diff --git a/managed_fine_tuning/03-core-rft/02-rft-math-reasoning/.env.template b/managed_fine_tuning/03-core-rft/02-rft-math-reasoning/.env.template index ae53cf4..331a92d 100644 --- a/managed_fine_tuning/03-core-rft/02-rft-math-reasoning/.env.template +++ b/managed_fine_tuning/03-core-rft/02-rft-math-reasoning/.env.template @@ -1,5 +1,4 @@ FOUNDRY_PROJECT_ENDPOINT= -FOUNDRY_BASE_MODEL= FOUNDRY_MATH_BASELINE_DEPLOYMENT= FOUNDRY_MATH_FINE_TUNED_DEPLOYMENT= FOUNDRY_EXISTING_MATH_RFT_JOB_ID= diff --git a/managed_fine_tuning/03-core-rft/02-rft-math-reasoning/README.md b/managed_fine_tuning/03-core-rft/02-rft-math-reasoning/README.md index 72f2b04..d0d3304 100644 --- a/managed_fine_tuning/03-core-rft/02-rft-math-reasoning/README.md +++ b/managed_fine_tuning/03-core-rft/02-rft-math-reasoning/README.md @@ -4,19 +4,19 @@ **Level:** Advanced / quota-dependent **Canonical notebook:** [`notebooks/demo.ipynb`](notebooks/demo.ipynb) -This notebook preserves the OpenR1-Math-220k subsets and the custom boxed-answer -grader while making the grader contract, adversarial tests, bounded monitoring, -and validation reward history explicit. +This notebook uses [OpenR1-Math-220k subsets](data/README.md) +and a custom boxed-answer grader. It includes adversarial grader tests, +bounded monitoring, and validation reward history. ## Safe execution -Copy this module's `.env.template` to a module-local `.env` and configure your own project endpoint and base model. Offline integrity and grader tests require no Azure resources. Executing the upload/training cell submits or resumes a paid job. The existing-job option is consulted when that cell runs. Reuse accepts pending, validating, queued, running, or succeeded jobs only when their model, input file IDs, and reinforcement recipe match. A mismatched, failed, or cancelled job raises an error rather than submitting a replacement. +The training model is `qwen3.6-35b-a3b`, defined by `MODEL` in the notebook. Copy this module's `.env.template` to a module-local `.env` and configure your own project endpoint. Confirm model access, region support, and quota before training. Offline integrity and grader tests require no Azure resources. Executing the upload/training cell submits or resumes a paid job. The existing-job option is consulted when that cell runs. Reuse accepts pending, validating, queued, running, or succeeded jobs only when their model, input file IDs, and reinforcement recipe match. A mismatched, failed, or cancelled job raises an error rather than submitting a replacement. Before interpreting a completed job as equivalent, also verify training and validation file sizes and agreement between service scores and local regrading. [`live_validation.py`](live_validation.py) is a reusable contract-checking library, not an automation runner. It provides these additional checks and parses the reward and loss columns from the downloaded result CSV; the notebook's recipe check does not automatically perform local/service regrade parity. -Job-creation POSTs are submitted once, with SDK retries disabled. Reconcile an ambiguous submission failure in Foundry before retrying. Read and polling operations may retry transient errors. The separately guarded advanced-math baseline and endpoint-evaluation methodology is retained. +Job-creation POSTs are submitted once, with SDK retries disabled. Reconcile an ambiguous submission failure in Foundry before retrying. Read and polling operations may retry transient errors. Baseline and endpoint evaluation are optional and separately enabled. The representative source run completed training and produced validation reward history `[0.05, 0.2]`. -See [`assets/charts/representative-validation-reward.svg`](assets/charts/representative-validation-reward.svg) and [`assets/metrics/representative-run.json`](assets/metrics/representative-run.json). These values are evidence from one run, not guaranteed outcomes; model availability, quota, data sampling, grader behavior, and service updates can change results. +See [`assets/charts/representative-validation-reward.svg`](assets/charts/representative-validation-reward.svg) and [`assets/metrics/representative-run.json`](assets/metrics/representative-run.json). These assets are historical evidence, not a benchmark for the bundled dataset or guaranteed outcomes; model availability, quota, data sampling, grader behavior, and service updates can change results. diff --git a/managed_fine_tuning/03-core-rft/02-rft-math-reasoning/data/README.md b/managed_fine_tuning/03-core-rft/02-rft-math-reasoning/data/README.md index b342250..e56afbb 100644 --- a/managed_fine_tuning/03-core-rft/02-rft-math-reasoning/data/README.md +++ b/managed_fine_tuning/03-core-rft/02-rft-math-reasoning/data/README.md @@ -1,10 +1,20 @@ # Advanced math RFT data -These preserve the exact existing curated OpenR1-Math-220k records: +The notebook uses 100 training and 10 validation records under [preserved](preserved/), with separate, non-overlapping problem prompts. -- `openr1-math-training-rft-100.jsonl`: 100 training prompts and reference answers. -- `openr1-math-validation-rft-10.jsonl`: 10 validation prompts and reference answers. +The source dataset is [OpenR1-Math-220k](https://huggingface.co/datasets/open-r1/OpenR1-Math-220k/tree/e4e141ec9dea9f8326f4d347be56105859b2bd68), revision `e4e141ec9dea9f8326f4d347be56105859b2bd68`, `default/train` (Apache-2.0). The [manifest](hashes.json) records provenance, row counts, canonical-LF byte counts, and SHA-256 integrity values. + +Reference answers include both equation roots (training 8), all four real pairs (60), both side-length branches (90; discard zero when `a=b`), and both sphere radii (92). Training 58 uses real parameters with complex roots allowed, yielding `p = ±2^(1/8)`; training 17 uses integers `k ≥ 1`. Training 71 specifies one valid magic square; the text grader does not recognize equivalent rotations/reflections. Multipart prompts use the final-subproblem reference convention. + +Hash, schema, split, and boxed-answer checks do not prove every answer is mathematically correct or every equivalent expression receives credit. + +## Dataset files + +These are the notebook's upload inputs: + +- [Training data](preserved/openr1-math-training-rft-100.jsonl): 100 training prompts and reference answers. +- [Validation data](preserved/openr1-math-validation-rft-10.jsonl): 10 validation prompts and reference answers. Each record contains user messages plus an `answer` field used by the grader. It intentionally has no assistant message: reinforcement fine-tuning explores responses and receives reward rather than imitating a stored reasoning trace. -See `hashes.json` for source mapping and canonical LF byte counts and SHA-256 integrity values. Checks normalize checkout line endings without rewriting or changing any dataset record. +Integrity checks normalize checkout line endings without modifying dataset records. diff --git a/managed_fine_tuning/03-core-rft/02-rft-math-reasoning/data/hashes.json b/managed_fine_tuning/03-core-rft/02-rft-math-reasoning/data/hashes.json index 1fa09a1..00180fc 100644 --- a/managed_fine_tuning/03-core-rft/02-rft-math-reasoning/data/hashes.json +++ b/managed_fine_tuning/03-core-rft/02-rft-math-reasoning/data/hashes.json @@ -4,17 +4,24 @@ { "path": "data/preserved/openr1-math-training-rft-100.jsonl", "source": "Demos/RFT_Math_Reasoning/training_rft.jsonl", - "bytes": 54807, + "bytes": 55253, "rows": 100, - "sha256": "c6b7b4c86b21c796780b8d2fedcfe58433fbeacef77546522c19b8635f6a4184" + "sha256": "37e5573f18ea12e4be1d423deabfd4036c282fb935c28e61a29e9f4351f60b02" }, { "path": "data/preserved/openr1-math-validation-rft-10.jsonl", "source": "Demos/RFT_Math_Reasoning/validation_rft.jsonl", - "bytes": 4868, + "bytes": 4921, "rows": 10, - "sha256": "fa953157b93d657506a2c3f6d02ff7abeb752c0488b8677ba2167d534e182f28" + "sha256": "beabdabc9ec3bf5509f03cb9a7e93cef6f068b9c0fbc970a105910b3de97b4dd" } ], - "normalization": "CRLF-to-LF" + "normalization": "CRLF-to-LF", + "source_dataset": "open-r1/OpenR1-Math-220k", + "source_revision": "e4e141ec9dea9f8326f4d347be56105859b2bd68", + "license": "Apache-2.0", + "corrected_rows": { + "training": [2, 3, 8, 17, 23, 25, 27, 32, 33, 35, 58, 60, 64, 69, 71, 77, 78, 80, 81, 83, 90, 92, 99], + "validation": [1, 5, 6, 7, 8, 9] + } } diff --git a/managed_fine_tuning/03-core-rft/02-rft-math-reasoning/data/preserved/openr1-math-training-rft-100.jsonl b/managed_fine_tuning/03-core-rft/02-rft-math-reasoning/data/preserved/openr1-math-training-rft-100.jsonl index df428dd..6b70891 100644 --- a/managed_fine_tuning/03-core-rft/02-rft-math-reasoning/data/preserved/openr1-math-training-rft-100.jsonl +++ b/managed_fine_tuning/03-core-rft/02-rft-math-reasoning/data/preserved/openr1-math-training-rft-100.jsonl @@ -1,11 +1,11 @@ {"messages": [{"content": "You are a mathematical reasoning expert. Solve problems with detailed step-by-step thinking and provide final answers in \\boxed{} format. Show all intermediate calculations and explain your reasoning clearly.