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Given four bags containing an unlimited number of 1s, 4s, 7s, and 10s, what is the largest integer that cannot be formed as a sum using any combination of these numbers? | Okay, so I have this problem here: there are four bags with an unlimited number of 1s, 4s, 7s, and 10s. I need to find the largest integer that cannot be formed as a sum using any combination of these numbers. Hmm, interesting. Let me try to figure this out step by step.
First, I know that when dealing with problems l... | Given four bags containing an unlimited number of 1s, 4s, 7s, and 10s, we need to find the largest integer that cannot be formed as a sum using any combination of these numbers.
1. **Key Insight**: Since one of the numbers is 1, which is the smallest positive integer, we can form any number by combining 1s with other ... | 33,372 | math-ai/AutoMathText | <think>
Okay, so I have this problem here: there are four bags with an unlimited number of 1s, 4s, 7s, and 10s. I need to find the largest integer that cannot be formed as a sum using any combination of these numbers. Hmm, interesting. Let me try to figure this out step by step.
First, I know that when dealing with pr... | [
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"value": "Given four bags containing an unlimited number of 1s, 4s, 7s, and 10s, what is the largest integer that cannot be formed as a sum using any combination of these numbers?"
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"from": "gpt",
"value": "<think>\nOkay, so I have this problem here: there are four bags wi... | Search by Topic
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What Numbers Can We Make Now?
Stage: 3 and 4 Challenge Level:
Imagine we have four bags containing numbers from a sequence. What numbers can we make now?
Magic Squares II
Stage: 4 and 5
An ... | |
"Let \\((\\Sigma,g)\\) be a complete, simply connected Riemannian surface with curvature satisfying (...TRUNCATED) | "Okay, so I need to figure out how many points must be in the image of a one-harmonic map F from a c(...TRUNCATED) | "Given a complete, simply connected Riemannian surface \\((\\Sigma, g)\\) with curvature satisfying (...TRUNCATED) | 22,927 | mlfoundations-dev/gair_mathpile | "<think>\nOkay, so I need to figure out how many points must be in the image of a one-harmonic map F(...TRUNCATED) | [{"from":"human","value":"Let \\((\\Sigma,g)\\) be a complete, simply connected Riemannian surface w(...TRUNCATED) | null | |
"Given the matrices \n\n\\[\nA = \\begin{bmatrix} 1 & 2 \\\\ 3 & 4 \\end{bmatrix}, \\quad B = \\begi(...TRUNCATED) | "Okay, let's see. I need to compute AB - C where A, B, and C are given 2x2 matrices. Hmm, matrix ope(...TRUNCATED) | "To compute \\( AB - C \\) given the matrices \n\n\\[\nA = \\begin{bmatrix} 1 & 2 \\\\ 3 & 4 \\end{b(...TRUNCATED) | 35,878 | math-ai/AutoMathText | "<think>\nOkay, let's see. I need to compute AB - C where A, B, and C are given 2x2 matrices. Hmm, m(...TRUNCATED) | [{"from":"human","value":"Given the matrices \n\n\\[\nA = \\begin{bmatrix} 1 & 2 \\\\ 3 & 4 \\end{bm(...TRUNCATED) | "# 9.5 Matrices and matrix operations (Page 5/10)\n\n Page 5 / 10\n\n## Using a calculator to perf(...TRUNCATED) | |
Given $f\left(x\right)=\frac{3}{x}+2$, then $f^{-1}(1)=$____. | null | "Okay, so I need to find the inverse function of f(x) = 3/x + 2, and then evaluate that inverse func(...TRUNCATED) | "To find the inverse function \\( f^{-1}(x) \\) for \\( f(x) = \\frac{3}{x} + 2 \\), we start by set(...TRUNCATED) | null | AI-MO/NuminaMath-1.5 | "<think>\nOkay, so I need to find the inverse function of f(x) = 3/x + 2, and then evaluate that inv(...TRUNCATED) | [{"from":"human","value":"Given $f\\left(x\\right)=\\frac{3}{x}+2$, then $f^{-1}(1)=$____."},{"from"(...TRUNCATED) | null |
