query: Question from pathfinder for Olympiad mathematics 2
positive_passages.docid: 148983
positive_passages.text: If $a$, $b$, $c$ are the roots of $x^3-6x^2+3x+1=0$, find all possible values of $a^2b+b^2c+c^2a$
negative_passages.docid: 88184
negative_passages.text: Finding the value of $k$ for parallel/orthogonal planes
negative_passages.docid: 61555
negative_passages.text: Rounding up to next power of 2
negative_passages.docid: 61745
negative_passages.text: How do people come up with difficult math Olympiad questions?
negative_passages.docid: 85832
negative_passages.text: Tough contest problem
negative_passages.docid: 22029
negative_passages.text: Solving modular arithmetic questions
negative_passages.docid: 105594
negative_passages.text: Fixed point, union of $\aleph_0, \aleph_{\aleph_0},\aleph_{\aleph_{\aleph_0}}\dots$ [see Noah's comment on notation]
negative_passages.docid: 112359
negative_passages.text: How to deal with a Pell's equation type problem with two primes
negative_passages.docid: 73287
negative_passages.text: Project Euler Question 14 (Collatz Problem)
negative_passages.docid: 132346
negative_passages.text: a linear algebra multiple choice problem
negative_passages.docid: 157717
negative_passages.text: What is a mathematical solution to this problem? (Project Euler #106)
negative_passages.docid: 66423
negative_passages.text: Previous year Olympiad problem (polynomials)
negative_passages.docid: 101751
negative_passages.text: The number of words that can be made by permuting the letters of _MATHEMATICS_ is
negative_passages.docid: 132826
negative_passages.text: What is the math behind the game Spot It?
negative_passages.docid: 156247
negative_passages.text: Question about permutations and cycles (Groups and Symmetries)
negative_passages.docid: 55186
negative_passages.text: How does A* pathfinding work?
negative_passages.docid: 26898
negative_passages.text: Trouble solving two number theoretical problems