\n\nCall a scalene triangle K [i]disguisable[/i] if there exists a triangle K′ similar to K with two shorter sides precisely as long as the two longer sides of K, respectively. Call a disguisable triangle [i]integral[/i] if the lengths of all its sides are integers.\r\n(a) Find the side lengths of the integral disguisable triangle with the smallest possible perimeter.\r\n(b) Let K be an arbitrary integral disguisable triangle for which no smaller integral\r\ndisguisable triangle similar to it exists. Prove that at least two side lengths of K are\r\nperfect squares.", "role": "user"}], "answer": "9"} -{"messages": [{"content": "You are a mathematical reasoning expert. Solve problems with detailed step-by-step thinking and provide final answers in \\boxed{} format. Show all intermediate calculations and explain your reasoning clearly.\n\n11. A math competition problem: the probabilities of A, B, and C solving this problem independently are $\\frac{1}{a}$, $\\frac{1}{b}$, and $\\frac{1}{c}$, respectively, where $a$, $b$, and $c$ are positive integers less than 10. Now A, B, and C are solving this problem independently. If the probability that exactly one of them solves the problem is $\\frac{7}{15}$, then the probability that none of them solves the problem is", "role": "user"}], "answer": "\\dfrac{4"} -{"messages": [{"content": "You are a mathematical reasoning expert. Solve problems with detailed step-by-step thinking and provide final answers in \\boxed{} format. Show all intermediate calculations and explain your reasoning clearly.\n\n8 There are six cards, each with a number $1, 2, 3, 4, 5, 6$ written on it. Each time, one card is drawn, the number on it is noted, and then it is put back. This is done 4 times. The probability that the difference between the maximum and minimum numbers drawn is equal to 5 is $\\qquad$.", "role": "user"}], "answer": "\\dfrac{151"} +{"messages": [{"content": "You are a mathematical reasoning expert. Solve problems with detailed step-by-step thinking and provide final answers in \\boxed{} format. Show all intermediate calculations and explain your reasoning clearly.\n\n11. A math competition problem: the probabilities of A, B, and C solving this problem independently are $\\frac{1}{a}$, $\\frac{1}{b}$, and $\\frac{1}{c}$, respectively, where $a$, $b$, and $c$ are positive integers less than 10. Now A, B, and C are solving this problem independently. If the probability that exactly one of them solves the problem is $\\frac{7}{15}$, then the probability that none of them solves the problem is", "role": "user"}], "answer": "\\dfrac{4}{15}"} +{"messages": [{"content": "You are a mathematical reasoning expert. Solve problems with detailed step-by-step thinking and provide final answers in \\boxed{} format. Show all intermediate calculations and explain your reasoning clearly.\n\n8 There are six cards, each with a number $1, 2, 3, 4, 5, 6$ written on it. Each time, one card is drawn, the number on it is noted, and then it is put back. This is done 4 times. The probability that the difference between the maximum and minimum numbers drawn is equal to 5 is $\\qquad$.", "role": "user"}], "answer": "\\dfrac{151}{648}"} {"messages": [{"content": "You are a mathematical reasoning expert. Solve problems with detailed step-by-step thinking and provide final answers in \\boxed{} format. Show all intermediate calculations and explain your reasoning clearly.\n\n5th Swedish 1965 Problem 2 Find all positive integers m, n such that m 3 - n 3 = 999.", "role": "user"}], "answer": "(12, 9)"} {"messages": [{"content": "You are a mathematical reasoning expert. Solve problems with detailed step-by-step thinking and provide final answers in \\boxed{} format. Show all intermediate calculations and explain your reasoning clearly.\n\n\n5. Given three positive real numbers $o, \\rho, v$, construct a triangle $A B C$ with perimeter equal to $o$, the radius of its $A$-excircle equal to $\\rho$, and the length of its $A$ altitude equal to $v$. Determine the number of solutions (non-congruent triangles) in terms of the given lengths.\n\n(Patrik Bak)\n", "role": "user"}], "answer": "0"} {"messages": [{"content": "You are a mathematical reasoning expert. Solve problems with detailed step-by-step thinking and provide final answers in \\boxed{} format. Show all intermediate calculations and explain your reasoning clearly.\n\n3. In the afternoon, 5 classes need to be scheduled: Physics, Chemistry, Biology, and two self-study periods. If the first class cannot be Biology and the last class cannot be Physics, then the number of different scheduling methods is ( ) kinds.\n(A) 36\n(B) 39\n(C) 60\n(D) 78", "role": "user"}], "answer": "B"} {"messages": [{"content": "You are a mathematical reasoning expert. Solve problems with detailed step-by-step thinking and provide final answers in \\boxed{} format. Show all intermediate calculations and explain your reasoning clearly.\n\n9. A, B, C, and D are comparing their heights. Among them, the sum of the heights of two people is the same as the sum of the heights of the other two. The average height of A and B is 4 cm more than the average height of A and C. D is 10 cm taller than A, and the sum of the heights of B and C is 288 cm. A's height is $\\qquad$ cm.", "role": "user"}], "answer": "139"} -{"messages": [{"content": "You are a mathematical reasoning expert. Solve problems with detailed step-by-step thinking and provide final answers in \\boxed{} format. Show all intermediate calculations and explain your reasoning clearly.\n\n1. Solve the equation $x^{\\log _{5}(0.008 x)}=\\frac{125}{x^{5}}$.", "role": "user"}], "answer": "\\dfrac{1"} +{"messages": [{"content": "You are a mathematical reasoning expert. Solve problems with detailed step-by-step thinking and provide final answers in \\boxed{} format. Show all intermediate calculations and explain your reasoning clearly.\n\n1. Solve the equation $x^{\\log _{5}(0.008 x)}=\\frac{125}{x^{5}}$.", "role": "user"}], "answer": "\\dfrac{1}{125}, 5"} {"messages": [{"content": "You are a mathematical reasoning expert. Solve problems with detailed step-by-step thinking and provide final answers in \\boxed{} format. Show all intermediate calculations and explain your reasoning clearly.\n\n4.9 If $b0\n$$", "role": "user"}], "answer": "1, 2, 3, 4, 5, 6, 7"} {"messages": [{"content": "You are a mathematical reasoning expert. Solve problems with detailed step-by-step thinking and provide final answers in \\boxed{} format. Show all intermediate calculations and explain your reasoning clearly.\n\nGiven $\\triangle A B C$ has a perimeter of 20, area of $01 \\sqrt{3}$, and $\\angle A=60^{\\circ}$. Find $\\sin A: \\sin B: \\sin C$.", "role": "user"}], "answer": "7:8:5"} {"messages": [{"content": "You are a mathematical reasoning expert. Solve problems with detailed step-by-step thinking and provide final answers in \\boxed{} format. Show all intermediate calculations and explain your reasoning clearly.\n\nB2 Points $A(-4,-2), B(2,-2)$ and $C(2,6)$ are the vertices of triangle $A B C$.\n\nA Draw triangle $A B C$ in the coordinate system.\n\nB Calculate the perimeter of triangle $A B C$.\n\nC Calculate the area of triangle $A B C$.\n\nD Circumscribe a circle around triangle $A B C$.", "role": "user"}], "answer": "(x + 1)^2 + (y - 2)^2 = 25"} {"messages": [{"content": "You are a mathematical reasoning expert. Solve problems with detailed step-by-step thinking and provide final answers in \\boxed{} format. Show all intermediate calculations and explain your reasoning clearly.\n\n【Question 1】Calculate: $2 \\times(999999+5 \\times 379 \\times 4789)=$", "role": "user"}], "answer": "20150308"} -{"messages": [{"content": "You are a mathematical reasoning expert. Solve problems with detailed step-by-step thinking and provide final answers in \\boxed{} format. Show all intermediate calculations and explain your reasoning clearly.\n\n2. Simplify the expression\n\n$$\nA=\\left(1+\\frac{1+i}{2}\\right)\\left(1+\\left(\\frac{1+i}{2}\\right)^{2}\\right)\\left(1+\\left(\\frac{1+i}{2}\\right)^{4}\\right)\\left(1+\\left(\\frac{1+i}{2}\\right)^{8}\\right)\n$$\n\n( $i$ is the imaginary unit)", "role": "user"}], "answer": "\\dfrac{255(1 + i)"} -{"messages": [{"content": "You are a mathematical reasoning expert. Solve problems with detailed step-by-step thinking and provide final answers in \\boxed{} format. Show all intermediate calculations and explain your reasoning clearly.