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• 2007 AMC 12A Problems/Problem 6
  ...cate|[[2007 AMC 12A Problems|2007 AMC 12A #6]] and [[2007 AMC 10A Problems/Problem 8|2007 AMC 10A #8]]}} ==Problem==
  2 KB (265 words) - 00:20, 30 October 2022
• 2005 AMC 12A Problems/Problem 6
  == Problem == (\mathrm {A}) \ 4 \qquad (\mathrm {B}) \ 5 \qquad (\mathrm {C})\ 6 \qquad (\mathrm {D}) \ 7 \qquad (\mathrm {E})\ 8
  1,006 bytes (166 words) - 21:18, 3 July 2013
• 2006 AIME II Problems/Problem 6
  == Problem == pair Ap = (0, (3 - sqrt(3))/6);
  7 KB (1,067 words) - 12:23, 8 April 2024
• 1988 IMO Problems/Problem 6
  ==Problem==
  4 KB (720 words) - 12:26, 7 April 2024
• 1961 IMO Problems/Problem 6
  ==Problem== ...riangle's vertices, we have <math>G=\frac{1}{3}\left(L+M+N\right)=\frac{1}{6}\left(A+B+C+A^\prime+B^\prime+C^\prime\right)</math>. It is clear now that
  2 KB (301 words) - 23:29, 18 July 2016
• 1960 IMO Problems/Problem 6
  ==Problem== <cmath>W_2 = 6(u^2 - 1)</cmath>
  7 KB (1,214 words) - 18:49, 29 January 2018
• 2004 AMC 12A Problems/Problem 6
  ==Problem==
  1 KB (139 words) - 02:10, 30 December 2020
• 2007 AMC 10A Problems/Problem 6
  == Problem == #<math>\frac{70 - 66}{66} \approx 6\%</math>
  2 KB (211 words) - 22:55, 2 June 2023
• 2002 AMC 12B Problems/Problem 6
  {{duplicate|[[2002 AMC 12B Problems|2002 AMC 12B #6]] and [[2002 AMC 10B Problems|2002 AMC 10B #10]]}} == Problem ==
  3 KB (457 words) - 14:53, 17 August 2023
• 1976 IMO Problems/Problem 6
  == Problem ==
  3 KB (531 words) - 16:30, 29 January 2021
• 2001 AMC 12 Problems/Problem 6
  {{duplicate|[[2001 AMC 12 Problems|2001 AMC 12 #6]] and [[2001 AMC 10 Problems|2001 AMC 10 #13]]}} == Problem ==
  2 KB (340 words) - 03:02, 28 June 2023
• 2008 AMC 12A Problems/Problem 6
  ...cate|[[2008 AMC 12A Problems|2008 AMC 12A #6]] and [[2008 AMC 10A Problems/Problem 8|2008 AMC 10A #8]]}} ==Problem ==
  2 KB (240 words) - 19:53, 4 June 2021
• 2008 AMC 12B Problems/Problem 6
  ==Problem==
  1 KB (165 words) - 14:18, 16 February 2021
• 2008 AIME I Problems/Problem 6
  == Problem == ...ffect divisibility by <math>67</math>). The second row will be <math>2, 4, 6, \cdots , 98</math>, the third row will be <math>3, 5, \cdots, 97</math>, a
  3 KB (509 words) - 17:21, 22 March 2018
• Mock AIME 1 2007-2008 Problems/Problem 6
  2 KB (288 words) - 17:35, 6 May 2024
• 2008 AIME II Problems/Problem 6
  == Problem ==
  1 KB (223 words) - 23:34, 4 July 2013
• 2006 Alabama ARML TST Problems/Problem 6
  ==Problem== ...loor x \rfloor+\{y\} +z+\{x\}+y +\lfloor z \rfloor=x+x+y+y+z+z=2(x+y+z)=45.6</math>
  862 bytes (139 words) - 12:13, 20 January 2018
• 2008 AMC 10B Problems/Problem 6
  ==Problem==
  2 KB (317 words) - 18:09, 12 April 2024
• 2008 AMC 10A Problems/Problem 6
  ==Problem== ...athrm{(A)}\ 3\qquad\mathrm{(B)}\ 4\qquad\mathrm{(C)}\ 5\qquad\mathrm{(D)}\ 6\qquad\mathrm{(E)}\ 7</math>
  1 KB (209 words) - 22:01, 2 September 2020
• 2008 USAMO Problems/Problem 6
  == Problem == ...ion]] and <math>f(v) = 1</math> otherwise (this corresponds, in the actual problem, to putting a mathematician in the first or second room). Then look at <mat
  13 KB (2,414 words) - 14:37, 11 July 2016

