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  • == Problem == ...mum we can get is <math>1+2+3 = 6</math>, so we only need to try the first 6 numbers.
    12 KB (1,859 words) - 18:16, 28 March 2022
  • == Problem == {{AIME box|year=1985|num-b=6|num-a=8}}
    1 KB (222 words) - 11:04, 4 November 2022
  • == