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• 2008 AMC 10A Problems
  ...qquad\mathrm{(C)}\ \text{3:30}\ {\small\text{PM}}\qquad\mathrm{(D)}\ \text{4:30}\ {\small\text{PM}}\qquad\mathrm{(E)}\ \text{5:50}\ {\small\text{PM}}</m ...e, <math>\langle 4\rangle=1+2=3</math> and <math>\langle 12 \rangle =1+2+3+4+6=16</math>. What is <math>\langle\langle\langle 6\rangle\rangle\rangle</ma
  14 KB (2,138 words) - 15:08, 18 February 2023
• Partition (combinatorics)
  ...wn for which values of <math>{n}</math> the number of partitions of <math>{n}</math> is [[even integer | even]], despite the presence of a formula! No ...the partition function, such as the number of ways to write a number <math>n</math> as the sum of [[odd integer | odd]] parts, or of distinct parts, or
  10 KB (1,508 words) - 14:24, 17 September 2017
• 2008 AMC 12A Problems
  ...qquad\mathrm{(C)}\ \text{3:30}\ {\small\text{PM}}\qquad\mathrm{(D)}\ \text{4:30}\ {\small\text{PM}}\qquad\mathrm{(E)}\ \text{5:50}\ {\small\text{PM}}</m ...{2}\qquad\mathrm{(C)}\ 3\qquad\mathrm{(D)}\ \frac{7}{2}\qquad\mathrm{(E)}\ 4</math>
  13 KB (2,025 words) - 13:56, 2 February 2021
• 2008 AMC 12A Problems/Problem 19
  ...e. For each <math>n \neq 0</math>, there is one and only one <math>x^{28 - n}</math> in <math>B</math>. For example, if I choose <math>x^2</math> from < <math>1 + x + x^2 + x^3 + x^4 + \cdots + x^{14} + </math>
  5 KB (895 words) - 22:54, 9 January 2021
• 2008 AMC 12A Problems/Problem 17
  ...f <math>a_{n-1}</math> is even and <math>a_n=3a_{n-1}+1</math> if <math>a_{n-1}</math> is odd. For how many positive integers <math>a_1 \le 2008</math> ...>, <math>4n+1</math>, <math>4n+2</math>, or <math>4n+3</math>, where <math>n</math> is a nonnegative integer.
  2 KB (386 words) - 13:52, 21 December 2020
• 2008 AMC 12A Problems/Problem 16
  ...t{th}</math> term of the sequence is <math>\log{b^n}</math>. What is <math>n</math>? ...22B</math>, and <math>31B</math>, the <math>k</math>th term is <math>(9k + 4)B</math>.
  3 KB (577 words) - 16:33, 9 October 2022
• 2008 AMC 12A Problems/Problem 13
  ...)}\ \frac{1}{8}\qquad\mathrm{(D)}\ \frac{1}{6}\qquad\mathrm{(E)}\ \frac{1}{4}</math> ...<math>30</math> degrees. Let the line tangent to the two circles at <math>N</math> intersect <math>OA</math> and <math>OB</math> at points <math>C</mat
  4 KB (630 words) - 20:32, 4 June 2021
• 2008 AMC 10A Problems/Problem 20
  pair A=7*K/4-3*C/4, B=7*K/4-3*D/4; D(MP("A",A,N)--MP("B",B,N)--MP("C",C)--MP("D",D)--A--C);D(B--D);D(A--MP("K",K)--D--cycle,linewidth(0.
  2 KB (294 words) - 21:53, 17 October 2023
• 2008 AMC 12A Problems/Problem 20
  Triangle <math>ABC</math> has <math>AC=3</math>, <math>BC=4</math>, and <math>AB=5</math>. Point <math>D</math> is on <math>\overline{A pair C=(0,0),A=(0,3),B=(4,0),D=(4-2.28571,1.71429);
  6 KB (951 words) - 16:31, 2 August 2019
• 2008 AMC 12A Problems/Problem 15
  <math>\mathrm{(A)}\ 0\qquad\mathrm{(B)}\ 2\qquad\mathrm{(C)}\ 4\qquad\mathrm{(D)}\ 6\qquad\mathrm{(E)}\ 8</math> <math>k \equiv 2008^2 + 2^{2008} \equiv 8^2 + 2^4 \equiv 4+6 \equiv 0 \pmod{10}</math>.
