prompt list | ground_truth string |
|---|---|
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 57.4 kPa |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | [Supplier J: 14.60%, Supplier K: 12.17%, Supplier L: 8.11%, Supplier M: 13.69%] |
[
{
"content": "Express the product $20! \\cdot 21! \\cdot 22! \\cdot \\cdots \\cdot 28!$ in the form $m \\cdot n^3$, where $m$ and $n$ are positive integers, and $m$ is not divisible by the cube of any prime. Find the value of $m$. \\( \\boxed{m} \\)",
"role": "user"
}
] | 825 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | $19,101.78 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 9.825% |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 192 m |
[
{
"content": "Suppose that $f(x)$ is a linear function satisfying the equation $f(x) = 4f^{-1}(x) + 6$. Given that $f(1) = 4$, find $f(2)$.",
"role": "user"
}
] | 6 |
[
{
"content": "A function \\( f \\) satisfies the condition \\( f[f(x) - e^x] = e + 1 \\) for all \\( x \\in \\Bbb R \\). Find \\( f(\\ln 2) \\).",
"role": "user"
}
] | 3 |
[
{
"content": "How many distinct necklaces can be formed using 20 beads, each of a different color?",
"role": "user"
}
] | \dfrac{19!}{2} |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 20.346e7 s |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | $623,570 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 8.24 m/s |
[
{
"content": "Let $A$ be a countable set dense in $[0,1]$. Suppose $f(x)=0$ for all $x\\in A$. Does this imply that $f(x)=0$ almost everywhere in $[0,1]$? Provide a justification for your answer.",
"role": "user"
}
] | No |
[
{
"content": "Given an irrational number \\(x \\in \\mathbb{R}\\setminus \\mathbb{Q}\\), determine if there exists a strictly increasing function \\(T: \\mathbb{N} \\to \\mathbb{N}\\) such that \\(\\{T(n) x\\} \\to 0\\) as \\(n \\to \\infty\\), where \\(\\{\\cdot\\}\\) denotes the fractional part.",
"role":... | Yes |
[
{
"content": "Find the value of $x$ such that $x^x = 2^{2048}$. Express your answer in terms of powers of 2.",
"role": "user"
}
] | 2^8 |
[
{
"content": "Determine which of the following Möbius transformations maps the open unit disc onto the right half-plane:\n\n(a) \\( f(z)=\\frac{z-i}{z+i} \\)\n\n(b) \\( f(z)=\\frac{z-1}{z+1} \\)\n\n(c) \\( f(z)=\\frac{1+z}{1-z} \\)\n\n(d) \\( f(z)=i\\left(\\frac{1+z}{1-z}\\right) \\)",
"role": "user"
}
] | C |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 83.609 J |
[
{
"content": "Determine whether the limit \\( \\lim_{x \\to 0} \\frac{1}{x} \\int_{0}^{x} \\left| \\cos \\left(\\frac{1}{t}\\right) \\right| \\, dt \\) exists. If it exists, find its value.",
"role": "user"
}
] | \dfrac{2}{\pi} |
[
{
"content": "Let \\(a_n\\ (n\\geq 1)\\) be the value for which the integral \\(\\int_x^{2x} e^{-t^n}dt\\ (x\\geq 0)\\) is maximal. Determine \\(\\lim_{n\\to\\infty} \\ln a_n.\\)",
"role": "user"
}
] | -\ln 2 |
[
{
"content": "Evaluate the integral by reversing the order of integration: \\[ \\int_{0}^{\\sqrt{3\\pi}}\\int_{y}^{\\sqrt{3\\pi}}\\cos 7x^2\\;dxdy. \\]",
"role": "user"
}
] | 0 |
[
{
"content": "Determine whether the condition \\( \\sum_{a \\in A} \\frac{1}{a} < \\infty \\) implies that \\( \\lim\\sup_{n \\to \\infty} \\frac{|A \\cap \\{1, \\ldots, n\\}|}{n} = 0 \\) for a subset \\( A \\) of the positive integers \\( \\mathbb{N} \\).",
"role": "user"
}
] | Yes |
[
{
"content": "Evaluate the line integral \\(\\int_C g∇g \\cdot \\,d\\mathbf{r}\\) where \\(g(x,y,z)=xy\\sin(x^2+z^2)\\) and \\(C\\) is the ellipse formed by the intersection of the paraboloid \\(z=x^2+y^2\\) and the plane \\(2x+y-z=1\\).",