"Let \\( f(x) \\) be an integrable function on the interval \\( (a, b) \\). Given that \n\n\\[\n\\in(...TRUNCATED) | "Okay, let me try to work through this problem step by step. The problem says:\n\nGiven that \n\n\\[(...TRUNCATED) | "Given the equation:\n\n\\[\n\\int_a^b f(x) \\cdot (-\\pi) \\, dx = F(b) - \\frac{1}{F(a)}\n\\]\n\nw(...TRUNCATED) | 18,318 | ddrg/named_math_formulas | "<think>\nOkay, let me try to work through this problem step by step. The problem says:\n\nGiven tha(...TRUNCATED) | [{"from":"human","value":"Let \\( f(x) \\) be an integrable function on the interval \\( (a, b) \\).(...TRUNCATED) | null | |
"(if in this order around the circle), then $f_{16} f_{25} f_{34}+f_{15} f_{24} f_{36}+f_{14} f_{26}(...TRUNCATED) | null | "Okay, so I need to prove this inequality involving these products of f's arranged in a circle. The (...TRUNCATED) | "To prove the given inequality involving products of functions arranged around a circle, we start by(...TRUNCATED) | null | AI-MO/NuminaMath-1.5 | "<think>\nOkay, so I need to prove this inequality involving these products of f's arranged in a cir(...TRUNCATED) | [{"from":"human","value":"(if in this order around the circle), then $f_{16} f_{25} f_{34}+f_{15} f_(...TRUNCATED) | null |
"An ordered pair of non-negative integers $(m,n)$ is considered \"simple\" if their sum $m+n$ in bas(...TRUNCATED) | "To determine the number of simple ordered pairs of non-negative integers \\((m, n)\\) that add up t(...TRUNCATED) | "Okay, so I need to find the number of simple ordered pairs (m, n) such that their sum m + n equals (...TRUNCATED) | "To determine the number of simple ordered pairs \\((m, n)\\) such that \\(m + n = 2567\\) and their(...TRUNCATED) | 28,333 | MetaMath-AIME | "<think>\nOkay, so I need to find the number of simple ordered pairs (m, n) such that their sum m + (...TRUNCATED) | [{"from":"human","value":"An ordered pair of non-negative integers $(m,n)$ is considered \"simple\" (...TRUNCATED) | null |
"If $\\angle \\text{CBD}$ is a [right angle](https://artofproblemsolving.com/wiki/index.php/Right_an(...TRUNCATED) | null | "Okay, so I need to figure out the measure of angle ABC using the information that angle CBD is a ri(...TRUNCATED) | "Given that \\(\\angle \\text{CBD}\\) is a right angle, we need to determine the measure of \\(\\ang(...TRUNCATED) | null | OpenMathInstruct-AIME | "<think>\nOkay, so I need to figure out the measure of angle ABC using the information that angle CB(...TRUNCATED) | [{"from":"human","value":"If $\\angle \\text{CBD}$ is a [right angle](https://artofproblemsolving.co(...TRUNCATED) | null |
"Makenna is selling candy for her Softball Team. The box contains 25 milk chocolate bars, 25 dark ch(...TRUNCATED) | null | "Okay, so Makenna has this box of candy bars she's selling for her softball team. The question is as(...TRUNCATED) | "The box contains a total of 100 candy bars (25 + 25 + 25 + 25). Each type of chocolate bar (milk, d(...TRUNCATED) | null | TIGER-Lab/MathInstruct | "<think>\nOkay, so Makenna has this box of candy bars she's selling for her softball team. The quest(...TRUNCATED) | [{"from":"human","value":"Makenna is selling candy for her Softball Team. The box contains 25 milk c(...TRUNCATED) | null |
"In a community of 250 residents, each person is involved in at least one of the activities: gardeni(...TRUNCATED) | "To solve this problem, let’s define the following: \n\nLet:\\n- G = Number of residents who gard(...TRUNCATED) | "Okay, so I have this problem here about a community of 250 residents where each person is involved (...TRUNCATED) | "Given a community of 250 residents where each person is involved in at least one of gardening, cook(...TRUNCATED) | 6,652 | MetaMath-AIME | "<think>\nOkay, so I have this problem here about a community of 250 residents where each person is (...TRUNCATED) | [{"from":"human","value":"In a community of 250 residents, each person is involved in at least one o(...TRUNCATED) | null |
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