instruction_seed stringlengths 51 1.88k | source stringclasses 2
values | difficulty int64 10 10 | difficulty_reasoning stringlengths 247 773 | __original_row_idx int64 0 999 | r1_distill_70b_response stringlengths 1.56k 72.8k | conversations listlengths 2 2 |
|---|---|---|---|---|---|---|
Jessica was trying to win a gift card to her favorite store. To win, she had to guess the total number of red & white jelly beans in the bowl of mixed color jelly beans. She figured it would take three bags of jelly beans to fill up the fishbowl. She assumed that each bag of jellybeans had a similar distribution of col... | tiger_math | 10 | This problem requires advanced combinatorial reasoning and the ability to estimate based on complex relationships between the distributions and sizes of jellybeans, integrating statistical inference with significant problem-solving skills. It involves understanding ratios, estimation, and possibly even principles of un... | 38 | <think>
First, I'll calculate the volume of each color and size of the jellybeans in the first bag. Since small jellybeans take up 0.6 times the space of a medium jellybean, I'll multiply the count of small jellybeans by 0.6 and add that to the count of medium jellybeans for each color.
Next, I'll determine the total ... | [
{
"from": "human",
"value": "Jessica was trying to win a gift card to her favorite store. To win, she had to guess the total number of red & white jelly beans in the bowl of mixed color jelly beans. She figured it would take three bags of jelly beans to fill up the fishbowl. She assumed that each bag of jel... |
Evaluate
\[\prod_{k = 1}^{10} \prod_{j = 1}^{12} (e^{2 \pi ji/13} - e^{2 \pi ki/11}).\] | tiger_math | 10 | This problem involves evaluating a double product of complex exponentials, which requires deep knowledge of roots of unity, advanced properties of complex functions, and likely some sophistication with symmetric functions in multiple variables. Such problems are typically found at the highest competition levels, which ... | 3 | <think>
Alright, so I've got this problem to evaluate the product:
\[
\prod_{k = 1}^{10} \prod_{j = 1}^{12} (e^{2 \pi ji/13} - e^{2 \pi ki/11}).
\]
Wow, that seems pretty complex with all those exponents and products. Let me try to break it down step by step.
First off, I notice that both products are over roots of ... | [
{
"from": "human",
"value": "Evaluate\n\\[\\prod_{k = 1}^{10} \\prod_{j = 1}^{12} (e^{2 \\pi ji/13} - e^{2 \\pi ki/11}).\\]"
},
{
"from": "gpt",
"value": "<think>\nAlright, so I've got this problem to evaluate the product:\n\n\\[\n\\prod_{k = 1}^{10} \\prod_{j = 1}^{12} (e^{2 \\pi ji/13} - e^{2 ... |
Given a positive integer $n$, it can be shown that every complex number of the form $r+si$, where $r$ and $s$ are integers, can be uniquely expressed in the "base" $-n+i$ using the integers $1,2,\ldots,n^2$ as "digits." That is, the equation\[r+si=a_m(-n+i)^m+a_{m-1}(-n+i)^{m-1}+\cdots +a_1(-n+i)+a_0\]is true for a uni... | tiger_math | 10 | This problem is highly advanced, requiring a deep understanding of complex numbers, number bases, and their unique representations. It not only involves complex manipulations but also insights into the limitations and properties of representations in non-standard bases. Such concepts are typically encountered at a high... | 26 | <think>
Alright, so I've got this problem here where I need to find all integers \( k + 0i \) that can be expressed as a three-digit number in base \(-2 + i\). That is, \( k = (a_2a_1a_0)_{-2+i} \) where each digit \( a_2, a_1, a_0 \) is from 0 to 4 (since \( n = 2 \), so \( n^2 = 4 \)), and \( a_2 \neq 0 \). Then, I n... | [
{
"from": "human",
"value": "Given a positive integer $n$, it can be shown that every complex number of the form $r+si$, where $r$ and $s$ are integers, can be uniquely expressed in the \"base\" $-n+i$ using the integers $1,2,\\ldots,n^2$ as \"digits.\" That is, the equation\\[r+si=a_m(-n+i)^m+a_{m-1}(-n+i)... |
A mixture of 2 moles of NaHSO3, 2 moles of HCl, 1 mole of Na2SO3, and 0.5 moles of H2O2 are reacted to form various products including SO2 gas. The following reactions may take place:
1) NaHSO3 + HCl β NaCl + H2O + SO2
2) Na2SO3 + 2 HCl β 2 NaCl + H2O + SO2
3) NaHSO3 + H2O2 β NaHSO4 + H2O
Calculate the theoretical yi... | tiger_math | 10 | The problem involves complex chemical reactions and stoichiometry requiring a thorough understanding of reaction mechanisms, limiting reagents, and the calculation of theoretical and percent yields. This is typically at a graduate level in chemistry, thus I rated it a 10, as it combines higher-level chemistry concepts ... | 82 | <think>
Okay, so I have this chemistry problem here, and it's about finding the theoretical yield of SO2 gas from a mixture of different chemicals. The problem also asks me to identify the limiting reagent and calculate the percent yield if the actual yield is 1.5 moles. Hmm, that sounds a bit involved, but let me brea... | [
{
"from": "human",
"value": "A mixture of 2 moles of NaHSO3, 2 moles of HCl, 1 mole of Na2SO3, and 0.5 moles of H2O2 are reacted to form various products including SO2 gas. The following reactions may take place:\n\n1) NaHSO3 + HCl β NaCl + H2O + SO2\n2) Na2SO3 + 2 HCl β 2 NaCl + H2O + SO2\n3) NaHSO3 + H2O2... |
In a cricket one-day match, taking into account varying number of balls per over (e.g., 6, 8, or 10 balls per over), specific rules for scoring such as batting powerplay and field restrictions, and incorporating real-life player statistics, what is the maximum number of runs that a batsman can score in an ideal case sc... | tiger_math | 10 | The problem requires a deep understanding of the complex rules of cricket, including scoring under various conditions and player statistics. Additionally, it involves high-level strategic thinking to maximize runs, integrating multiple variables in a real-world scenario, which is exceedingly challenging even for expert... | 79 | <think>
Okay, so I need to figure out the maximum number of runs a batsman can score in an ideal scenario in a one-day cricket match, considering all the variables like different balls per over, powerplays, field restrictions, and real player stats. Hmm, let me break this down.
