain": "nonnegative_integer"}], "facts": [{"category": "chicken", "measured_unit": "leg", "value": 2}, {"category": "cow", "measured_unit": "leg", "value": 4}], "constraints": [{"terms": [["chicken", 1], ["cow", 1]], "relation": "eq", "rhs": 18}, {"terms": [["chicken", 2], ["cow", 4]], "relation": "eq", "rhs": 50}], "query": {"symbol": "chicken", "unit": "animal"}, "gold": 11, "options": {"A": 11, "B": 7, "C": 9, "D": 13}, "answer": "A", "notes": "chicken+cow=18, 2*chicken+4*cow=50 -> chicken=11, cow=7."}
{"id": "r2-003-tickets", "expect": "solved", "text": "A family buys 40 tickets in total, some adult and some child. Each adult ticket costs 12 dollars and each child ticket costs 8 dollars. The tickets cost 400 dollars in total. How many adult tickets are there?", "unknowns": [{"symbol": "adult_ticket", "entity": "adult ticket", "unit": "ticket", "domain": "nonnegative_integer"}, {"symbol": "child_ticket", "entity": "child ticket", "unit": "ticket", "domain": "nonnegative_integer"}], "facts": [{"category": "adult_ticket", "measured_unit": "dollar", "value": 12}, {"category": "child_ticket", "measured_unit": "dollar", "value": 8}], "constraints": [{"terms": [["adult_ticket", 1], ["child_ticket", 1]], "relation": "eq", "rhs": 40}, {"terms": [["adult_ticket", 12], ["child_ticket", 8]], "relation": "eq", "rhs": 400}], "query": {"symbol": "adult_ticket", "unit": "ticket"}, "gold": 20, "options": {"A": 15, "B": 20, "C": 25, "D": 10}, "answer": "B", "notes": "adult+child=40, 12*adult+8*child=400 -> adult=20, child=20."}
{"id": "r2-004-coins", "expect": "solved", "text": "A jar holds 20 coins, all nickels and dimes. A nickel is worth 5 cents and a dime is worth 10 cents. The coins are worth 145 cents in total. How many dimes are there?", "unknowns": [{"symbol": "nickel", "entity": "nickel", "unit": "coin", "domain": "nonnegative_integer"}, {"symbol": "dime", "entity": "dime", "unit": "coin", "domain": "nonnegative_integer"}], "facts": [{"category": "nickel", "measured_unit": "cent", "value": 5}, {"category": "dime", "measured_unit": "cent", "value": 10}], "constraints": [{"terms": [["nickel", 1], ["dime", 1]], "relation": "eq", "rhs": 20}, {"terms": [["nickel", 5], ["dime", 10]], "relation": "eq", "rhs": 145}], "query": {"symbol": "dime", "unit": "coin"}, "gold": 9, "options": {"A": 9, "B": 11, "C": 7, "D": 13}, "answer": "A", "notes": "nickel+dime=20, 5*nickel+10*dime=145 -> nickel=11, dime=9. Query asks the SECOND category (dime), guarding against a solver that only returns the first variable."}
{"id": "r2-005-boxes", "expect": "solved", "text": "A warehouse packs 12 boxes, some large and some small. Each large box holds 20 items and each small box holds 8 items. The boxes hold 144 items in total. How many large boxes are there?", "unknowns": [{"symbol": "large_box", "entity": "large box", "unit": "box", "domain": "nonnegative_integer"}, {"symbol": "small_box", "entity": "small box", "unit": "box", "domain": "nonnegative_integer"}], "facts": [{"category": "large_box", "measured_unit": "item", "value": 20}, {"category": "small_box", "measured_unit": "item", "value": 8}], "constraints": [{"terms": [["large_box", 1], ["small_box", 1]], "relation": "eq", "rhs": 12}, {"terms": [["large_box", 20], ["small_box", 8]], "relation": "eq", "rhs": 144}], "query": {"symbol": "large_box", "unit": "box"}, "gold": 4, "options": {"A": 4, "B": 6, "C": 8, "D": 2}, "answer": "A", "notes": "large+small=12, 20*large+8*small=144 -> large=4, small=8."}
{"id": "r2-006-vehicles", "expect": "solved", "text": "A parking lot has 10 vehicles, all cars and motorcycles. Each car has 4 wheels and each motorcycle has 2 wheels. Together the vehicles have 32 wheels. How many cars are there?", "unknowns": [{"symbol": "car", "entity": "car", "unit": "vehicle", "domain": "nonnegative_integer"}, {"symbol": "motorcycle", "entity": "motorcycle", "unit": "vehicle", "domain": "nonnegative_integer"}], "facts": [{"category": "car", "measured_unit": "wheel", "value": 4}, {"category": "motorcycle", "measured_unit": "wheel", "value": 2}], "constraints": [{"terms": [["car", 1], ["motorcycle", 1]], "relation": "eq", "rhs": 10}, {"terms": [["car", 4], ["motorcycle", 2]], "relation": "eq", "rhs": 32}], "query": {"symbol": "car", "unit": "vehicle"}, "gold": 6, "options": {"A": 4, "B": 6, "C": 8, "D": 5}, "answer": "B", "notes": "car+motorcycle=10, 4*car+2*motorcycle=32 -> car=6, motorcycle=4."}
{"id": "r2-007-pens", "expect": "solved", "text": "A store sells 15 writing tools, all pens and pencils. Each pen costs 3 dollars and each pencil costs 1 dollar. The tools cost 33 dollars in total. How many pens are there?", "unknowns": [{"symbol": "pen", "entity": "pen", "unit": "tool", "domain": "nonnegative_integer"}, {"symbol": "pencil", "entity": "pencil", "unit": "tool", "domain": "nonnegative_integer"}], "facts": [{"category": "pen", "measured_unit": "dollar", "value": 3}, {"category": "pencil", "measured_unit": "dollar", "value": 1}], "constraints": [{"terms": [["pen", 1], ["pencil", 1]], "relation": "eq", "rhs": 15}, {"terms": [["pen", 3], ["pencil", 1]], "relation": "eq", "rhs": 33}], "query": {"symbol": "pen", "unit": "tool"}, "gold": 9, "options": {"A": 6, "B": 9, "C": 7, "D": 12}, "answer": "B", "notes": "pen+pencil=15, 3*pen+1*pencil=33 -> pen=9, pencil=6."}