\n\nExample 3 (1) Find the domain of the function $y=\\sqrt{\\frac{1}{2}-\\log _{2}(3-x)}$;\n(2) Given that the domain of $f(x)$ is $[0,1]$, find the domain of the function $y=f\\left(\\log _{\\frac{1}{2}}(3-x)\\right)$.", "role": "user"}], "answer": "[2, \\frac{5"} +{"messages": [{"content": "You are a mathematical reasoning expert. Solve problems with detailed step-by-step thinking and provide final answers in \\boxed{} format. Show all intermediate calculations and explain your reasoning clearly.\n\n2. Simplify the expression\n\n$$\nA=\\left(1+\\frac{1+i}{2}\\right)\\left(1+\\left(\\frac{1+i}{2}\\right)^{2}\\right)\\left(1+\\left(\\frac{1+i}{2}\\right)^{4}\\right)\\left(1+\\left(\\frac{1+i}{2}\\right)^{8}\\right)\n$$\n\n( $i$ is the imaginary unit)", "role": "user"}], "answer": "\\dfrac{255(1 + i)}{256}"} +{"messages": [{"content": "You are a mathematical reasoning expert. Solve problems with detailed step-by-step thinking and provide final answers in \\boxed{} format. Show all intermediate calculations and explain your reasoning clearly.\n\nExample 3 (1) Find the domain of the function $y=\\sqrt{\\frac{1}{2}-\\log _{2}(3-x)}$;\n(2) Given that the domain of $f(x)$ is $[0,1]$, find the domain of the function $y=f\\left(\\log _{\\frac{1}{2}}(3-x)\\right)$.", "role": "user"}], "answer": "[2, \\frac{5}{2}]"} {"messages": [{"content": "You are a mathematical reasoning expert. Solve problems with detailed step-by-step thinking and provide final answers in \\boxed{} format. Show all intermediate calculations and explain your reasoning clearly.\n\n8. As shown in Figure $3, A C=$ $B C, A C \\perp B C$ at point $C, A B=A D=B D$, $C D=C E=D E$. If $A B=\\sqrt{2}$, then $B E=$", "role": "user"}], "answer": "1"} -{"messages": [{"content": "You are a mathematical reasoning expert. Solve problems with detailed step-by-step thinking and provide final answers in \\boxed{} format. Show all intermediate calculations and explain your reasoning clearly.\n\nAt each vertex of a tetrahedron, there sits an ant. At a given moment, each of them starts to move along a randomly chosen edge and crosses over to the adjacent vertex. What is the probability that two ants meet either on the way or at the end of their journey?", "role": "user"}], "answer": "\\dfrac{25"} +{"messages": [{"content": "You are a mathematical reasoning expert. Solve problems with detailed step-by-step thinking and provide final answers in \\boxed{} format. Show all intermediate calculations and explain your reasoning clearly.\n\nAt each vertex of a tetrahedron, there sits an ant. At a given moment, each of them starts to move along a randomly chosen edge and crosses over to the adjacent vertex. What is the probability that two ants meet either on the way or at the end of their journey?", "role": "user"}], "answer": "\\dfrac{25}{27}"} {"messages": [{"content": "You are a mathematical reasoning expert. Solve problems with detailed step-by-step thinking and provide final answers in \\boxed{} format. Show all intermediate calculations and explain your reasoning clearly.\n\n7. A turtle and a rabbit are in a 1000-meter race. The rabbit took a nap 200 meters from the finish line. When it woke up, it found that the turtle was 10 meters from the finish line, so it immediately chased after and eventually both reached the finish line at the same time. If the turtle crawled at a constant speed throughout the race, and the rabbit's speed before and after the nap was the same, then, during the rabbit's nap, the turtle crawled $\\qquad$ meters.", "role": "user"}], "answer": "950"} {"messages": [{"content": "You are a mathematical reasoning expert. Solve problems with detailed step-by-step thinking and provide final answers in \\boxed{} format. Show all intermediate calculations and explain your reasoning clearly.\n\nWe are given 5771 weights weighing 1,2,3,...,5770,5771. We partition the weights into $n$ sets of equal weight. What is the maximal $n$ for which this is possible?", "role": "user"}], "answer": "2886"} {"messages": [{"content": "You are a mathematical reasoning expert. Solve problems with detailed step-by-step thinking and provide final answers in \\boxed{} format. Show all intermediate calculations and explain your reasoning clearly.\n\n7. As shown in the figure, the beads on the bracelet are numbered from 1 to 22 in a counterclockwise direction starting from the pendant bead. Xiao Ming is playing a bead counting game, with the rule being: starting from bead 1, count natural numbers in a clockwise direction, but skip any number that contains the digit 7 or is a multiple of 7, and directly count the next number. For example: after counting to 6, the next number is 8; after counting to 13, the next number is 15, and so on. So, when counting to 100, which bead number $\\qquad$ will it land on?", "role": "user"}], "answer": "19"} @@ -55,46 +55,46 @@ {"messages": [{"content": "You are a mathematical reasoning expert. Solve problems with detailed step-by-step thinking and provide final answers in \\boxed{} format. Show all intermediate calculations and explain your reasoning clearly.\n\n7. The program flowchart is shown in Figure 3. Given that the real number $x \\in [1, 9]$. Then the probability that the output $x$ is not less than 55 is ( ).\n(A) $\\frac{1}{3}$\n(B) $\\frac{2}{3}$\n(C) $\\frac{3}{8}$\n(D) $\\frac{5}{8}$", "role": "user"}], "answer": "D"} {"messages": [{"content": "You are a mathematical reasoning expert. Solve problems with detailed step-by-step thinking and provide final answers in \\boxed{} format. Show all intermediate calculations and explain your reasoning clearly.\n\n18. There are 30 students standing in a row, and from left to right, they are wearing hats in the order of \"red, yellow, blue, red, yellow, blue......\". The PE teacher asks the students to count off from left to right as \"1, 2, 1, 2, 1, 2.....\", and those who count off 2 step forward. Among the remaining students, those wearing red hats step back. At this point, the students are divided into 3 rows, and in the middle row, there are $\\qquad$ people wearing blue hats.", "role": "user"}], "answer": "5"} {"messages": [{"content": "You are a mathematical reasoning expert. Solve problems with detailed step-by-step thinking and provide final answers in \\boxed{} format. Show all intermediate calculations and explain your reasoning clearly.\n\n1. 19 If $\\frac{1}{x}+\\frac{1}{y}+\\frac{1}{z}=\\frac{1}{x+y+z}=1$. Then,\n(A) at least one of $x, y, z$ is equal to 1.\n(B) $x, y, z$ are all equal to 1.\n(C) $x, y, z$ are all not equal to 1.\n(D) none of the above conclusions is correct.\n(8th \"Jinyun Cup\" Junior High School Mathematics Invitational, 1991)", "role": "user"}], "answer": "A"} -{"messages": [{"content": "You are a mathematical reasoning expert. Solve problems with detailed step-by-step thinking and provide final answers in \\boxed{} format. Show all intermediate calculations and explain your reasoning clearly.\n\n3. Let $x_{1}$ and $x_{2}$ be the roots of the equation\n\n$$\np^{2} x^{2}+p^{3} x+1=0\n$$\n\nDetermine $p$ such that the expression $x_{1}^{4}+x_{2}^{4}$ has the smallest value.", "role": "user"}], "answer": "\\pm \\sqrt{2"} +{"messages": [{"content": "You are a mathematical reasoning expert. Solve problems with detailed step-by-step thinking and provide final answers in \\boxed{} format. Show all intermediate calculations and explain your reasoning clearly.\n\n3. Let $x_{1}$ and $x_{2}$ be the roots of the equation\n\n$$\np^{2} x^{2}+p^{3} x+1=0\n$$\n\nDetermine $p$ such that the expression $x_{1}^{4}+x_{2}^{4}$ has the smallest value.", "role": "user"}], "answer": "\\pm \\sqrt[8]{2}"} {"messages": [{"content": "You are a mathematical reasoning expert. Solve problems with detailed step-by-step thinking and provide final answers in \\boxed{} format. Show all intermediate calculations and explain your reasoning clearly.\n\n663. The grasshopper jumped from the point with coordinate 8 to the point with coordinate 17.5. Then it made another jump of the same length (in the same direction). At the point with what coordinate did it end up?", "role": "user"}], "answer": "27"} -{"messages": [{"content": "You are a mathematical reasoning expert. Solve problems with detailed step-by-step thinking and provide final answers in \\boxed{} format. Show all intermediate calculations and explain your reasoning clearly.