| """Math and formal reasoning: one-shot problems with an exact answer and a single-field action.""" |
|
|
| import itertools |
| import math |
| from fractions import Fraction |
|
|
| from pydantic import Field |
|
|
| from ..core import Action, ProxyTask, Step |
|
|
|
|
| class AnswerAction(Action): |
| answer: str = Field(description="Your final answer, exactly in the requested format. One reply only.") |
|
|
|
|
| def norm(text): |
| return str(text).strip().lower().replace(" ", "").rstrip(".") |
|
|
|
|
| class OneShotMath(ProxyTask): |
| family = "math-oneshot" |
| domain = "mathematics-or-formal-reasoning" |
| Action = AnswerAction |
| max_steps = 1 |
| finish_action = {"answer": ""} |
|
|
| def setup(self): |
| r = self.rng |
| v = self.seed % 5 |
| if v == 0: |
| w, h = r.randint(4, 7), r.randint(4, 7) |
| bx, by = r.randint(1, w - 1), r.randint(1, h - 1) |
| total = math.comb(w + h, w) - math.comb(bx + by, bx) * math.comb(w - bx + h - by, w - bx) |
| self.text = (f"How many shortest grid paths go from (0,0) to ({w},{h}) moving only right or up, " |
| f"without passing through the point ({bx},{by})? Answer with an integer.") |
| self.truth = str(total) |
| elif v == 1: |
| red, blue = r.randint(3, 7), r.randint(3, 7) |
| k = 3 |
| p = Fraction(math.comb(red, 2) * blue, math.comb(red + blue, k)) |
| self.text = (f"A bag has {red} red and {blue} blue marbles. Three are drawn without replacement. What " |
| f"is the probability that exactly two are red? Answer as a reduced fraction a/b.") |
| self.truth = f"{p.numerator}/{p.denominator}" |
| elif v == 2: |
| n, k, cap = r.randint(10, 16), 3, r.randint(5, 7) |
| count = sum(1 for xs in itertools.product(range(cap + 1), repeat=k) if sum(xs) == n) |
| self.text = (f"How many ordered triples of integers (x, y, z) with 0 <= x, y, z <= {cap} satisfy " |
| f"x + y + z = {n}? Answer with an integer.") |
| self.truth = str(count) |
| elif v == 3: |
| a, b = r.choice([3, 7, 13, 17]), r.randint(200, 999) |
| self.text = f"What are the last two digits of {a}^{b}? Answer with two digits, e.g. 07." |
| self.truth = f"{pow(a, b, 100):02d}" |
| else: |
| while True: |
| truth = [r.random() < 0.5 for _ in range(3)] |
| names = ["A", "B", "C"] |
| stmts = [] |
| for i in range(3): |
| j = r.choice([x for x in range(3) if x != i]) |
| kind = r.choice(["is_knave", "same", "count"]) |
| stmts.append((i, j, kind, r.randint(1, 2))) |
|
|
| def holds(world, s): |
| i, j, kind, c = s |
| if kind == "is_knave": |
| return not world[j] |
| if kind == "same": |
| return world[i] == world[j] |
| return sum(world) == c |
|
|
| worlds = [w for w in itertools.product([True, False], repeat=3) |
| if all(holds(w, s) == w[s[0]] for s in stmts)] |
| if len(worlds) == 1: |
| break |
| say = {"is_knave": lambda i, j, c: f"{names[j]} is a knave.", |
| "same": lambda i, j, c: f"{names[j]} and I are the same type.", |
| "count": lambda i, j, c: f"Exactly {c} of us {'is a knight' if c == 1 else 'are knights'}."} |
| lines = " ".join(f"{names[i]} says: \"{say[kind](i, j, c)}\"" for i, j, kind, c in stmts) |
| self.text = (f"On an island, knights always tell the truth and knaves always lie. {lines} Which of A, " |
| f"B, C are knights? Answer with the letters in alphabetical order separated by commas, " |
| f"or 'none'.") |
| knights = [names[i] for i in range(3) if worlds[0][i]] |
| self.truth = ",".join(knights) if knights else "none" |
|
|
| def reset(self): |
| return {"problem": self.text} |
|
|
| def act(self, a): |
| got = norm(a.answer) |
| ok = got == norm(self.truth) |
| if not ok and "/" in self.truth: |
| try: |
| ok = Fraction(got) == Fraction(self.truth) and "/" in got |
| ok = ok and Fraction(got).denominator == int(got.split("/")[1]) |
| except (ValueError, ZeroDivisionError): |
| ok = False |
| return Step({"problem": "", "result": "recorded"}, True, 1.0 if ok else 0.0) |
|
|
| def oracle(self): |
| return [{"answer": self.truth}] |
|
|
