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Create the page "2005 AIME I Problem 13" on this wiki! See also the search results found.
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- == Problem == ...e principle]] all of at least one of the two letters must be all together (i.e., stay in a row).5 KB (897 words) - 00:21, 29 July 2022
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- ...d only once. In particular, memorizing a formula for PIE is a bad idea for problem solving. ==== Problem ====9 KB (1,703 words) - 01:20, 7 December 2024
- This is a problem where constructive counting is not the simplest way to proceed. This next e ...proceed with the construction. If we were to go like before and break the problem down by each box, we'd get a fairly messy solution.13 KB (2,018 words) - 15:31, 10 January 2025
- ...ver, it is possible to define a number, <math> i </math>, such that <math> i = \sqrt{-1} </math>. If we add this new number to the reals, we will have ...rm <math> a + bi </math> where <math> a,b\in \mathbb{R} </math> and <math> i = \sqrt{-1} </math> is the [[imaginary unit]]. The set of complex numbers i5 KB (860 words) - 15:36, 10 December 2023
- ...re in the form <math>(P_{ia},Q_{ia})</math> for [[positive]] integer <math>i</math>. ...s for any given Diophantine equations. This is known as [[Hilbert's tenth problem]]. The answer, however, is no.9 KB (1,434 words) - 01:15, 4 July 2024
- ...contains the full set of test problems. The rest contain each individual problem and its solution. * [[2004 AIME II Problems]]1 KB (135 words) - 12:24, 22 March 2011
- ...contains the full set of test problems. The rest contain each individual problem and its solution. * [[2005 AIME I Problems]]1 KB (154 words) - 12:30, 22 March 2011
- ...contains the full set of test problems. The rest contain each individual problem and its solution. * [[2006 AIME I Problems]]1 KB (135 words) - 12:31, 22 March 2011
- ...contains the full set of test problems. The rest contain each individual problem and its solution. * [[2005 AIME II Problems]]1 KB (135 words) - 12:30, 22 March 2011
- {{AIME Problems|year=2006|n=I}} == Problem 1 ==7 KB (1,173 words) - 03:31, 4 January 2023
- ...S'</math> and <math>S''</math> are equal if they include the same objects, i.e., if for every object <math>x</math>, we have <math>x\in S'</math> if and ...describe sets should be used with extreme caution. One way to avoid this problem is as follows: given a property <math>P</math>, choose a known set <math>T<11 KB (2,019 words) - 17:20, 7 July 2024
- {{AIME Problems|year=2005|n=II}} == Problem 1 ==7 KB (1,119 words) - 21:12, 28 February 2020
- == Problem == ...^2</math> equal and solving for <math>x</math> (it is helpful to scale the problem down by a factor of 50 first), we get <math>x = 250\pm 50\sqrt{7}</math>. S13 KB (2,080 words) - 13:14, 23 July 2024
- {{AIME Problems|year=2005|n=I}} == Problem 1 ==6 KB (983 words) - 05:06, 20 February 2019
- == Problem == ...ss than <math>50</math>. There are fifteen of these (<math>2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43</math> and <math>47</math>) so there are <m2 KB (249 words) - 09:37, 23 January 2024
- == Problem == ...th>. When <math>n = 28</math>, this product is <math>980</math>, and since AIME answers are nonnegative integers less than <math>1000</math>, we don't have8 KB (1,249 words) - 21:25, 20 November 2024
- == Problem == ...let <math> b </math> denote the number of positive integers <math> n \leq 2005 </math> with <math> S(n) </math> [[even integer | even]]. Find <math> |a-b|4 KB (647 words) - 02:29, 4 May 2021
- == Problem == ...e principle]] all of at least one of the two letters must be all together (i.e., stay in a row).5 KB (897 words) - 00:21, 29 July 2022
- == Problem == ...</math>, the area is <math>K=\frac{1936}{10}</math>, and the answer to the problem is <math>\boxed{936}</math>.3 KB (561 words) - 14:11, 18 February 2018
- == Problem == label("$\ell$",(13,l(13)),SE,fontsize(9));12 KB (2,001 words) - 20:26, 23 July 2024
- {{AIME Problems|year=2004|n=II}} == Problem 1 ==9 KB (1,410 words) - 05:05, 20 February 2019