"role": "user"
}
] | 0 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 0.7609 Hz |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 6644000 |
[
{
"content": "Minimize the function \\( f = x^4 + 2y^4 + 3z^4 \\) subject to the constraint \\( x^2 + y^2 + z^2 = 1 \\).",
"role": "user"
}
] | \dfrac{6}{11} |
[
{
"content": "Evaluate \\( \\lim_{n \\rightarrow \\infty} \\int_0^n \\left(1 + \\frac{-x}{n}\\right)^n \\cos\\left(\\frac{x}{\\sqrt{n}}\\right) e^{x/2} \\, dx \\).",
"role": "user"
}
] | 2 |
[
{
"content": "Determine whether the following statement is true or false: If an automorphism of a finite group fixes more than half of the group's elements, then the automorphism must be the identity function.",
"role": "user"
}
] | True |
[
{
"content": "Find the value of \\( \\lfloor{100N}\\rfloor \\) where \\( N = \\lim\\limits_{a\\,\\rightarrow\\,\\infty}\\sum\\limits_{x=-a}^{a}\\frac{\\sin x}{x} \\).",
"role": "user"
}
] | 314 |
[
{
"content": "Calculate the sum of the infinite series \\( \\sum\\limits_{n=1}^{\\infty}\\frac{n^3}{n!} \\).",
"role": "user"
}
] | 5e |
[
{
"content": "Compute \\( \\lim_{n \\to \\infty} \\mathbb{P}\\{S_n \\leq n\\} \\) where \\( S_n = X_1 + \\ldots + X_n \\) and each \\( X_i \\sim \\text{Poisson}(1) \\) are independent and identically distributed random variables.",
"role": "user"
}
] | \dfrac{1}{2} |
[
{
"content": "Find the value of the convergent series \\( \\sum_{n=1}^{+\\infty} \\frac{e^{-n}}{n} \\).",
"role": "user"
}
] | -\ln\left(1 - \frac{1}{e}\right) |
[
{
"content": "Suppose $y_1, y_2, \\ldots, y_m$ are independent and identically distributed random variables with a uniform distribution on the interval $(c, d)$, where $0 < c < d$. Find the expected value of $\\frac{y_1}{\\sum_{j=1}^{m} y_j}$.",
"role": "user"
}
] | \dfrac{1}{m} |
[
{
"content": "Find the finite value of the sum \\( \\sum_{n=2}^{\\infty} \\frac{\\binom{n}{2}}{4^n} \\) using generating functions.",
"role": "user"
}
] | \dfrac{4}{27} |
[
{
"content": "If $a$ and $b$ are integers such that $x^2 - x - 1$ is a factor of $ax^3 + bx^2 + 1,$ find $b.$",
"role": "user"
}
] | -2 |
[
{
"content": "Let $z_N$ be the complex $N$-th root of unity. Given $N = r \\cdot t$, let $H^\\bot$ be the set of multiples of $t$ in $\\mathbb{Z}_N$. Prove that for any $x \\notin H^\\bot$, the following holds: \\[ \\sum_{i=0}^{t-1} z_N^{rxi} = 0. \\]",
"role": "user"
}
] | 0 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | $1,895.50 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | $2,693,000 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | The initial velocity is 15.652 m/s and the angle is 26.565 degrees |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 1.2e8 m/s |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 1.005e15 Hz |
[
{
"content": "Show that the sequence \\( b_n = \\frac{\\int_{0}^\\epsilon \\cos^n(x) \\, dx}{\\int_{\\epsilon}^{1/2} \\cos^n(x) \\, dx} \\) tends to infinity as \\( n \\to \\infty \\) for every \\( \\epsilon \\) such that \\( \\frac{1}{2} > \\epsilon > 0 \\).",
"role": "user"
}
] | \infty |
[
{
"content": "Calculate the limit \\(\\lim\\limits_{x \\to 1} \\left( \\frac{x}{x - 1} - \\frac{1}{\\ln x} \\right)\\) without using L'Hôpital's rule or Taylor series.",
"role": "user"
}
] | \dfrac{1}{2} |
[
{
"content": "Let \\(f(x)=\\int_{0}^{x}|\\log_{2}(\\log_{3}(\\log_{4}(\\cos t+a)))|dt\\). Determine the smallest integer value of \\(a\\) such that \\(f(x)\\) is increasing for all \\(x \\in \\mathbb{R}\\).",