  4 KB (547 words) - 04:19, 30 September 2023
• 2007 AMC 12B Problems/Problem 24
  <math>\mathrm {(A)}\ 4\quad\mathrm {(B)}\ 6\quad\mathrm {(C)}\ 9\quad\mathrm {(D)}\ 12\quad\mathrm Since <math>b = 3n</math> for some positive integer <math>n</math>, we can rewrite the fraction(divide by <math>9</math> on both top an
  9 KB (1,522 words) - 22:46, 12 May 2022
• 2007 AMC 10B Problems/Problem 18
  A circle of radius <math>1</math> is surrounded by <math>4</math> circles of radius <math>r</math> as shown. What is <math>r</math>? dotfactor=4;
  2 KB (385 words) - 14:17, 4 June 2021
• 1992 USAMO Problems/Problem 3
  ...e is a subset <math>S</math> of <math>A</math> for which <math>\sigma(S) = n</math>. What is the smallest possible value of <math>a_{10}</math>? ...th> such that <math>Z=\{a_1,a_2,\cdots,a_n\}</math>, where <math>\forall i<n</math>, <math>i\in \mathbb{Z}^+</math>, <math>a_i<a_{i+1}</math>, and for e
  5 KB (858 words) - 07:52, 19 July 2016
• 2008 AMC 12A Problems/Problem 24
  ...e]] <math>ABC</math> has <math>\angle C = 60^{\circ}</math> and <math>BC = 4</math>. Point <math>D</math> is the [[midpoint]] of <math>BC</math>. What ...mathrm{(C)}\ \frac{\sqrt{3}}{2\sqrt{2}}\qquad\mathrm{(D)}\ \frac{\sqrt{3}}{4\sqrt{2}-3}\qquad\mathrm{(E)}\ 1</math>
  3 KB (513 words) - 14:35, 7 June 2018
• 2008 AMC 12A Problems/Problem 25
  ...}, b_{n + 1}) = (\sqrt {3}a_n - b_n, \sqrt {3}b_n + a_n)</math> for <math>n = 1,2,3,\ldots</math>. Suppose that <math>(a_{100},b_{100}) = (2,4)</math>. What is <math>a_1 + b_1</math>?
  5 KB (745 words) - 10:58, 9 December 2022
• 2004 AMC 12A Problems/Problem 19
  https://www.youtube.com/watch?v=4-lbEZkFJdc pair OA1=(-2+2*t,0),OB1=(4/3+2*t,16/9),OC1=(4/3+2*t,-16/9),OD1=(0+2*t,0),E1=(4/3+2*t,0);
  5 KB (785 words) - 00:29, 31 July 2023
• 2004 AMC 12A Problems/Problem 24
  ...3}{2} \qquad \textbf {(D) } \frac {10\pi}{3} - \sqrt3 \qquad \textbf {(E) }4\pi - 2\sqrt3</math> label("\(1\)",(0,0),N);
  3 KB (434 words) - 22:25, 22 November 2021
• 2008 AMC 10B Problems
  <math>\mathrm{(A)}\ 2\qquad\mathrm{(B)}\ 3\qquad\mathrm{(C)}\ 4\qquad\mathrm{(D)}\ 5\qquad\mathrm{(E)}\ 6</math> A <math>4\times 4</math> block of calendar dates is shown. The order of the numbers in the se
  12 KB (1,838 words) - 16:52, 7 October 2022
• 2008 AMC 12B Problems
  <math>\textbf{(A)}\ 2 \qquad \textbf{(B)}\ 3 \qquad \textbf{(C)}\ 4 \qquad \textbf{(D)}\ 5 \qquad \textbf{(E)}\ 6</math> A <math>4\times 4</math> block of calendar dates is shown. The order of the numbers in the se
  14 KB (2,199 words) - 13:43, 28 August 2020
• 2005 Alabama ARML TST Problems/Problem 13
  Let the number be <math>n</math>, and let <math>p_1</math> and <math>p_2</math> be primes. Therefore, *<math>n=p_1^5</math>
  2 KB (279 words) - 19:14, 10 March 2015

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