\n\n## Task 1 - 251211\n\nDetermine all pairs $(x ; y)$ of real numbers that satisfy the following system of equations (1), (2).\n\n$$\n\\begin{aligned}\n& x^{2}+y=1 \\\\\n& x+y^{2}=1\n\\end{aligned}\n$$", "role": "user"}], "answer": "\\left( \\frac{-1 - \\sqrt{5"} +{"messages": [{"content": "You are a mathematical reasoning expert. Solve problems with detailed step-by-step thinking and provide final answers in \\boxed{} format. Show all intermediate calculations and explain your reasoning clearly.\n\n## Task 1 - 251211\n\nDetermine all pairs $(x ; y)$ of real numbers that satisfy the following system of equations (1), (2).\n\n$$\n\\begin{aligned}\n& x^{2}+y=1 \\\\\n& x+y^{2}=1\n\\end{aligned}\n$$", "role": "user"}], "answer": "\\left( \\frac{-1 - \\sqrt{5}}{2}, \\frac{-1 - \\sqrt{5}}{2} \\right), \\left( \\frac{-1 + \\sqrt{5}}{2}, \\frac{-1 + \\sqrt{5}}{2} \\right), (0, 1), (1, 0)"} {"messages": [{"content": "You are a mathematical reasoning expert. Solve problems with detailed step-by-step thinking and provide final answers in \\boxed{} format. Show all intermediate calculations and explain your reasoning clearly.\n\nThe radius of the Earth measures approximately $6378 \\mathrm{~km}$ at the Equator. Suppose a wire is exactly adjusted over the Equator.\n\nThen, suppose the length of the wire is increased by $1 \\mathrm{~m}$, so that the wire and the Equator form concentric circles around the Earth. Would a man standing, an ant, or an elephant be able to pass under this wire?", "role": "user"}], "answer": "An ant"} {"messages": [{"content": "You are a mathematical reasoning expert. Solve problems with detailed step-by-step thinking and provide final answers in \\boxed{} format. Show all intermediate calculations and explain your reasoning clearly.\n\n10) In a bag there are some marbles. Maria says: \"In the bag there are three marbles in total and they are black.\" Luca says: \"In the bag there are two black marbles and two red marbles.\" Giorgio says: \"In the bag there are only black marbles.\" Knowing that only one of the three is lying, how many marbles are in the bag?\n\n(A) one, (B) two, (C) three, (D) four, (E) it is not possible to determine the number based on the information given in the problem.", "role": "user"}], "answer": "C"} {"messages": [{"content": "You are a mathematical reasoning expert. Solve problems with detailed step-by-step thinking and provide final answers in \\boxed{} format. Show all intermediate calculations and explain your reasoning clearly.\n\n9. Four cousins Alan, Bob, Carl and Dan are $3,8,12$ and 14 years old, although not necessarily in that order. Alan is younger than Carl. The sum of the ages of Alan and Dan is divisible by 5. The sum of the ages of Carl and Dan is divisible by 5. What is the sum of the ages of Alan and Bob?\nA 26\nB 22\nC 17\nD 15\nE 11", "role": "user"}], "answer": "C"} -{"messages": [{"content": "You are a mathematical reasoning expert. Solve problems with detailed step-by-step thinking and provide final answers in \\boxed{} format. Show all intermediate calculations and explain your reasoning clearly.\n\n4. In $\\triangle A B C$, $\\angle A=30^{\\circ}, \\angle B=105^{\\circ}$, a line $D E$ is drawn through a point $D$ on side $A C$, intersecting side $A B$ or side $B C$ at point $E$, such that $\\angle C D E=60^{\\circ}$, and $D E$ bisects the area of $\\triangle A B C$. Then $\\left(\\frac{C D}{A C}\\right)^{2}=$ $\\qquad$ -", "role": "user"}], "answer": "\\dfrac{\\sqrt{3"} +{"messages": [{"content": "You are a mathematical reasoning expert. Solve problems with detailed step-by-step thinking and provide final answers in \\boxed{} format. Show all intermediate calculations and explain your reasoning clearly.\n\n4. In $\\triangle A B C$, $\\angle A=30^{\\circ}, \\angle B=105^{\\circ}$, a line $D E$ is drawn through a point $D$ on side $A C$, intersecting side $A B$ or side $B C$ at point $E$, such that $\\angle C D E=60^{\\circ}$, and $D E$ bisects the area of $\\triangle A B C$. Then $\\left(\\frac{C D}{A C}\\right)^{2}=$ $\\qquad$ -", "role": "user"}], "answer": "\\dfrac{\\sqrt{3}}{6}"} {"messages": [{"content": "You are a mathematical reasoning expert. Solve problems with detailed step-by-step thinking and provide final answers in \\boxed{} format. Show all intermediate calculations and explain your reasoning clearly.\n\n1. (1) Use the Factor Theorem to prove that $a-b, b-c, c-a$ are all factors of $a^{2}(b-c)+b^{2}(c-a)+c^{2}(a-b)$.\n(2) Using the conclusion from (1), factorize $a^{2}(b-c)+b^{2}(c-a)+c^{2}(a-b)$.\n(3) Factorize: $(x+y+z)^{3}-x^{3}-y^{3}-z^{3}$.", "role": "user"}], "answer": "3(x + y)(y + z)(z + x)"} {"messages": [{"content": "You are a mathematical reasoning expert. Solve problems with detailed step-by-step thinking and provide final answers in \\boxed{} format. Show all intermediate calculations and explain your reasoning clearly.\n\n## Problem Statement\n\nFind the point of intersection of the line and the plane.\n\n$\\frac{x+1}{3}=\\frac{y-3}{-4}=\\frac{z+1}{5}$\n\n$x+2 y-5 z+20=0$", "role": "user"}], "answer": "(2, -1, 4)"} {"messages": [{"content": "You are a mathematical reasoning expert. Solve problems with detailed step-by-step thinking and provide final answers in \\boxed{} format. Show all intermediate calculations and explain your reasoning clearly.\n\nThe repeating decimals $0.abab\\overline{ab}$ and $0.abcabc\\overline{abc}$ satisfy\n\\[0.abab\\overline{ab}+0.abcabc\\overline{abc}=\\frac{33}{37},\\]\nwhere $a,b$, and $c$ are (not necessarily distinct) digits. Find the three-digit number $abc$.", "role": "user"}], "answer": "447"} {"messages": [{"content": "You are a mathematical reasoning expert. Solve problems with detailed step-by-step thinking and provide final answers in \\boxed{} format. Show all intermediate calculations and explain your reasoning clearly.\n\n2 Find all integer $x$ such that $\\left|4 x^{2}-12 x-27\\right|$ is a prime number.\n\nFind all integer $x$ such that $\\left|4 x^{2}-12 x-27\\right|$ is a prime number.", "role": "user"}], "answer": "5"} -{"messages": [{"content": "You are a mathematical reasoning expert. Solve problems with detailed step-by-step thinking and provide final answers in \\boxed{} format. Show all intermediate calculations and explain your reasoning clearly.\n\n10,11\n\nThe angle in the development of the lateral surface of a cone is $120^{\\circ}$. Find the angle at the vertex of the axial section of the cone.", "role": "user"}], "answer": "\\arccos \\left( \\dfrac{7"} +{"messages": [{"content": "You are a mathematical reasoning expert. Solve problems with detailed step-by-step thinking and provide final answers in \\boxed{} format. Show all intermediate calculations and explain your reasoning clearly.\n\n10,11\n\nThe angle in the development of the lateral surface of a cone is $120^{\\circ}$. Find the angle at the vertex of the axial section of the cone.", "role": "user"}], "answer": "\\arccos \\left( \\dfrac{7}{9} \\right)"} {"messages": [{"content": "You are a mathematical reasoning expert. Solve problems with detailed step-by-step thinking and provide final answers in \\boxed{} format. Show all intermediate calculations and explain your reasoning clearly.\n\nExample 6 Find the number of $n$-digit numbers formed by $1,2,3$, where each of 1, 2, and 3 must appear at least once in the $n$-digit number.", "role": "user"}], "answer": "3^n - 3 \\cdot 2^n + 3"} -{"messages": [{"content": "You are a mathematical reasoning expert. Solve problems with detailed step-by-step thinking and provide final answers in \\boxed{} format. Show all intermediate calculations and explain your reasoning clearly.\n\n15 . In a $3 \\times 3$ grid, fill in the numbers $1,2,3,4,5,6,7,8,9$ so that the sum of the numbers in any three squares in a row, column, or diagonal is equal.", "role": "user"}], "answer": "\\begin{array"} +{"messages": [{"content": "You are a mathematical reasoning expert. Solve problems with detailed step-by-step thinking and provide final answers in \\boxed{} format. Show all intermediate calculations and explain your reasoning clearly.\n\n15 . In a $3 \\times 3$ grid, fill in the numbers $1,2,3,4,5,6,7,8,9$ so that the sum of the numbers in any three squares in a row, column, or diagonal is equal.", "role": "user"}], "answer": "\\begin{array}{|c|c|c|}\n\\hline\n8 & 1 & 6 \\\\\n\\hline\n3 & 5 & 7 \\\\\n\\hline\n4 & 9 & 2 \\\\\n\\hline\n\\end{array}"} {"messages": [{"content": "You are a mathematical reasoning expert. Solve problems with detailed step-by-step thinking and provide final answers in \\boxed{} format. Show all intermediate calculations and explain your reasoning clearly.