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• 2004 AMC 12A Problems
  ...xt{(A) } 11 \qquad \text{(B) } 13 \qquad \text{(C) } 14 \qquad \text{(D) } 16 \qquad \text{(E) } 17</math> == Problem 16 ==
  13 KB (1,953 words) - 00:31, 26 January 2023
• 2000 AMC 12 Problems
  ...cdot O = 2001 </math>. What is the largest possible value of the sum <math>I + M + O</math>? == Problem 16 ==
  13 KB (1,948 words) - 10:35, 16 June 2024
• 2001 AMC 12 Problems
  ...that is, <math>A > B > C</math>, <math>D > E > F</math>, and <math>G > H > I > J</math>. Furthermore, ...</math> are consecutive even digits; <math>G</math>, <math>H</math>, <math>I</math>, and <math>J</math> are consecutive odd
  13 KB (1,957 words) - 12:53, 24 January 2024
• 2004 AMC 12B Problems
  ...A}) 13\qquad (\mathrm {B}) 14 \qquad (\mathrm {C}) 15 \qquad (\mathrm {D}) 16 \qquad (\mathrm {E}) 17</math> == Problem 16 ==
  13 KB (2,049 words) - 13:03, 19 February 2020
• 2005 AMC 12B Problems
  \mathrm{(C)}\ 16 \qquad ...\mathrm{(C)}\ {{{4}}} \qquad \mathrm{(D)}\ {{{8}}} \qquad \mathrm{(E)}\ {{{16}}}</math>
  12 KB (1,781 words) - 12:38, 14 July 2022
• 2006 AMC 12B Problems/Problem 17
  \mathrm{(D)}\ \frac 16 See also [[2016 AIME I Problems/Problem 2]]
  1 KB (188 words) - 22:10, 9 June 2016
• 2006 AMC 12A Problems/Problem 25
  ...s. For each configuration, we can subtract <math>i-1</math> from the <math>i</math>-th element in your subset. This converts your configuration into a c ...subset is <math>15</math>. This is a total of <math>15-s+1</math> or <math>16-s</math> possible elements.
  8 KB (1,405 words) - 11:52, 27 September 2022
• 2005 AMC 12B Problems/Problem 24
  ...> \mathrm{(A)}\ {{{14}}}\qquad\mathrm{(B)}\ {{{15}}}\qquad\mathrm{(C)}\ {{{16}}}\qquad\mathrm{(D)}\ {{{17}}}\qquad\mathrm{(E)}\ {{{18}}} </math> ...tiplying the two complex numbers <math>1 + 2i</math> and <math>1 + \sqrt{3}i</math>. What this does is generate the complex number that is at a <math>60
  4 KB (761 words) - 09:10, 1 August 2023
• 2006 AMC 10A Problems
  D((0,0)--(16,0)--(16,-16)--(0,-16)--cycle); D((16,-8)--(24,-8));
  13 KB (2,028 words) - 16:32, 22 March 2022
• 2006 AMC 10A Problems/Problem 12
  ...s dog with an 8-foot rope to a [[square (geometry) | square]] shed that is 16 feet on each side. His preliminary drawings are shown. D((0,0)--(16,0)--(16,-16)--(0,-16)--cycle);
  3 KB (424 words) - 10:14, 17 December 2021
• 2022 USAJMO Problems/Problem 1
  ...math> (<math>x</math> and <math>y</math> can be equal), ie. <math>4,8,9,12,16,18,20,24,25,\dots </math>. ...s that all non square-free m (4, 8, 9, 16, 18, 25...) should all work, but I don't have a proof. However, if you edit the one above, you can see non squ
  5 KB (883 words) - 01:05, 2 June 2024
• 2005 AIME II Problems
  Let <math> x=\frac{4}{(\sqrt{5}+1)(\sqrt[4]{5}+1)(\sqrt[8]{5}+1)(\sqrt[16]{5}+1)}. </math> Find <math> (x+1)^{48}. </math> ...th> less than or equal to 1000 is <math> (\sin t + i \cos t)^n = \sin nt + i \cos nt </math> true for all real <math> t </math>?
  7 KB (1,119 words) - 21:12, 28 February 2020
• 2005 AIME I Problems/Problem 4
  16 & 368 & no\\ \hline {{AIME box|year=2005|n=I|num-b=3|num-a=5}}
  8 KB (1,248 words) - 11:43, 16 August 2022
• 2005 AIME I Problems/Problem 9
  ...contribute a probability of <math>\left(\frac{1}{4}\right)^8 = \frac{1}{2^{16}}</math> ...<math>\frac{2^6}{3^6} \cdot \frac{5^{12}}{2^{24}3^{12}} \cdot \frac{1}{2^{16}} = \frac{5^{12}}{2^{34}\cdot 3^{18}}</math> and so the answer is <math>2 +
  4 KB (600 words) - 21:44, 20 November 2023
• 2005 AIME I Problems/Problem 11
  [[Image:2005 AIME I Problem 11.png]] ...+ r\sqrt{2} = 8\sqrt{2}</math> so <math>r = \frac{8\sqrt{2}}{1+\sqrt{2}} = 16 - 8\sqrt{2}</math>. Then the diameter is <math>32 - \sqrt{512}</math> givin
  4 KB (707 words) - 11:11, 16 September 2021
• 2005 AIME II Problems/Problem 15
  ...ns as <math>(x+5)^2 + (y-12)^2 = 256</math> and <math>(x-5)^2 + (y-12)^2 = 16</math>. 16 - r &= \sqrt{(x+5)^2 + (y-12)^2} \end{align*} </cmath>
  12 KB (2,000 words) - 13:17, 28 December 2020
• 2004 AIME I Problems/Problem 15
  6&0&0&0&0&0&1&1&2&4&8&16\\ 7&0&0&0&0&1&1&2&4&8&16&32\\
  9 KB (1,491 words) - 01:23, 26 December 2022
• 2004 AIME I Problems/Problem 12
  ...\cup \left(\frac{1}{8},\frac{1}{4}\right) \cup \left(\frac{1}{32},\frac{1}{16}\right) \cup \cdots</cmath> {{AIME box|year=2004|n=I|num-b=11|num-a=13}}
  2 KB (303 words) - 22:28, 11 September 2020
• 2004 AIME II Problems/Problem 14
  ...big\rfloor + 1 = 112</math> positive integers that satisfy both conditions i.e. <math>\{1, 10, 19, 28, 37, 46, . . . , 1000\}.</math> ...th>n = 24 + (\cdots)</math> then just put the values of <math>a,b,c</math> i am sure you will get it :) )
  11 KB (1,857 words) - 21:55, 19 June 2023
• 2004 AIME II Problems/Problem 6
  <math>x = \frac{1}{4}b_1 + \frac{1}{8}b_2 + \frac{11}{72}b_3 = \frac{1}{16}b_1 + \frac{1}{8}b_2 + \frac{11}{48}b_3 = \frac{1}{8}b_1 + \frac{3}{8}b_2 + ...d monkey take <math>8y</math>, and the third monkey take <math>24z</math>. I chose these numbers to make it so, when each monkey splits his bananas, the
  6 KB (950 words) - 14:18, 15 January 2024

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