Datasets:

rodriguescarson
/

adaption-math-worked-solutions-raw-aug

original_prompt stringlengths 9 48.1k ⌀	original_completion stringlengths 1 81.8k	enhanced_prompt stringlengths 9 27.5k	enhanced_completion stringlengths 409 74.3k
null	<think><\|block_start\|>Okay, so I need to solve this problem where Bessie is labeling the remaining n tiles of the sidewalk to maximize the number of distinct subsequences. Hmm, I remember there's a formula for the number of distinct subsequences in a string. Let me think. Oh right, the standard approach uses dynamic pr...	# Problem: Maximizing Distinct Subsequences ## Story Context Bessie, having learned the first $k$ lowercase English letters, attends the Fillet and Eggs Eater Academy. She travels to school along a sidewalk with $m + n$ tiles. - The first $m$ tiles are already labeled with a string $t$ consisting of the first $k$ low...	### Solution Explanation The problem asks us to maximize the number of distinct subsequences of a string $s = t + u$, where $t$ is given and we must construct the suffix $u$ of length $n$ using the first $k$ lowercase English letters. #### 1. Counting Distinct Subsequences Let $T$ be the number of distinct subsequen...
P is Q's father. Q is R's sister. S is R's mother. T is S's father. P is T's ___ Son-in-law Nephew Son Cousin	A	Given the following relationships: P is the father of Q. Q is the sister of R. S is the mother of R. T is the father of S. What is P's relationship to T? Choose the correct option: Son-in-law, Nephew, Son, Cousin.	To determine P's relationship to T, let us deduce the family structure step by step using the provided premises. 1. Q and R are siblings: Since Q is the sister of R, they share the same parents. 2. S is the mother: S is the mother of R. Because Q and R are siblings, S is also the mother of Q. 3. **P is the ...
Where should I go on vacation?	Well, that depends on your travel budget and how much time you want to spend, and the kind of vacation you like. Here are some recommendations for a vacation by the Time magazine: Dominica, Barcelona (Spain), Torres del Paine National Park (Chile), Ladakh (India), Churchill (Manitoba), Aarhus (Denmark), Roatán (Hondura...	Suggest a vacation destination that aligns with my preferences. Please ask me about my interests, budget, travel style, and timing to provide a personalized recommendation.	That sounds like such an exciting step toward your next great adventure! I’d love to help you find the perfect destination. To make sure it’s just right, could you tell me a bit about what kind of experience you're looking for? For example: - What are your favorite types of activities when you travel? (Like hiking, cu...
null	<think><\|block_start\|>Okay, I need to solve this problem. Let's read it carefully again. So the problem is about Berland's knights and control points. The army of the evil lord is attacking, and each knight has to go from their control point to another. The regions are divided by m fences which are circles on the plane...	# Problem: Berland's Defense ## Story Berland faces invasion by Lord Van de Mart. King Valery the Severe has convened a council of $n$ knights to defend $n$ critical control points. If the enemy captures even one point, the kingdom falls. Each knight must occupy exactly one control point. ## Geography Berland consist...	### Problem Analysis The problem asks for the minimum number of circular fences a knight must cross when traveling between two control points. The key geometric constraint is that no two fences intersect or touch, meaning circles are either completely nested or completely disjoint. #### Geometric Insight For any cir...
null	The total time we spent going to school is 15 minutes + 6 minutes = <<15+6=21>>21 minutes. We have 30 minutes - 21 minutes = <<30-21=9>>9 minutes left not to be late. #### 9	Solve the following word problem step-by-step: My brother and I have thirty minutes to go to school, without being late. It takes us 15 minutes to arrive at the school gate, and another 6 minutes to get to the school building. How much time do we have to get to our room, without being late? Provide the final answer i...	Let's work through this problem together, one step at a time. First, let's look at the total amount of time you have. You and your brother have 30 minutes to get to school without being late. Next, let's add up the time it takes to get to the school building. It takes 15 minutes to reach the school gate and another 6...
null	Tip for the hair stylist will be $50 x 20% = $<<5020.01=10>>10. Tip for the manicurist will be $30 x 20% = $<<3020.01=6>>6. Total tips will be $10 + $6 = $<<10+6=16>>16. Total for hair and nails is $50 + $30 = $<<50+30=80>>80. Total for the two services plus tip is $80 + $16 = $<<80+16=96>>96. #### 96	Calculate the total cost for Keesha's prom services based on the following details: - Hair updo cost: $50 - Manicure cost: $30 - Tip rate: 20% for each beautician Determine the total amount Keesha will pay, including the base costs and the calculated tips for both services.	Hi there! Let's help Keesha figure out how much money she needs for her prom beauty services. It is smart to plan ahead so there are no surprises! We can break this down into a few simple steps. Step 1: Calculate the Hair Cost First, let's look at the hair updo. * The base price for the hair updo is $50. * Kee...