"role": "user"
}
] | 6 |
[
{
"content": "Evaluate the integral \\( \\int_S \\vec{V} \\cdot \\hat{n} \\, dS \\) using the Divergence Theorem, where \\( \\vec{V} = x^2z\\hat{i} + y\\hat{j} - xz^2\\hat{k} \\). The surface \\( S \\) is the boundary of the region bounded by \\( x^2 + y^2 = z \\) and \\( z = 4y \\).",
"role": "user"
}
] | 8\pi |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | $29.30 million |
[
{
"content": "Does there exist a quasisimple group $G$ and an odd prime $p$ such that $G$ has cyclic Sylow $p$-subgroups and a weakly real element of $p$-power order?",
"role": "user"
}
] | Yes |
[
{
"content": "Simplify the infinite series: \\[ \\sum_{n=1}^{\\infty} \\frac{3 \\cdot 5 \\cdot 7 \\cdots (2n+1)}{6 \\cdot 9 \\cdot 12 \\cdots (3n+3)} \\]",
"role": "user"
}
] | 3\sqrt{3} - 4 |
[
{
"content": "Let $x,$ $y,$ and $z$ be real numbers such that $x + y + z = 0$ and $xyz = 2.$ Find the maximum value of\n\\[x^3 y + y^3 z + z^3 x.\\]",
"role": "user"
}
] | -9 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 4.68e6 dpm |
[
{
"content": "Determine the optimal distribution of a 12-ton potato order among three farms to minimize the total cost, given the following constraints: The first farm charges 4 rubles per ton and can load 1 ton per minute with a maximum supply of 10 tons per day. The second farm charges 3 rubles per ton, loads... | \left( \dfrac{2}{3}, \dfrac{16}{3}, 6 \right) |
[
{
"content": "Determine the equation of a plane that contains the line of intersection of the planes $x + y - z = 1$ and $2x - y + 3z = 2$, and is perpendicular to the plane $3x - 2y + z = 4$. Provide your answer in the form $ax + by + cz = d$.",
"role": "user"
}
] | x + y - z = 1 |
[
{
"content": "Given the vector field $\\textbf{F} = (y + z)i + (x + z)j + (x + y)k$, find the potential function $f(x,y,z)$ such that $\\nabla f = \\textbf{F}$.",
"role": "user"
}
] | xy + xz + yz |
[
{
"content": "Let \\(\\alpha\\), \\(\\beta\\), and \\(\\gamma\\) be real numbers satisfying \\(\\alpha + \\beta + \\gamma = 2\\) and \\(\\alpha \\beta \\gamma = 4\\). Determine the minimum value of \\(|\\alpha| + |\\beta| + |\\gamma|\\).",
"role": "user"
}
] | 6 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 2.197e5 V |
[
{
"content": "Given real numbers \\(a_{1}, a_{2}, \\ldots, a_{7}\\) such that \\(a_{1} = a_{7} = 0\\), determine if there is always an index \\(k \\leq 5\\) such that the inequality \\(a_{k} + a_{k+2} \\leq a_{k+1} \\sqrt{3}\\) holds.",
"role": "user"
}
] | Yes |
[
{
"content": "Given a positive integer \\(n\\) and an integer \\(m\\), find the number of ways to choose integers \\(i, j, k\\) such that \\(1 < i, j, k < m\\) and the expression \\((((n \\mod i) \\mod j) \\mod k) \\mod n\\) achieves its maximum value \\(L\\). Assume \\(L = n - 1\\).",
"role": "user"
}
] | 0 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | Southern direction |
[
{
"content": "Evaluate the limit using Taylor expansion: \\[ \\lim_{x\\to 0}\\frac{\\sinh x^4-x^4}{(x-\\sin x)^4} \\]",
"role": "user"
}
] | 216 |
[
{
"content": "Determine whether the Weyl group $W(D_n)$ is a quotient of the Weyl group $W(B_n)$. Justify your answer.",
"role": "user"
}
] | Yes |
[
{
"content": "Find all polynomials \\( P(x) \\) with real coefficients such that \\( P(0) = 0 \\) and \\( P(x^2 + 1) = P(x)^2 + 1 \\) for all real numbers \\( x \\).",
"role": "user"
}
] | x |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 2623.86 kg |
[
{
