messages listlengths 2 2 |
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"role": "user",
"content": "At a convention, four experts on a certain topic were asked to choose one book each from a list of 20 books. Each expert knows exactly half of the authors (10 authors) and likes exactly half of them (5 authors). If an expert is randomly selected and then a book by one of their ... |
[
{
"role": "user",
"content": "Let A=(2,3,4,6,7,10,12,13) and (p,q,r,s,t,u,v,w) be distinct elements in A. What is the minimum possible value of pqrs+tuwu?\nPlease reason step by step, and put your final answer within \\boxed{{}}.\n"
},
{
"role": "assistant",
"content": "<think>\nOkay, so I need ... |
[
{
"role": "user",
"content": "The number $x$ can be expressed as a three-place decimal $0.abc,$ where $a, b,$ and $c$ represent digits, any of which could be zero. It is desired to approximate $x$ by a fraction whose numerator is 1 or 3 and whose denominator is an integer. The closest such fraction to $x$ i... |
[{"role":"user","content":"Find the maximum value of \n\\[abc + def\\]\nwhere $a, b, c, d, e, f$ are(...TRUNCATED) |
[{"role":"user","content":"In the following grid, each square is to be colored red, white, or blue, (...TRUNCATED) |
[{"role":"user","content":"Find all values of $x$ such that $x + \\lfloor x \\rfloor^2 = 22.5$.\n\n((...TRUNCATED) |
[{"role":"user","content":"A bookshelf contains 20 books, each written by a different author. If you(...TRUNCATED) |
[{"role":"user","content":"Find the largest positive integer that is not the sum of a positive integ(...TRUNCATED) |
[{"role":"user","content":"A nonzero polynomial with rational coefficients has all of the numbers \n(...TRUNCATED) |
[{"role":"user","content":"Given the right triangles XYZ and XZW, what is the length of segment YZ, (...TRUNCATED) |
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