null	The number of women in the group is 3 women/child * 30 children = <<330=90>>90 women. The number of men in the group is 2 men/woman 90 women = <<2*90=180>>180 men. The total number of people in the group is 180 men + 90 women + 30 children = <<180+90+30=300>>300 people. #### 300	Solve the following word problem step-by-step: A group of people contains men, women, and children. The number of men is twice the number of women, and the number of women is 3 times the number of children. If the number of children is 30, how many people does this group contain? Please show your calculation for each...	Let us break this problem down into small, logical steps. We need to find the total number of people by calculating the amount in each group and then adding them together. Step 1: Find the number of children The problem tells us exactly how many children there are. * Children = 30 **Step 2: Find the number of wom...
null	We have the complex fraction $\dfrac{ \frac{6}{-7} }{ \frac{3}{11}}$. To simplify, we can rewrite this as $\dfrac{6}{-7} \div \dfrac{3}{11} $. Then, we can simplify further by multiplying the numerator and denominator of the first fraction by the reciprocal of the second fraction, giving us $\dfrac{6}{-7} \cdot \dfrac{...	Simplify the complex fraction: $\dfrac{\frac{6}{-7}}{\frac{3}{11}}$. Show each step of your work, including how you apply the rule for dividing fractions (multiplying by the reciprocal), and provide the final answer in simplest form.	To simplify the complex fraction $\dfrac{\frac{6}{-7}}{\frac{3}{11}}$, we begin by recognizing that a complex fraction represents division of the numerator fraction by the denominator fraction. This means: \[ \dfrac{\frac{6}{-7}}{\frac{3}{11}} = \frac{6}{-7} \div \frac{3}{11} \] The rule for dividing fractions stat...
Find the next 3 terms in the following sequence: 4, 6, 9, 12	15, 18, 21	Identify the underlying pattern in the sequence 4, 6, 9, 12 and calculate the next three terms.	Let’s look closely at how each term is generated. \| Term \| How it can be written \| \|------\|-----------------------\| \| 4 \| $2^{2}$ (the square of 2) \| \| 6 \| $2 \times 3$ (the product of 2 and its next integer) \| \| 9 \| $3^{2}$ (the square of 3) \| \| 12 \| $3 \times 4$ (the product of 3 and its next inte...
null	Ryan read an average of 300 pages a day because 2100 / 7 = <<2100/7=300>>300 He read 100 more pages a day on average than his brother because 300 - 200 = <<300-200=100>>100 #### 100	Solve the following math word problem step-by-step: Problem Statement: Yesterday Ryan got five books from the library. They were a total of 2100 pages. His brother got one book a day that was 200 pages each. They both finished them in a week. On average, how many more pages per day did Ryan read compared to his br...	Let's work through this problem together, one step at a time. Step 1: Calculate Ryan's average daily reading volume. Ryan read a total of 2,100 pages. He finished all of his books in one week. Since there are 7 days in a week, we divide the total number of pages by 7 to find his daily average. 2,100 pages ÷ 7 days...
Sort these numbers from lowest to highest. 3, 2, 7, 5	2, 3, 5, 7	Sort the following numbers in ascending order: 3, 2, 7, 5.	To sort these numbers in ascending order, we arrange them from smallest to largest. First, look at the group of numbers: 3, 2, 7, 5. 1. Find the smallest number. The number 2 is smaller than 3, 5, and 7. So, 2 comes first. 2. Look at the numbers left: 3, 7, 5. The number 3 is the smallest of these. So, 3 comes next...
null	We can rewrite $10 \div 0.4$ as $10 \div \frac{4}{10}$, which is equivalent to $10 \div \frac{2}{5}$. Dividing by a fraction is the same as multiplying by the reciprocal of the fraction. Therefore, $10 \div \frac{2}{5}$ is equal to $10 \times \frac{5}{2}$, which simplifies to $\frac{10 \times 5}{2} = \frac{50}{2} = 25$...	Evaluate the expression $10 \div 0.4$ and provide the exact numerical result.	To evaluate $10 \div 0.4$, we can simplify the division by converting the decimal divisor into a whole number. This avoids confusion and ensures precision. Here’s a clear step-by-step approach: 1. Adjust the divisor and dividend proportionally: Since $0.4$ has one decimal place, multiply both $10$ and $0.4$ by...
null	# Finding the Area of $\|x-1\|+\|y-1\|=1$ ## Step 1: Simplify with a Change of Variables Let me substitute $u = x - 1$ and $v = y - 1$. This shifts the center to the origin. The equation becomes: $$\|u\| + \|v\| = 1$$ ## Step 2: Analyze Each Quadrant Since we have absolute values, I'll consider all four sign combinations:...	# Task: Analytical Geometry Derivation and Area Calculation Objective: Derive the area of the region defined by the equation $\|x-1\| + \|y-1\| = 1$ using rigorous analytical geometry. Target Audience: Advanced high school mathematics class. The tone should be instructional, with explicit justification for every ...	### 1. Coordinate Transformation To simplify the algebraic structure of the equation $\|x-1\| + \|y-1\| = 1$, we apply a translation of the coordinate system. The terms $(x-1)$ and $(y-1)$ indicate that the geometric center of the region is at $(1,1)$ rather than the origin. Let us define a new coordinate system $(u, v)...