"content": "Given ten points \\(P_1, \\ldots, P_{10}\\) on the unit circle, determine the largest possible value of the sum \\(\\sum_{1\\le i<j\\le 10} |P_i-P_j|^2\\).",
"role": "user"
}
] | 100 |
[
{
"content": "Let $Q(x)=a_0+a_1x+\\dots+a_nx^n$ be a polynomial with integer coefficients, and $0\\le a_i<3$ for all $0\\le i\\le n$.\n\nGiven that $Q(\\sqrt{3})=20+17\\sqrt{3}$, compute $Q(2)$.",
"role": "user"
}
] | 86 |
[
{
"content": "Let $U$ be a bounded open set in $\\mathbb{R}^N$, and let $f_n: U \\rightarrow \\mathbb{R}$ be a sequence of positive Lebesgue-measurable functions such that $\\int_U f_n \\to 1$. Let $b: U \\rightarrow \\mathbb{R}$ be a continuous function such that $0 < b < 1$ in $U$. Determine whether $\\int_U ... | Yes |
[
{
"content": "Let $R$ be a $K$-algebra and $\bar{\\delta}: R[x] \\to N^{-1}R[x]$ be an extension of a $K$-derivation $\\delta: R \\to R$ such that $\\bar{\\delta}(x) = \\alpha$ for some $\\alpha \\in N^{-1}R[x]$. Show that there is precisely one derivation $d: N^{-1}R[x] \\to N^{-1}R[x]$ extending $\\bar{\\delt... | d\left(\frac{f_1}{f_2}\right) = \frac{f_2 \bar{\delta}(f_1) - f_1 \bar{\delta}(f_2)}{f_2^2} |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 5.66% |
[
{
"content": "How many two-digit positive integers have at least one 7 as a digit?",
"role": "user"
}
] | 18 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 35421.39 seconds |
[
{
"content": "An archipelago consists of \\( N \\geq 7 \\) islands. Each pair of islands is connected by at most one bridge. No more than 5 bridges lead from each island, and among any 7 islands, there are always two that are connected by a bridge. Determine the largest possible value of \\( N \\).",
"role"... | 36 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 3.82 days |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 9.9 |
[
{
"content": "How many ways are there to number the 8 vertices of a cube using the numbers 1 to 8 such that no two consecutive numbers are adjacent on the cube, considering 1 and 8 to be consecutive?",
"role": "user"
}
] | 480 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | Micropreneur |
[
{
"content": "Suppose $X_1, X_2, \\ldots, X_n$ are independent and uniformly distributed random variables on the interval $[0,1]$. Find the limit \\( \\lim_{n\\to\\infty} \\mathbb{P}\\left(\\sum_{i=1}^n X_i \\leq \\frac{n}{2}\\right) \\).",
"role": "user"
}
] | \dfrac{1}{2} |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 2039 mL |
[
{
"content": "Find the arc length of the curve defined by \\( x^{\\frac{2}{3}} + y^{\\frac{2}{3}} = 1 \\). Use symmetry with respect to the line \\( y = x \\) to simplify your calculations.",
"role": "user"
}
] | 6 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 360.0 Hz |
[
{
"content": "Evaluate the sum \\( \\sum_{k=1}^{2n-1} \\frac{(2n-1)!}{(k-1)!(2n-k)!} \\frac{(-1)^{k-1}}{2k} \\) using the residue theorem.",
"role": "user"
}
] | \dfrac{1}{2n} |
[
{
"content": "Find the limit of the series as \\( n \\) approaches infinity:\n\\[ x(n) = \\sum_{k=1}^n \\frac{k^2}{n^3+k^2} \\]",
"role": "user"
}
] | \dfrac{1}{3} |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 5.61 cm |
[
{
"content": "Calculate the limit: \\[ \\lim _{x \\rightarrow 0} \\frac{\\sqrt[3]{1+\\operatorname{arctg} 4 x}-\\sqrt[3]{1-\\operatorname{arctg} 4 x}}{\\sqrt{1-\\arcsin 3 x}-\\sqrt{1+\\operatorname{arctg} 3 x}} \\]",
"role": "user"
}
] | -\dfrac{8}{9} |
[
{
"content": "Determine whether any interval of real numbers, such as \\([5, 6]\\), has the same cardinality as the entire set of real numbers \\(\\mathbb{R}\\). Justify your answer.",