\n\n\n4. How many 6-tuples $\\left(a_{1}, a_{2}, a_{3}, a_{4}, a_{5}, a_{6}\\right)$ are there such that each of $a_{1}, a_{2}, a_{3}, a_{4}, a_{5}, a_{6}$ is from the set $\\{1,2,3,4\\}$ and the six expressions\n\n$$\na_{j}^{2}-a_{j} a_{j+1}+a_{j+1}^{2}\n$$\n\nfor $j=1,2,3,4,5,6$ (where $a_{7}$ is to be taken as $a_{1}$ ) are all equal to one another?\n", "role": "user"}], "answer": "40"} {"messages": [{"content": "You are a mathematical reasoning expert. Solve problems with detailed step-by-step thinking and provide final answers in \\boxed{} format. Show all intermediate calculations and explain your reasoning clearly.\n\n3. In a right trapezoid $A B C D$, $A D / / B C$, $B C \\perp C D$, $E$ is the midpoint of side $A B$, $B C=C D=C E$. Then the degree measure of $\\angle B$ is ( ).\n(A) $52.5^{\\circ}$\n(B) $62.5^{\\circ}$\n(C) $60^{\\circ}$\n(D) $75^{\\circ}$", "role": "user"}], "answer": "D"} {"messages": [{"content": "You are a mathematical reasoning expert. Solve problems with detailed step-by-step thinking and provide final answers in \\boxed{} format. Show all intermediate calculations and explain your reasoning clearly.\n\nProblem 4. The sum of eight consecutive natural numbers is equal to 92. What are these numbers?", "role": "user"}], "answer": "15"} {"messages": [{"content": "You are a mathematical reasoning expert. Solve problems with detailed step-by-step thinking and provide final answers in \\boxed{} format. Show all intermediate calculations and explain your reasoning clearly.\n\nIn a tournament, any two players play against each other. Each player gets one point for a win, 1/2 for a draw, and 0 points for a loss. Let $S$ be the set of the 10 lowest scores. We know that each player obtained half of their score playing against players from $S$.\n\na) What is the sum of the scores of the players in $S$?\n\nb) Determine how many participants are in the tournament.\n\nNote: Each player plays only once against each opponent.", "role": "user"}], "answer": "25"} {"messages": [{"content": "You are a mathematical reasoning expert. Solve problems with detailed step-by-step thinking and provide final answers in \\boxed{} format. Show all intermediate calculations and explain your reasoning clearly.\n\n9. (16 points) For a given positive integer $M$, define $f_{1}(M)$ as the square of the sum of the digits of $M$. When $n>1$ and $n \\in \\mathbf{N}$, $f_{n}\\left(f_{n-1}(M)\\right)$ represents the $r_{n}$-th power of the sum of the digits of $f_{n-1}(M)$, where, when $n$ is odd, $r_{n}=2$; when $n$ is even, $r_{n}=3$. Find the value of $f_{2012}\\left(f_{2011}\\left(3^{2010}\\right)\\right)$.", "role": "user"}], "answer": "should be \\( f_{2012}(f_{2011}(3^{2010})) \\)."} -{"messages": [{"content": "You are a mathematical reasoning expert. Solve problems with detailed step-by-step thinking and provide final answers in \\boxed{} format. Show all intermediate calculations and explain your reasoning clearly.\n\nExample 4 Given $A(-2,2)$, and $B$ is a moving point on the ellipse $\\frac{x^{2}}{25}+\\frac{y^{2}}{16}=1$, $F$ is the left focus. When $\\mid A B \\mid +\\frac{5}{3}|B F|$ takes the minimum value, find the coordinates of point $B$.\n(1999, National High School Mathematics Competition)", "role": "user"}], "answer": "\\left( -\\dfrac{5\\sqrt{3"} -{"messages": [{"content": "You are a mathematical reasoning expert. Solve problems with detailed step-by-step thinking and provide final answers in \\boxed{} format. Show all intermediate calculations and explain your reasoning clearly.\n\n3. Given the sequence $\\left\\{a_{n}\\right\\}$ satisfies $a_{1}=\\frac{7}{6}$, and for any positive integer $n$, the quadratic equation $a_{n} x^{2}-$ $a_{n+1} x+1=0$ has two roots $\\alpha_{n}, \\beta_{n}$ that satisfy $6 \\alpha_{n}-2 \\alpha_{n} \\beta_{n}+6 \\beta_{n}=3$. Then the general term formula for $\\left\\{a_{n}\\right\\}$ is $a_{n}=$ $\\qquad$", "role": "user"}], "answer": "\\dfrac{2"} +{"messages": [{"content": "You are a mathematical reasoning expert. Solve problems with detailed step-by-step thinking and provide final answers in \\boxed{} format. Show all intermediate calculations and explain your reasoning clearly.\n\nExample 4 Given $A(-2,2)$, and $B$ is a moving point on the ellipse $\\frac{x^{2}}{25}+\\frac{y^{2}}{16}=1$, $F$ is the left focus. When $\\mid A B \\mid +\\frac{5}{3}|B F|$ takes the minimum value, find the coordinates of point $B$.\n(1999, National High School Mathematics Competition)", "role": "user"}], "answer": "\\left( -\\dfrac{5\\sqrt{3}}{2}, 2 \\right)"} +{"messages": [{"content": "You are a mathematical reasoning expert. Solve problems with detailed step-by-step thinking and provide final answers in \\boxed{} format. Show all intermediate calculations and explain your reasoning clearly.\n\n3. Given the sequence $\\left\\{a_{n}\\right\\}$ satisfies $a_{1}=\\frac{7}{6}$, and for any positive integer $n$, the quadratic equation $a_{n} x^{2}-$ $a_{n+1} x+1=0$ has two roots $\\alpha_{n}, \\beta_{n}$ that satisfy $6 \\alpha_{n}-2 \\alpha_{n} \\beta_{n}+6 \\beta_{n}=3$. Then the general term formula for $\\left\\{a_{n}\\right\\}$ is $a_{n}=$ $\\qquad$", "role": "user"}], "answer": "\\dfrac{2^{n+1} + 3}{3 \\cdot 2^n}"} {"messages": [{"content": "You are a mathematical reasoning expert. Solve problems with detailed step-by-step thinking and provide final answers in \\boxed{} format. Show all intermediate calculations and explain your reasoning clearly.\n\n4.1. Mom baked four raisin buns for breakfast for her two sons. $V$ In the first three buns, she put 7, 7, 23 raisins, and some more in the fourth. It turned out that the boys ate an equal number of raisins and did not divide any bun into parts. How many raisins could Mom have put in the fourth bun? List all the options.", "role": "user"}], "answer": "37"} -{"messages": [{"content": "You are a mathematical reasoning expert. Solve problems with detailed step-by-step thinking and provide final answers in \\boxed{} format. Show all intermediate calculations and explain your reasoning clearly.\n\nFind the number of ways in which three numbers can be selected from the set $\\{1,2,\\cdots ,4n\\}$, such that the sum of the three selected numbers is divisible by $4$.", "role": "user"}], "answer": "\\dfrac{n(4n -1)(2n -1)"} -{"messages": [{"content": "You are a mathematical reasoning expert. Solve problems with detailed step-by-step thinking and provide final answers in \\boxed{} format. Show all intermediate calculations and explain your reasoning clearly.\n\nAs shown in Figure $3, \\odot O$ is inside the rectangle $ABCD$. Tangents are drawn from vertices $A, B, C, D$ to $\\odot O$, with points of tangency being $A_{1}, B_{1}, C_{1}, D_{1}$, respectively. If $AA_{1}=3, BB_{1}=4$, $CC_{1}=5$, find the length of $DD_{1}$.", "role": "user"}], "answer": "3\\sqrt{2"} +{"messages": [{"content": "You are a mathematical reasoning expert. Solve problems with detailed step-by-step thinking and provide final answers in \\boxed{} format. Show all intermediate calculations and explain your reasoning clearly.\n\nFind the number of ways in which three numbers can be selected from the set $\\{1,2,\\cdots ,4n\\}$, such that the sum of the three selected numbers is divisible by $4$.", "role": "user"}], "answer": "\\dfrac{n(4n -1)(2n -1)}{3}"} +{"messages": [{"content": "You are a mathematical reasoning expert. Solve problems with detailed step-by-step thinking and provide final answers in \\boxed{} format. Show all intermediate calculations and explain your reasoning clearly.\n\nAs shown in Figure $3, \\odot O$ is inside the rectangle $ABCD$. Tangents are drawn from vertices $A, B, C, D$ to $\\odot O$, with points of tangency being $A_{1}, B_{1}, C_{1}, D_{1}$, respectively. If $AA_{1}=3, BB_{1}=4$, $CC_{1}=5$, find the length of $DD_{1}$.", "role": "user"}], "answer": "3\\sqrt{2}"} {"messages": [{"content": "You are a mathematical reasoning expert. Solve problems with detailed step-by-step thinking and provide final answers in \\boxed{} format. Show all intermediate calculations and explain your reasoning clearly.\n\nCondition of the problem\n\nCalculate the limit of the function:\n\n$\\lim _{x \\rightarrow 1}\\left(\\frac{x^{3}-1}{x-1}\\right)^{\\frac{1}{x^{2}}}$", "role": "user"}], "answer": "3"} -{"messages": [{"content": "You are a mathematical reasoning expert. Solve problems with detailed step-by-step thinking and provide final answers in \\boxed{} format. Show all intermediate calculations and explain your reasoning clearly.