First, what are the typical rules in an ... | [
{
"from": "human",
"value": "In a cricket one-day match, taking into account varying number of balls per over (e.g., 6, 8, or 10 balls per over), specific rules for scoring such as batting powerplay and field restrictions, and incorporating real-life player statistics, what is the maximum number of runs tha... |
In the context of field theory, let \( K \) be a field, and consider two proofs demonstrating that if \( x \neq 0 \) and \( xy = xz \), then \( y = z \).
1. By applying the field axioms and using the existence of the multiplicative inverse, derive the conclusion \( y = z \) directly from the equation \( xy = xz \).
... | automath | 10 | This problem is assigned a difficulty of 10 because it involves higher-level abstract reasoning within the field of mathematics, particularly field theory and proof construction. It expects a deep understanding of mathematical axioms and the ability to manipulate abstract concepts effectively, traits characteristic of ... | 175 | <think>
Okay, so I'm trying to figure out two different proofs that show if x isn't zero and xy equals xz, then y must equal z in a field K. I remember that a field has certain properties like every non-zero element has a multiplicative inverse, and operations like addition and multiplication are commutative and associ... | [
{
"from": "human",
"value": "In the context of field theory, let \\( K \\) be a field, and consider two proofs demonstrating that if \\( x \\neq 0 \\) and \\( xy = xz \\), then \\( y = z \\). \n\n1. By applying the field axioms and using the existence of the multiplicative inverse, derive the conclusion \\(... |
A major airplane manufacturer announced the sale of various aircraft types to multiple international customers: 150 small airliners (Type A), 100 propeller-driven regional aircraft (Type B), 75 medium-sized airliners (Type C), and 60 large airliners (Type D). The base price for each aircraft is as follows: Type A - $12... | tiger_math | 10 | This problem involves multiple complex financial considerations and requires advanced mathematical reasoning. It combines elements such as percentage calculations, variable costs based on flight hours, and variable tax rates, all of which need a comprehensive understanding of both mathematics and the financial implicat... | 41 | <think>
Okay, so I need to figure out the percentage of the company's income that comes from medium and large airliners, which are Types C and D. The problem says I have to consider discount rates, exchange rate fluctuations, maintenance and running costs, and varying tax rates over a two-year period. Hmm, this seems a... | [
{
"from": "human",
"value": "A major airplane manufacturer announced the sale of various aircraft types to multiple international customers: 150 small airliners (Type A), 100 propeller-driven regional aircraft (Type B), 75 medium-sized airliners (Type C), and 60 large airliners (Type D). The base price for ... |
"Calculate the equilibrium constant (K) of the reaction between H2CO3 and its dissociation products (...TRUNCATED) | tiger_math | 10 | "The problem involves calculating the equilibrium constant of a chemical reaction, which requires kn(...TRUNCATED) | 85 | "<think>\nOkay, so I need to calculate the equilibrium constant (K) for the dissociation of carbonic(...TRUNCATED) | [{"from":"human","value":"Calculate the equilibrium constant (K) of the reaction between H2CO3 and i(...TRUNCATED) |
"Find the number of functions $f : \\mathbb{R} \\to \\mathbb{R}$ such that\n\\[f(xy) + f(xz) - f(x)(...TRUNCATED) | tiger_math | 10 | "The problem involves finding functions that satisfy a specific inequality for all real numbers. Suc(...TRUNCATED) | 126 | "<think>\nOkay, I have this problem where I need to find the number of functions \\( f : \\mathbb{R}(...TRUNCATED) | [{"from":"human","value":"Find the number of functions $f : \\mathbb{R} \\to \\mathbb{R}$ such that(...TRUNCATED) |
"Consider the function $f: \\mathbb{R} \\to \\mathbb{R}$, where $f(f(x) - y) = f(x) + f(f(y) - f(-x)(...TRUNCATED) | tiger_math | 10 | "The problem involves a complex functional equation that requires deep understanding and advanced te(...TRUNCATED) | 121 | "<think>\nAlright, so I've come across this functional equation problem, and I want to figure it out(...TRUNCATED) | [{"from":"human","value":"Consider the function $f: \\mathbb{R} \\to \\mathbb{R}$, where $f(f(x) - y(...TRUNCATED) |
End of preview. Expand in Data Studio
README.md exists but content is empty.
- Downloads last month
- 8