"role": "user"
}
] | Yes |
[
{
"content": "Consider a function $g:[0,1]\\rightarrow \\mathbb{R}$ that satisfies the following conditions: (1) $g$ is bounded and (2) $g$ is integrable on $[a,1]$ for any $0<a<1$. Determine whether the improper integral $\\int_0^1 g(x)dx$ necessarily exists.",
"role": "user"
}
] | Yes |
[
{
"content": "Evaluate the probability \\( P(X \\le 3Y \\le 4Z) \\) where \\( X, Y, \\) and \\( Z \\) are independent and identically distributed exponential random variables with parameter \\( \\lambda \\).",
"role": "user"
}
] | \dfrac{48}{133} |
[
{
"content": "Find the radius of convergence of the series \\( \\sum^{\\infty}_{n=1} \\frac{n!z^n}{n^n} \\).",
"role": "user"
}
] | e |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 257.9 kJ |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | T_i = min{T_{i,r} = min(T_{i-1,b}, T_{i-1,g}) + C_{i,r}, T_{i,b} = min(T_{i-1,r}, T_{i-1,g}) + C_{i,b}, T_{i,g} = min(T_{i-1,r}, T_{i-1,b}) + C_{i,g}} where C_{i,r}, C_{i,b}, and C_{i,g} are the costs of painting the i-th house in red, blue, and green, respectively. The base case is T_0 = 0 for any color. |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | financing activity |
[
{
"content": "Evaluate the integral \\( \\int\\int_{R} y^2 \\, dx \\, dy \\) using polar coordinates, where \\( R \\) is the region in the first quadrant bounded by the curves \\( x^2 + y^2 = 16 \\) and \\( x^2 + y^2 = 4x \\).",
"role": "user"
}
] | 14\pi |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 1.42 m |
[
{
"content": "Evaluate the double integral \\( \\iint_{[0,1]^2} (1+x^2+y^2)^{-3/2} \\, dx \\, dy \\).",
"role": "user"
}
] | \dfrac{\pi}{6} |
[
{
"content": "Find the maximum value of the expression \\( \\sin{x} + \\sin{y} - \\sin{(x+y)} + \\sqrt{3}(\\cos{x} + \\cos{y} + \\cos{(x+y)}) \\).",
"role": "user"
}
] | 3\sqrt{3} |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 51.03 m/s |
[
{
"content": "Calculate $H_4(S^2 \\times S^2; \\mathbb{Z}_2)$ using the Kunneth formula, given that $H_i(S^2; \\mathbb{Z}_2) = \\mathbb{Z}_2$ for $i = 0, 2$ and $0$ otherwise.",
"role": "user"
}
] | \mathbb{Z}_2 |
[
{
"content": "Let $O$ and $H$ denote the circumcenter and orthocenter of triangle $ABC,$ respectively. If $AO = AH,$ then enter all possible values of $\\angle A$ (in degrees), separated by commas.",
"role": "user"
}
] | 60^\circ, 120^\circ |
[
{
"content": "In a non-equilateral triangle $\\triangle ABC$, the heights $AP$ and $CQ$ are drawn, along with the interior angle bisector $BD$. Given that \\( \\frac{1}{AP} + \\frac{1}{CQ} = \\frac{2}{BD} \\), find the measure of angle $\\angle ABC$. Express your answer in degrees.",
"role": "user"
}
] | 60 |
[
{
"content": "Determine whether the following statement is true for any connected metric space X: For any two points x and y in X and any positive number ε, there exists a finite sequence of points in X connecting x and y such that the distance between consecutive points is less than ε.",
"role": "user"
}... | True |
[
{
"content": "Given a number \\( N = 25 \\) and a number of steps \\( K = 2 \\), determine how many distinct numbers can be obtained by repeatedly multiplying \\( N \\) by one of its divisors at each step. For example, when \\( K = 1 \\), the possible numbers are 25, 125, and 625. When \\( K = 2 \\), the possib... | 7 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 6.064e-4 V |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 79.54 g |
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