\n\n$$\n\\begin{array}{l}\n\\text { Three. (20 points) (1) The quadratic function } \\\\\nf(x)=a x^{2}+b x+c(a, b, c \\in \\mathbf{R}, a \\neq 0)\n\\end{array}\n$$\n\nsatisfies\n(i) For $x \\in \\mathbf{R}$, there is $4 x \\leqslant f(x) \\leqslant \\frac{1}{2}(x+2)^{2}$\n\nalways holds;\n(ii) $f(-4+2 \\sqrt{3})=0$.\nFind $f(x)$.\n(2) Let $f_{1}(x)=\\frac{3}{2+x}, f_{n+1}(x)=f_{1}\\left(f_{n}(x)\\right)$, find $f_{2009}(0)$.", "role": "user"}], "answer": "\\dfrac{3^{2010"} +{"messages": [{"content": "You are a mathematical reasoning expert. Solve problems with detailed step-by-step thinking and provide final answers in \\boxed{} format. Show all intermediate calculations and explain your reasoning clearly.\n\n$$\n\\begin{array}{l}\n\\text { Three. (20 points) (1) The quadratic function } \\\\\nf(x)=a x^{2}+b x+c(a, b, c \\in \\mathbf{R}, a \\neq 0)\n\\end{array}\n$$\n\nsatisfies\n(i) For $x \\in \\mathbf{R}$, there is $4 x \\leqslant f(x) \\leqslant \\frac{1}{2}(x+2)^{2}$\n\nalways holds;\n(ii) $f(-4+2 \\sqrt{3})=0$.\nFind $f(x)$.\n(2) Let $f_{1}(x)=\\frac{3}{2+x}, f_{n+1}(x)=f_{1}\\left(f_{n}(x)\\right)$, find $f_{2009}(0)$.", "role": "user"}], "answer": "\\dfrac{3^{2010} + 3}{3^{2010} - 1}"} {"messages": [{"content": "You are a mathematical reasoning expert. Solve problems with detailed step-by-step thinking and provide final answers in \\boxed{} format. Show all intermediate calculations and explain your reasoning clearly.\n\n5. Let $S=\\left\\{(x, y) \\mid x^{2}-y^{2}=\\right.$ odd, $\\left.x, y \\in R\\right\\}, T=\\{(x, y) \\mid$ $\\left.\\sin \\left(2 \\pi x^{2}\\right)-\\sin \\left(2 \\pi y^{2}\\right)=\\cos \\left(2 \\pi x^{2}\\right)-\\cos \\left(2 \\pi y^{2}\\right), x, y \\in R\\right\\}$. Then\n(A) $S \\subset T$;\n(B) $T \\subset S$;\n(C) $S=T$;\n(D) $S \\cap T=\\Phi$.", "role": "user"}], "answer": "A"} {"messages": [{"content": "You are a mathematical reasoning expert. Solve problems with detailed step-by-step thinking and provide final answers in \\boxed{} format. Show all intermediate calculations and explain your reasoning clearly.\n\n5. In trapezoid $A B C D$, $A B / / C D$, the base angles $\\angle D A B=36^{\\circ}, \\angle C B A=54^{\\circ}, M$ and $N$ are the midpoints of sides $A B$ and $C D$, respectively. If the lower base $A B$ is exactly 2008 units longer than the upper base $C D$, then the line segment $M N=$ $\\qquad$", "role": "user"}], "answer": "1004"} {"messages": [{"content": "You are a mathematical reasoning expert. Solve problems with detailed step-by-step thinking and provide final answers in \\boxed{} format. Show all intermediate calculations and explain your reasoning clearly.\n\nThe seventh grades of our school competed in collecting caps from PET bottles. Class A collected half of what classes B and C collected together, class B collected a third of what classes A and C collected together, and class C collected 150 caps.\n\nDetermine how many caps these three classes collected in total.\n\n(M. Volfová)", "role": "user"}], "answer": "360"} {"messages": [{"content": "You are a mathematical reasoning expert. Solve problems with detailed step-by-step thinking and provide final answers in \\boxed{} format. Show all intermediate calculations and explain your reasoning clearly.\n\nIn a certain year the price of gasoline rose by $20\\%$ during January, fell by $20\\%$ during February, rose by $25\\%$ during March, and fell by $x\\%$ during April. The price of gasoline at the end of April was the same as it had been at the beginning of January. To the nearest integer, what is $x$\n$\\mathrm{(A)}\\ 12\\qquad \\mathrm{(B)}\\ 17\\qquad \\mathrm{(C)}\\ 20\\qquad \\mathrm{(D)}\\ 25\\qquad \\mathrm{(E)}\\ 35$", "role": "user"}], "answer": "B"} {"messages": [{"content": "You are a mathematical reasoning expert. Solve problems with detailed step-by-step thinking and provide final answers in \\boxed{} format. Show all intermediate calculations and explain your reasoning clearly.\n\n15. Given $f(x)=x^{2}+c$, and $f(f(x))=f\\left(x^{2}+1\\right)$.\n(1) Let $g(x)=f(f(x))$, find the analytical expression of the function $g(x)$;\n(2) Let $\\varphi(x)=g(x)-\\lambda f(x)$, try to find the value of the real number $\\lambda$ such that $\\varphi(x)$ is a decreasing function on $(-\\infty,-1]$ and an increasing function on $[-1,0)$.", "role": "user"}], "answer": "4"} {"messages": [{"content": "You are a mathematical reasoning expert. Solve problems with detailed step-by-step thinking and provide final answers in \\boxed{} format. Show all intermediate calculations and explain your reasoning clearly.\n\nThe number $6545$ can be written as a product of a pair of positive two-digit numbers. What is the sum of this pair of numbers?\n$\\text{(A)}\\ 162 \\qquad \\text{(B)}\\ 172 \\qquad \\text{(C)}\\ 173 \\qquad \\text{(D)}\\ 174 \\qquad \\text{(E)}\\ 222$", "role": "user"}], "answer": "A"} -{"messages": [{"content": "You are a mathematical reasoning expert. Solve problems with detailed step-by-step thinking and provide final answers in \\boxed{} format. Show all intermediate calculations and explain your reasoning clearly.\n\n3. Given are the sides $a = BC$ and $b = CA$ of triangle $ABC$. Determine the length of the third side if it is equal to the length of the corresponding height. For which values of $a$ and $b$ does the problem have a solution?", "role": "user"}], "answer": "\\sqrt{\\dfrac{a^2 + b^2 + 2\\sqrt{3a^2b^2 - a^4 - b^4"} +{"messages": [{"content": "You are a mathematical reasoning expert. Solve problems with detailed step-by-step thinking and provide final answers in \\boxed{} format. Show all intermediate calculations and explain your reasoning clearly.\n\n3. Given are the sides $a = BC$ and $b = CA$ of triangle $ABC$. Determine the length of the third side if it is equal to the length of the corresponding height. For which values of $a$ and $b$ does the problem have a solution?", "role": "user"}], "answer": "\\sqrt{\\dfrac{a^2 + b^2 \\pm 2\\sqrt{3a^2b^2 - a^4 - b^4}}{5}}"} {"messages": [{"content": "You are a mathematical reasoning expert. Solve problems with detailed step-by-step thinking and provide final answers in \\boxed{} format. Show all intermediate calculations and explain your reasoning clearly.\n\n## Task 15/85\n\nLet the numbers $a ; b ; c$ represent the side lengths of a triangle with perimeter $U$, and let $a^{2}$; $b^{2} ; c^{2}$ represent the side lengths of another triangle with perimeter $U^{\\prime}$. Determine the lower bound of the ratio $U^{2}: U^{\\prime}$!", "role": "user"}], "answer": "2"} -{"messages": [{"content": "You are a mathematical reasoning expert. Solve problems with detailed step-by-step thinking and provide final answers in \\boxed{} format. Show all intermediate calculations and explain your reasoning clearly.\n\n7. Let the edge length of a regular tetrahedron be $2 \\sqrt{6}$, and let a sphere be constructed with the center $O$ of the tetrahedron as its center. The total length of the curves formed by the intersection of the sphere's surface with the four faces of the tetrahedron is $4 \\pi$. Then the radius of the sphere $O$ is $\\qquad$", "role": "user"}], "answer": "\\dfrac{\\sqrt{5"} +{"messages": [{"content": "You are a mathematical reasoning expert. Solve problems with detailed step-by-step thinking and provide final answers in \\boxed{} format. Show all intermediate calculations and explain your reasoning clearly.\n\n7. Let the edge length of a regular tetrahedron be $2 \\sqrt{6}$, and let a sphere be constructed with the center $O$ of the tetrahedron as its center. The total length of the curves formed by the intersection of the sphere's surface with the four faces of the tetrahedron is $4 \\pi$. Then the radius of the sphere $O$ is $\\qquad$", "role": "user"}], "answer": "\\dfrac{\\sqrt{5}}{2}, \\sqrt{5}"} {"messages": [{"content": "You are a mathematical reasoning expert. Solve problems with detailed step-by-step thinking and provide final answers in \\boxed{} format. Show all intermediate calculations and explain your reasoning clearly.\n\nExample 2.65. Calculate the volume of the body formed by the rotation around the $O Y$ axis of the curvilinear trapezoid bounded by the hyperbola $x y=2$ and the lines $y_{1}=1, y_{2}=4$ and $y_{3}=0$.", "role": "user"}], "answer": "3\\pi"} {"messages": [{"content": "You are a mathematical reasoning expert. Solve problems with detailed step-by-step thinking and provide final answers in \\boxed{} format. Show all intermediate calculations and explain your reasoning clearly.\n\nFor two quadratic trinomials $P(x)$ and $Q(x)$ there is a linear function $\\ell(x)$ such that $P(x)=Q(\\ell(x))$ for all real $x$. How many such linear functions $\\ell(x)$ can exist?