{"id": "r2-008-negative", "expect": "solver_refuses", "solver_reason": "negative_solution", "text": "A school rents 6 buses. Each large bus holds 50 students and each small bus holds 30 students. The buses carry 400 students in total. How many large buses are there?", "unknowns": [{"symbol": "large_bus", "entity": "large bus", "unit": "bus", "domain": "nonnegative_integer"}, {"symbol": "small_bus", "entity": "small bus", "unit": "bus", "domain": "nonnegative_integer"}], "facts": [{"category": "large_bus", "measured_unit": "student", "value": 50}, {"category": "small_bus", "measured_unit": "student", "value": 30}], "constraints": [{"terms": [["large_bus", 1], ["small_bus", 1]], "relation": "eq", "rhs": 6}, {"terms": [["large_bus", 50], ["small_bus", 30]], "relation": "eq", "rhs": 400}], "query": {"symbol": "large_bus", "unit": "bus"}, "gold": null, "notes": "Well-formed setup but 400 students needs large=11 > 6 buses -> small=-5 < 0. The solver REFUSES (negative_solution); no nonnegative-integer answer exists."}
{"id": "r2-009-non-integer", "expect": "solver_refuses", "solver_reason": "non_integer_solution", "text": "A shop sells 10 items, all pens and notebooks. Each pen costs 3 dollars and each notebook costs 5 dollars. The items cost 37 dollars in total. How many pens are there?", "unknowns": [{"symbol": "pen", "entity": "pen", "unit": "item", "domain": "nonnegative_integer"}, {"symbol": "notebook", "entity": "notebook", "unit": "item", "domain": "nonnegative_integer"}], "facts": [{"category": "pen", "measured_unit": "dollar", "value": 3}, {"category": "notebook", "measured_unit": "dollar", "value": 5}], "constraints": [{"terms": [["pen", 1], ["notebook", 1]], "relation": "eq", "rhs": 10}, {"terms": [["pen", 3], ["notebook", 5]], "relation": "eq", "rhs": 37}], "query": {"symbol": "pen", "unit": "item"}, "gold": null, "notes": "pen+notebook=10, 3*pen+5*notebook=37 -> pen=6.5: no integer solution. The solver REFUSES (non_integer_solution), never rounds."}
{"id": "r2-010-indistinguishable", "expect": "solver_refuses", "solver_reason": "indistinguishable_weights", "text": "A lot has 8 vehicles, all cars and trucks. Each car has 4 wheels and each truck has 4 wheels. Together the vehicles have 32 wheels. How many cars are there?", "unknowns": [{"symbol": "car", "entity": "car", "unit": "vehicle", "domain": "nonnegative_integer"}, {"symbol": "truck", "entity": "truck", "unit": "vehicle", "domain": "nonnegative_integer"}], "facts": [{"category": "car", "measured_unit": "wheel", "value": 4}, {"category": "truck", "measured_unit": "wheel", "value": 4}], "constraints": [{"terms": [["car", 1], ["truck", 1]], "relation": "eq", "rhs": 8}, {"terms": [["car", 4], ["truck", 4]], "relation": "eq", "rhs": 32}], "query": {"symbol": "car", "unit": "vehicle"}, "gold": null, "notes": "Equal coefficients (4 == 4): the weighted total carries no information beyond the count, so the system is underdetermined. The solver REFUSES (indistinguishable_weights)."}
{"id": "r2-011-missing-total-count", "expect": "reader_refuses", "reader_reason": "missing_total_count", "text": "Each large bus holds 50 students and each small bus holds 30 students. The buses carry 260 students in total. How many large buses are there?", "gold": null, "notes": "The weighted total (260 students) is given but the total number of buses is NOT. With only one constraint the system is underdetermined; the reader must REFUSE to assemble it (missing_total_count), never invent a count."}
{"id": "r2-012-missing-weighted-total", "expect": "reader_refuses", "reader_reason": "missing_weighted_total", "text": "A school rents 6 buses. Each large bus holds 50 students and each small bus holds 30 students. How many large buses are there?", "gold": null, "notes": "The total bus count (6) is given but no student total. Only the count constraint exists; the system is underdetermined. The reader must REFUSE (missing_weighted_total)."}
{"id": "r2-013-too-many-categories", "expect": "reader_refuses", "reader_reason": "too_many_categories", "text": "A lot has 10 vehicles: cars, motorcycles, and trucks. Each car has 4 wheels, each motorcycle has 2 wheels, and each truck has 6 wheels. Together the vehicles have 34 wheels. How many cars are there?", "gold": null, "notes": "Three categories — v1 admits exactly two. A two-variable count/weight solver cannot determine three unknowns from two totals; the reader must REFUSE (too_many_categories)."}