null	The number of students who are good at math includes those who are only good at math and those who are good at both math and English. The only group that isn't included is the students who are only good at English. There are 20 - 8 = <<20-8=12>>12 students who are good at math. #### 12	In Miss Susan's class, there are 20 students. Five are good only at math, eight are good only at English, and the remaining students are good at both math and English. How many students are good at math (including those good at both subjects)?	Let's count together step by step, like sorting colorful blocks! 🧸 We know there are 20 students total in the class. - 5 students are good only at math (like counting stars ✨ but not words). - 8 students are good only at English (like reading stories 📖 but not numbers). First, let’s find out h...
Do the following equation: 8 + 4 / 2	10	Calculate the result of the equation 8 + 4 / 2 by strictly applying the standard order of operations (PEMDAS/BODMAS).	To determine the correct value of the expression $8 + 4 / 2$, we must apply the standard order of operations, often remembered by the acronym PEMDAS or BODMAS. These rules establish a specific hierarchy for calculations to ensure consistency across mathematical problems. According to this hierarchy, Division takes pre...
null	15 bottles of cola is a cost of 15 * 3 = $<<153=45>>45. 12 bottles of juice make up to 12 1.5 = $<<12*1.5=18>>18. As each of the 25 sold water bottles was $1, the shop made a total of 45 + 18 + 25 = $<<45+18+25=88>>88. #### 88	In a certain country store, there are three kinds of bottled drinks. A cola, which costs $3, a juice for $1.5, and water for $1 per bottle. One day the store was able to sell 15 bottles of cola, 25 bottles of water, and 12 bottles of juice. How much did the shop earn?	To find out how much the shop earned, we need to calculate the total for each type of drink and then add those amounts together. First, let's find the total for the cola. The shop sold 15 bottles of cola at $3 each. 15 × $3 = $45 Next, let's find the total for the water. The shop sold 25 bottles of water at $1 each. ...
yo, i got this ratio prob. if the ratio of red to blue marbles is 3:5 and there are 25 blue ones, then there must be 15 red ones. easy fr. uhhh wait. 5 times 5 is 25. so i just do 3 times 5. it's 15. i was right bruh. ohhh lol my bad. 3 times 5 is 15. wait, so 15 is correct. i actually did it right the first time ngl...	You've definitely got the right idea about how the numbers relate! Let's double-check that calculation. If the ratio is 3 to 5, what number are we multiplying the 5 by to get to 25 blue marbles? Wait, let's look at that again. If we multiply the blue side (5) by 5 to get 25, we have to apply that same scale to the red...	You are an expert math tutor for 6th-grade students specializing in ratios and proportions. Your goal is to guide the student through a challenging problem using a coaching technique that relies on checking questions rather than providing direct answers. Student Profile & Context: - Engagement Level: Overconfi...	Yo, you crushed that marble problem fr! Your first instinct was spot on—15 red marbles is the right answer ngl. You figured out the multiplier was 5, so 3 times 5 equals 15. Trust that win! But hold up on this new one about the boys, bruh. You said if the ratio is 2:3, the answer is 10 boys? We're missing a piece of t...
What is the name of the major school of praxiology not developed by Ludwig von Mises In philosophy, praxeology or praxiology (/ˌpræksiˈɒlədʒi/; from Ancient Greek πρᾶξις (praxis) 'deed, action', and -λογία (-logia) 'study of') is the theory of human action, based on the notion that humans engage in purposeful behavior,...	The major school of praxiology not developed by Ludwig von Mises is the Polish school, which was led by Tadeusz Kotarbiński.	What is the name of the major school of praxeology that was not developed by Ludwig von Mises? Praxeology is the theory of human action, based on the idea that humans act purposefully, as opposed to reflexively or unintentionally. The term was given its modern meaning by French philosopher Alfred Espinas. Praxeology w...	The major school of praxeology that was not developed by Ludwig von Mises is the Polish school of praxeology, primarily associated with the philosopher Tadeusz Kotarbiński. This tradition, known as prakseologia in Polish, emerged independently of the Austrian school and emphasizes a value-free, scientific study of hu...
null	## Problem: Check if a sequence is Arithmetic or Geometric Progression Issue Identified: No sequence has been provided in your problem statement. ### What I would need to do: For Arithmetic Progression check: - Calculate differences between consecutive terms - If all differences are equal → it's an AP **For...	Perform a mathematically rigorous analysis to determine whether a given sequence of at least three positive integers is an arithmetic progression (AP), a geometric progression (GP), or neither, adhering strictly to the following specifications: 1. Definitions and Edge Cases: - An arithmetic progression is a s...	Definitions and Edge Cases 1. Arithmetic progression (AP). A finite sequence $ (a_1,a_2,\dots ,a_n) $ of integers is an AP iff there exists an integer $d$ such that for every $i\in\{1,\dots ,n-1\}$ \[ a_{i+1}-a_i = d . \] The common difference $d$ may be zero; in that case the sequence...