\n\n[i](A. Golovanov)[/i]", "role": "user"}], "answer": "2"} {"messages": [{"content": "You are a mathematical reasoning expert. Solve problems with detailed step-by-step thinking and provide final answers in \\boxed{} format. Show all intermediate calculations and explain your reasoning clearly.\n\n1. A car is driving at a constant speed in one direction along a straight road, near which there are two houses. At noon, when the car had not yet reached the houses, the sum of the distances from it to these houses was 10 km. After 10 minutes, when the car had already passed both houses, it turned out that the sum of the distances from it to the houses was again 10 km. What is the speed of the car? (Problem author - I. Rubanov)", "role": "user"}], "answer": "60"} {"messages": [{"content": "You are a mathematical reasoning expert. Solve problems with detailed step-by-step thinking and provide final answers in \\boxed{} format. Show all intermediate calculations and explain your reasoning clearly.\n\n$18 \\cdot 110$ As shown, $A B C D$ is an isosceles trapezoid, $A D$ $=B C=5, A B=4, D C=10$, point $C$ is on $D F$, and $B$ is the midpoint of the hypotenuse of the right triangle $\\triangle D E F$. Then $C F$ equals\n(A) 3.25 .\n(B) 3.5 .\n(C) 3.75 .\n(D) 4.0 .\n(E) 4.25 .", "role": "user"}], "answer": "D"} {"messages": [{"content": "You are a mathematical reasoning expert. Solve problems with detailed step-by-step thinking and provide final answers in \\boxed{} format. Show all intermediate calculations and explain your reasoning clearly.\n\n1. Given 2117 cards, on which natural numbers from 1 to 2117 are written (each card has exactly one number, and the numbers do not repeat). It is required to choose two cards such that the sum of the numbers written on them is divisible by 100. In how many ways can this be done?", "role": "user"}], "answer": "22386"} {"messages": [{"content": "You are a mathematical reasoning expert. Solve problems with detailed step-by-step thinking and provide final answers in \\boxed{} format. Show all intermediate calculations and explain your reasoning clearly.\n\n2. (6 points) A certain duplicator can print 3600 sheets of paper per hour, so printing 240 sheets of paper requires $\\qquad$ minutes.", "role": "user"}], "answer": "4"} -{"messages": [{"content": "You are a mathematical reasoning expert. Solve problems with detailed step-by-step thinking and provide final answers in \\boxed{} format. Show all intermediate calculations and explain your reasoning clearly.\n\n1 $\\left[\\begin{array}{ll}\\text { Common fractions }\\end{array}\\right]$\n\nWhich of the three fractions is the largest: $3 / 4, 4 / 5$ or $5 / 6$?", "role": "user"}], "answer": "\\dfrac{5"} -{"messages": [{"content": "You are a mathematical reasoning expert. Solve problems with detailed step-by-step thinking and provide final answers in \\boxed{} format. Show all intermediate calculations and explain your reasoning clearly.\n\nIn the given operation, the letters $a, b$, and $c$ represent distinct digits and are different from 1. Determine the values of $a, b$, and $c$.\n\n$$\n\\begin{array}{r}\na b b \\\\\n\\times \\quad c \\\\\n\\hline b c b 1\n\\end{array}\n$$", "role": "user"}], "answer": "c=7"} \ No newline at end of file +{"messages": [{"content": "You are a mathematical reasoning expert. Solve problems with detailed step-by-step thinking and provide final answers in \\boxed{} format. Show all intermediate calculations and explain your reasoning clearly.\n\n1 $\\left[\\begin{array}{ll}\\text { Common fractions }\\end{array}\\right]$\n\nWhich of the three fractions is the largest: $3 / 4, 4 / 5$ or $5 / 6$?", "role": "user"}], "answer": "\\dfrac{5}{6}"} +{"messages": [{"content": "You are a mathematical reasoning expert. Solve problems with detailed step-by-step thinking and provide final answers in \\boxed{} format. Show all intermediate calculations and explain your reasoning clearly.\n\nIn the given operation, the letters $a, b$, and $c$ represent distinct digits and are different from 1. Determine the values of $a, b$, and $c$.\n\n$$\n\\begin{array}{r}\na b b \\\\\n\\times \\quad c \\\\\n\\hline b c b 1\n\\end{array}\n$$", "role": "user"}], "answer": "c=7"} diff --git a/managed_fine_tuning/03-core-rft/02-rft-math-reasoning/data/preserved/openr1-math-validation-rft-10.jsonl b/managed_fine_tuning/03-core-rft/02-rft-math-reasoning/data/preserved/openr1-math-validation-rft-10.jsonl index 1330779..e3488e2 100644 --- a/managed_fine_tuning/03-core-rft/02-rft-math-reasoning/data/preserved/openr1-math-validation-rft-10.jsonl +++ b/managed_fine_tuning/03-core-rft/02-rft-math-reasoning/data/preserved/openr1-math-validation-rft-10.jsonl @@ -1,10 +1,10 @@ -{"messages": [{"content": "You are a mathematical reasoning expert. Solve problems with detailed step-by-step thinking and provide final answers in \\boxed{} format. Show all intermediate calculations and explain your reasoning clearly.\n\nExample 3 Given $a=\\frac{1}{2} \\sqrt{\\sqrt{2}+\\frac{1}{8}}-\\frac{\\sqrt{2}}{8}$. Try to find the value of $a^{2}+\\sqrt{a^{4}+a+1}$.", "role": "user"}], "answer": "\\sqrt{2"} +{"messages": [{"content": "You are a mathematical reasoning expert. Solve problems with detailed step-by-step thinking and provide final answers in \\boxed{} format. Show all intermediate calculations and explain your reasoning clearly.\n\nExample 3 Given $a=\\frac{1}{2} \\sqrt{\\sqrt{2}+\\frac{1}{8}}-\\frac{\\sqrt{2}}{8}$. Try to find the value of $a^{2}+\\sqrt{a^{4}+a+1}$.", "role": "user"}], "answer": "\\sqrt{2}"} {"messages": [{"content": "You are a mathematical reasoning expert. Solve problems with detailed step-by-step thinking and provide final answers in \\boxed{} format. Show all intermediate calculations and explain your reasoning clearly.\n\nThe surface area of a cube is 24 . The volume of the cube is\n(A) 4\n(B) $3 \\sqrt{3}$\n(C) 9\n(D) 16\n(E) 8", "role": "user"}], "answer": "E"} {"messages": [{"content": "You are a mathematical reasoning expert. Solve problems with detailed step-by-step thinking and provide final answers in \\boxed{} format. Show all intermediate calculations and explain your reasoning clearly.\n\n2. Given $\\sin 2 x=\\frac{\\sin \\theta+\\cos \\theta}{2}$, $\\cos ^{2} x=\\sin \\theta \\cdot \\cos \\theta$.\nThen, the value of $\\cos 2 x$ is ( ).\n(A) $\\frac{-1 \\pm \\sqrt{33}}{8}$\n(B) $\\frac{-1+\\sqrt{33}}{8}$\n(C) $\\frac{-1-\\sqrt{33}}{8}$\n(D) 0", "role": "user"}], "answer": "C"} {"messages": [{"content": "You are a mathematical reasoning expert. Solve problems with detailed step-by-step thinking and provide final answers in \\boxed{} format. Show all intermediate calculations and explain your reasoning clearly.\n\n4. Find the sum\n\n$$\n\\log \\operatorname{tg} 1^{\\circ}+\\log \\operatorname{tg} 2^{\\circ}+\\ldots+\\log \\operatorname{tg} 89^{\\circ}\n$$", "role": "user"}], "answer": "0"} -{"messages": [{"content": "You are a mathematical reasoning expert. Solve problems with detailed step-by-step thinking and provide final answers in \\boxed{} format. Show all intermediate calculations and explain your reasoning clearly.\n\n1. Find the sum of the numbers:\n\n$$\n3+33+333+3333+\\cdots+\\underbrace{33333 \\ldots 3}_{2018 \\text { of them }} .\n$$", "role": "user"}], "answer": "\\dfrac{10^{2019"} -{"messages": [{"content": "You are a mathematical reasoning expert. Solve problems with detailed step-by-step thinking and provide final answers in \\boxed{} format. Show all intermediate calculations and explain your reasoning clearly.\n\n12.407 A line perpendicular to the chord of a segment divides the chord in the ratio 1:4, and the arc - in the ratio $1: 2$. Find the cosine of the central angle subtended by this arc.", "role": "user"}], "answer": "-\\dfrac{23"} -{"messages": [{"content": "You are a mathematical reasoning expert. Solve problems with detailed step-by-step thinking and provide final answers in \\boxed{} format. Show all intermediate calculations and explain your reasoning clearly.\n\nFor some positive integer $n$, a coin will be flipped $n$ times to obtain a sequence of $n$ heads and tails. For each flip of the coin, there is probability $p$ of obtaining a head and probability $1-p$ of obtaining a tail, where $0 **Training costs:** Executing upload and training cells performs Azure calls and can incur charges. Local data and grader tests do not submit jobs." ] @@ -19,7 +19,20 @@ "id": "0559d17ccbc7", "metadata": {}, "source": [ - "## 1. Imports, paths, and execution gates" + "## 1. Imports, paths, and execution gates\n", + "\n", + "Copy [the blank template](../.env.template) to a demo-local `.env` and set your own values. The training model is `qwen3.6-35b-a3b`, defined by `MODEL` in the preparation cell; the notebook does not read model defaults from `demo.yaml`.