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"role": "user",
"content": "Suppose real numbers $a$, $b$, and $c$ are positive, and $ab + ac + bc + 2\\sqrt{5} = 6 - a^2$. Determine the minimum value of $2a + b + c$.\n\nA: $\\sqrt{5} - 1$\nB: $\\sqrt{5} + 1$\nC: $2\\sqrt{5} + 2$\nD: $2\\sqrt{5} - 2$",
"info": {
"source": "GeneralThought-Feb25... |
[
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"role": "user",
"content": "Your answer must contain exactly 3 bullet points. Use the markdown bullet points such as: * This is point 1. * Your response should contain at least 2 placeholders represented by square brackets, such as [address]. * Answer the following question: What are the key factors to co... |
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"content": "def get_histogram(input_list: list) -> dict:\n \"\"\"\n Takes a list of hashable elements and returns a dictionary representing the histogram of the input list.\n Keys of the dictionary are unique elements from the list and values are the counts of how often each eleme... |
[
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"role": "user",
"content": "On the circumference of a circle, three points are chosen randomly and independently. What is the probability that the triangle formed by these points is acute-angled?",
"info": {
"source": "openThoughts",
"reference_answer": null,
"test_case": null,
... |
[
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"role": "user",
"content": "from typing import List, Tuple\nimport itertools\n\ndef is_valid_permutation(perm: Tuple[int], k: int) -> bool:\n \"\"\"\n Check if the permutation is valid by ensuring the absolute difference\n between each adjacent element is at least k.\n\n >>> is_valid_permutati... |
[
{
"role": "user",
"content": "4. If the following conditions about a triangle are known, the one that cannot uniquely determine the shape of the triangle is ( ).\n(A) the ratio of two sides and the included angle\n(B) the ratio of the three altitudes\n(C) the ratio of the three medians\n(D) the ratio of one... |
[
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"role": "user",
"content": "from typing import List\n\ndef sort_colors(nums: List[int]) -> None:\n \"\"\" Sorts the given list nums in-place so that all 0s come first,\n followed by all 1s, then all 2s. Uses the Dutch National Flag algorithm.\n \n >>> nums = [2, 0, 2, 1, 1, 0]\n >>> sort_co... |
[{"role":"user","content":"In a given list, every element appears an even number of times except for(...TRUNCATED) |
[{"role":"user","content":"def is_palindromic(num):\n \"\"\"\n Check if the number is palindro(...TRUNCATED) |
[{"role":"user","content":"Allen flips a fair two sided coin and rolls a fair $6$ sided die with fac(...TRUNCATED) |
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