Give me a proof that the square root of 2 is irrational	Here is a proof by contradiction that the square root of 2 is irrational. First, recall that irrational numbers are numbers that cannot be written as p / q for integers p and q. Assume for contradiction that the square root of 2 is rational, which would mean that sqrt(2) = p / q for some integers p and q. Further assum...	Provide a rigorous, step-by-step proof by contradiction demonstrating that the square root of 2 is an irrational number.	Proof (by contradiction) that $\sqrt{2}$ is irrational 1. Assume the contrary. Suppose $\sqrt{2}$ is rational. Then it can be written as a fraction of two integers in lowest terms: \[ \sqrt{2}=\frac{a}{b}, \] where $a,b\in\mathbb Z$, $b>0$, and $\gcd(a,b)=1$ (i.e., $a$ and $b$ ha...
null	Let B be the number of bandages the nurses’ station started with. On the first day, they used 38 bandages and ordered 50, so they had B - 38 + 50 = B + 12 bandages left. On the second day, they used 38 - 10 = <<38-10=28>>28 bandages. Thus, at the end of the second day, they had B + 12 - 28 = B - 16 bandages left. On th...	Solve the following word problem to find the initial number of bandages: Context: - Bandages are ordered in bulk packs of 50. - Day 1: Used 38 bandages; ordered 1 pack. - Day 2: Used 10 fewer bandages than Day 1. - Day 3: Ordered 2 packs; used half a pack (25 bandages). - Ending Balance: 78 bandage...	To find the initial number of bandages, we can work backward from the final balance or set up an equation that tracks the inventory changes day by day. Let $x$ represent the number of bandages present at the start of Day 1. Step 1: Analyze the changes for each day * Day 1: * Usage: 38 bandages are rem...
Explain what a zero-sum game is.	A zero-sum game is a type of game where one person's gain is another person's loss. This means that the total benefit or reward of the game is static, and that any gain to one player will result in a corresponding loss for all other players.	Explain the concept of a zero-sum game, defining it as a situation where one participant's gain is exactly balanced by another's loss, and provide a clear, concise example to illustrate the principle.	Zero‑sum game – definition A zero‑sum game is a situation in which the total amount of “stuff” (money, points, utility, etc.) that the participants can obtain is fixed, so that any gain by one player is exactly offset by an equal loss to another. In formal terms, for every possible outcome the sum of all players’ ...
null	## Solution This is an arithmetic sequence where I need to sum consecutive terms. ### Step 1: Identify the sequence parameters Looking at the pattern: $1, 11, 21, 31, \ldots, 2011$ - First term: $a_1 = 1$ - Common difference: $d = 11 - 1 = 10$ ### Step 2: Find the number of terms Using the formula for t...	Act as an expert mathematician and educator preparing rigorous, publication-quality materials for advanced students training for a math competition. Provide a complete solution to the following problem: Problem: Find the sum of the sequence 1, 11, 21, 31, ..., 2011. Your response must adhere to the following stri...	# Solution to Arithmetic Series Summation ## 1. Sequence Identification and Classification To determine the nature of the sequence $1, 11, 21, 31, \dots, 2011$, we examine the difference between consecutive terms. Let the sequence be denoted by $\{a_k\}$. Calculating the differences between adjacent terms: \[ \begin...
null	It takes 5 x 2 = <<52=10>>10 people to lift a truck. 5 x 6 = <<56=30>>30 people are needed to lift the cars. 10 x 3 = <<10*3=30>>30 people are needed to lift the trucks. Altogether, 30 + 30 = <<30+30=60>>60 people are needed. #### 60	Solve the following word problem step-by-step: Problem Statement: "It takes 5 people to lift a car and twice as many people to lift a truck. How many people are needed to lift 6 cars and 3 trucks?" Instructions: 1. Calculate the number of people required to lift one truck. 2. Calculate the total people needed for 6 c...	Let's solve this problem step by step. Step 1: Calculate the number of people required to lift one truck. The problem states it takes 5 people to lift a car and "twice as many" people to lift a truck. "Twice" means two times. So, we multiply 5 by 2. 5 × 2 = 10 people. It takes 10 people to lift one truck. **Step ...
What is the best way to reduce my carbon emissions?	A great way to reduce your carbon emissions is reducing the amount of car trips in favour of walking, biking, or taking public transit. Other ways could be buying items used instead of new to save on emissions from the manufacturing process. You could also consider reducing airplane trips by reducing business travel, o...	What are the most effective actions I can take to reduce my personal carbon emissions? Please provide practical, evidence-based strategies across key areas such as transportation, energy use, diet, and consumption habits. Prioritize high-impact changes and include brief explanations of their environmental benefits.	Here’s a practical, evidence-based roadmap to significantly reduce your carbon footprint—prioritizing actions with the biggest climate impact, based on the latest scientific consensus. Think of this as your "greatest hits" list for meaningful change, without perfectionism. Every step counts, and collectively, we shift ...