\n", + "\n", + "| Setting / value | Meaning and when required |\n", + "|---|---|\n", + "| `FOUNDRY_PROJECT_ENDPOINT` | Foundry project endpoint; required for every remote section. |\n", + "| `MODEL` | Fixed training model ID: `qwen3.6-35b-a3b`. Confirm model access, region support, and quota before Section 5. |\n", + "| `completed_job.fine_tuned_model` | Trained artifact ID returned by Foundry, not an inference deployment name. |\n", + "| `FOUNDRY_MATH_BASELINE_DEPLOYMENT` | Existing base-model deployment **name**; required only when `FOUNDRY_RUN_REMOTE_BASELINE=true` (Section 4). |\n", + "| `FOUNDRY_MATH_FINE_TUNED_DEPLOYMENT` | Existing fine-tuned deployment **name**; required only when `FOUNDRY_RUN_REMOTE_EVALUATION=true` (Section 9). |\n", + "| `FOUNDRY_EXISTING_MATH_RFT_JOB_ID` | Optional job ID to reuse in Section 5; blank creates a new paid job. |\n", + "\n", + "Both inference flags default to false when blank/unset. They do **not** disable Section 5 uploads or training. Training can finish without either inference deployment." ] }, { @@ -38,6 +51,8 @@ "\n", "from dotenv import load_dotenv\n", "\n", + "MODEL = \"qwen3.6-35b-a3b\"\n", + "\n", "cwd = Path.cwd().resolve()\n", "demo_candidates = [cwd, cwd.parent] if cwd.name == \"notebooks\" else [cwd]\n", "DEMO_ROOT = next(\n", @@ -69,7 +84,7 @@ "FOUNDRY_RUN_REMOTE_EVALUATION = env_flag(\"FOUNDRY_RUN_REMOTE_EVALUATION\")\n", "print(\n", " {\"remote_baseline\": FOUNDRY_RUN_REMOTE_BASELINE, \"remote_evaluation\": FOUNDRY_RUN_REMOTE_EVALUATION}\n", - ")" + ")\n" ] }, { @@ -77,7 +92,9 @@ "id": "10dec0f7ade4", "metadata": {}, "source": [ - "## 2. Verify preserved datasets and inspect the task" + "## 2. Verify datasets and inspect the task\n", + "\n", + "The [data notes](../data/README.md) record the source revision and in-place answer corrections. The existing dataset files are hash-checked before use." ] }, { @@ -262,9 +279,15 @@ "source": [ "## 5. Prepare content-addressed files and the RFT job\n", "\n", - "The unchanged reinforcement recipe is visible offline below. Copy this module's blank `.env.template` to a module-local `.env`; executing the upload/training cell submits or resumes a paid job. Existing jobs, including pending jobs, must match the model, input file IDs, and full reinforcement recipe. A mismatch or failed/cancelled job raises an error.\n", + "Running the upload/training cell starts a new paid job when `FOUNDRY_EXISTING_MATH_RFT_JOB_ID` is blank. Failed or cancelled jobs cannot be reused.\n", + "\n", + "**To use the same job again:**\n", + "1. Copy the job ID shown after submission and save it in a private note.\n", + "2. Open this demo's `.env` file. And assign to this `FOUNDRY_EXISTING_MATH_RFT_JOB_ID`\n", + "3. In the notebook toolbar, click **Restart Kernel**, then run Sections 1–5 again.\n", + "4. Keep the same project, model, data, and training settings.\n", "\n", - "Creation is attempted once with SDK retries disabled. Reconcile an ambiguous submission failure in Foundry before retrying.\n" + "If submission shows an error, check Foundry to see whether the job was created before trying again. If it exists, use its job ID by following the steps above. Leave the ID blank only when you want to start a new paid job." ] }, { @@ -307,7 +330,7 @@ "training_client = None\n", "project_client = None\n", "\n", - "values = require_env(\"FOUNDRY_PROJECT_ENDPOINT\", \"FOUNDRY_BASE_MODEL\")\n", + "values = require_env(\"FOUNDRY_PROJECT_ENDPOINT\")\n", "from azure.ai.projects import AIProjectClient\n", "from azure.identity import DefaultAzureCredential\n", "\n", @@ -333,7 +356,7 @@ " return training_client.with_options(max_retries=0).fine_tuning.jobs.create(\n", " training_file=training_file.id,\n", " validation_file=validation_file.id,\n", - " model=values[\"FOUNDRY_BASE_MODEL\"],\n", + " model=MODEL,\n", " method=MATH_METHOD,\n", " extra_body={\"trainingType\": \"GlobalStandard\"},\n", " suffix=\"core-rft-openr1-math\",\n", @@ -343,7 +366,7 @@ " training_client,\n", " existing_job_id=os.getenv(\"FOUNDRY_EXISTING_MATH_RFT_JOB_ID\") or None,\n", " expected={\n", - " \"model\": values[\"FOUNDRY_BASE_MODEL\"],\n", + " \"model\": MODEL,\n", " \"training_file\": training_file.id,\n", " \"validation_file\": validation_file.id,\n", " \"method\": MATH_METHOD,\n", @@ -358,7 +381,9 @@ "id": "e696e092c255", "metadata": {}, "source": [ - "## 6. Monitor with a timeout and collect real reward/loss events" + "## 6. Monitor with a timeout and collect real reward/loss events\n", + "\n", + "The six-hour timeout stops local monitoring, **not** the remote job. Check its status in Foundry before retrying. With the kernel intact, rerun only this monitoring cell; after kernel loss, recover the existing job as described in Section 5. Cancellation is a separate, explicit operation; see [post-training guidance](../../../POST_TRAINING.md)." ] }, { @@ -397,7 +422,7 @@ "source": [ "![Representative validation reward](../assets/charts/representative-validation-reward.svg)\n", "\n", - "The committed curve contains the two validation means recorded by the existing run: `0.05` and `0.20`. A current run should use service events and evaluation outputs from the previous cell; never substitute this historical curve for current evidence." + "The committed curve contains the two validation means from the historical run using pre-correction inputs: `0.05` and `0.20`. These are not results for the current corrected data. A current run should use service events and evaluation outputs from the previous cell; never substitute this historical curve for current evidence." ] }, { @@ -514,7 +539,13 @@ "id": "54465a655b2b", "metadata": {}, "source": [ - "A succeeded RFT job registers a model. Deployment availability is checked separately for your configured project." + "**Manual deployment handoff:** Section 8 only lists/checks deployments; no section creates one. A succeeded job registers `completed_job.fine_tuned_model`.\n", + "\n", + "1. If no matching deployment exists, pause here. In Foundry, deploy that exact trained artifact into a project-accessible endpoint after checking model/region support, permissions, quota, deployment type, capacity, and serving cost.\n", + "2. Once ready, copy its **deployment name**, not the artifact ID, into `FOUNDRY_MATH_FINE_TUNED_DEPLOYMENT`. Verify its model/version matches this completed job; Section 9 does not enforce that identity and does not automatically use Section 8's selected name.\n", + "3. Enable `FOUNDRY_RUN_REMOTE_EVALUATION` and run Section 9. If configuration was already loaded, update the deployment's `os.environ` entry and set the kernel variable `FOUNDRY_RUN_REMOTE_EVALUATION = True`; editing `.env` alone does not refresh cached settings. Do not use **Run All** to enable evaluation: Section 5 could submit another job.\n", + "\n", + "Without deployment, training and service validation remain available. Leave endpoint evaluation disabled and continue to the summary; enabling it with a blank name raises an error, while a missing/unready deployment cannot be evaluated. See [serving guidance](../../../POST_TRAINING.md)." ] }, { @@ -605,7 +636,7 @@ "\n", "**Next step:** secure supported deployment capacity, add an untouched test split, evaluate the base and fine-tuned deployments on that independent set, and manually review correct and incorrect chains for reasoning quality—not just final-answer reward.\n", "\n", - "*Variability footnote:* the `0.05 → 0.20` validation rewards and 257-word correct response come from one existing run. Model availability, quota, service updates, grader behavior, data composition, and training stochasticity can materially change results.\n", + "*Variability footnote:* the `0.05 → 0.20` validation rewards and 257-word correct response come from one historical run using pre-correction inputs, not the current corrected data. Model availability, quota, service updates, grader behavior, data composition, and training stochasticity can materially change results.\n", "\n", "> **Variability note:** Actual results may vary by model version, data, configuration, region availability, and service conditions." ] @@ -618,8 +649,16 @@ "name": "python3" }, "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", "name": "python", - "version": "3.10" + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.13.14" } }, "nbformat": 4,