Page text matches

• Functional equation
  ...function: <math>f(x) = x^2 + 6</math>. The function <math>g(x) = \sqrt{x-6}</math> has the property that <math>f(g(x)) = x</math>. In this case, <mat ...ns can significantly help in solving functional identities. Consider this problem:
  2 KB (361 words) - 14:40, 24 August 2021
• Floor function
  ...math>n</math> satisfy the equation <math>\left[\frac{n}{5}\right]=\frac{n}{6}</math>. [[1985 AIME Problems/Problem 10|(1985 AIME)]]
  3 KB (508 words) - 21:05, 26 February 2024
• 1985 IMO Problems/Problem 5
  == Problem == {{IMO box|year=1985|num-b=4|num-a=6}}
  3 KB (496 words) - 13:35, 18 January 2023
• 2006 AMC 10B
  ...contains the full set of test problems. The rest contain each individual problem and its solution. * [[2006 AMC 10B Problems/Problem 1]]
  2 KB (182 words) - 21:57, 23 January 2021
• Goldbach Conjecture
  <math>6 = 3 + 3</math> Euler, becoming interested in the problem, answered with an equivalent version of the conjecture:
  7 KB (1,201 words) - 16:59, 19 February 2024
• Riemann Hypothesis
  ...nction, it is easy to see that <math>\zeta(s)=0</math> when <math>s=-2,-4,-6,\ldots</math>. These are called the trivial zeros. This hypothesis is one The Riemann Hypothesis is an important problem in the study of [[prime number]]s. Let <math>\pi(x)</math> denote the numbe
  2 KB (425 words) - 12:01, 20 October 2016
• 2004 AIME I
  ...contains the full set of test problems. The rest contain each individual problem and its solution. * [[2004 AIME I Problems/Problem 1]]
  1 KB (135 words) - 18:15, 19 April 2021
• 2004 AIME II
  ...contains the full set of test problems. The rest contain each individual problem and its solution. * [[2004 AIME II Problems/Problem 1]]
  1 KB (135 words) - 12:24, 22 March 2011
• 2005 AIME I
  ...contains the full set of test problems. The rest contain each individual problem and its solution. * [[2005 AIME I Problems/Problem 1 | Problem 1]]
  1 KB (154 words) - 12:30, 22 March 2011
• International Mathematical Olympiad
  ...c competitions. Each year, countries from around the world send a team of 6 students to compete in a grueling competition. .../u>: 9.5<br><u>Problem SL1-2</u>: 5.5-7<br><u>Problem SL3-4</u>: 7-8<br><u>Problem SL5+</u>: 8-10}}
  3 KB (490 words) - 03:32, 23 July 2023
• AoPS Wiki:AoPS Community Awards
  * Kiran Kedlaya (1990, 1991, 1992) ([[Art of Problem Solving Foundation]] board member) * Kiran Kedlaya (1990, 1992) ([[Art of Problem Solving Foundation]] board member)
  20 KB (2,025 words) - 01:33, 11 June 2024
• 2006 AIME I
  ...contains the full set of test problems. The rest contain each individual problem and its solution. * [[2006 AIME I Problems/Problem 1]]
  1 KB (135 words) - 12:31, 22 March 2011
• 2005 AIME II
  ...contains the full set of test problems. The rest contain each individual problem and its solution. * [[2005 AIME II Problems/Problem 1]]
  1 KB (135 words) - 12:30, 22 March 2011
• 2006 AMC 12B
  ...contains the full set of test problems. The rest contain each individual problem and its solution. * [[2006 AMC 12B Problems/Problem 1 | Problem 1]]
  2 KB (210 words) - 00:06, 7 October 2014
• Euler's Polyhedral Formula
  ...on &4 &6 & 4 \\ \hline Cube/Hexahedron & 8 & 12 & 6\\ \hline Octahedron & 6 & 12 & 8\\ \hline Dodecahedron & 20 & 30 & 12\\ \hline Icosahedron & 12 & 3 ==Problem==
  1,006 bytes (134 words) - 14:15, 6 March 2022
• Mock AMC
  ...A number of '''Mock AMC''' competitions have been hosted on the [[Art of Problem Solving]] message boards. They are generally made by one community member ...amous theorems and formulas and see if there's any way you can make a good problem out of them.
  51 KB (6,175 words) - 20:58, 6 December 2023
• Modular arithmetic/Introduction
  <math>1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 0, \ldots </math> ...\not\equiv 18 \pmod{6}</math> because <math>\frac{91 - 18}{6} = \frac{73}{6}</math>, which is not an integer.
  15 KB (2,396 words) - 20:24, 21 February 2024
• Modular arithmetic/Intermediate
  <math>\{ \ldots, -6, -3, 0, 3, 6, \ldots \}</math> <math>\overline{6} \cdot \overline{6} = \overline{6 \cdot 6} = \overline{36} = \overline{1}</math>
  14 KB (2,317 words) - 19:01, 29 October 2021
• Right triangle
  label("$45^{\circ}$", A, 6*dir(290)); [[2007 AMC 12A Problems/Problem 10 | 2007 AMC 12A Problem 10]]
  3 KB (499 words) - 23:41, 11 June 2022
• 2006 AMC 10A
  ...k contains the full set of test problems. The rest contain each individual problem and its solution. * [[2006 AMC 10A Problems/Problem 1]]
  2 KB (180 words) - 18:06, 6 October 2014

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