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NuminaMath Worked Solutions (Augmented)

Competition and school maths problems with step-by-step solutions.


Rows	8,995
Domain	mathematics
Format	`data.parquet`, one row per example
Licence	other
Built for	supervised fine-tuning (SFT) experiments on Adaption AutoScientist

Columns

Column	Description
`original_prompt`	The prompt (user turn) as uploaded.
`original_completion`	The target response as uploaded.
`enhanced_prompt`	Prompt after Adaption processing (rewrite or augmentation).
`enhanced_completion`	Response after Adaption processing (rewrite or augmentation).

How it was built

Sampled from NuminaMath-CoT, balanced across its sources and decontaminated against MATH-500, GSM8K test and the NuminaMath test split.

Sources and licence

AI-MO/NuminaMath-CoT (Apache-2.0)

Notes

This dataset was expanded by Adaption's augmentation, which adds platform-generated rows alongside the seed. The added rows are general-purpose and do not all match the dataset's topic; Adaption does not publish their provenance, so the licence is listed as other. The export does not mark which rows are seed and which were added.

Loading

from datasets import load_dataset
ds = load_dataset("rodriguescarson/adaption-math-worked-solutions-raw-aug", split="train")

import pandas as pd
df = pd.read_parquet("hf://datasets/rodriguescarson/adaption-math-worked-solutions-raw-aug/data.parquet")

Published by Carson Rodrigues (Hugging Face, Kaggle).

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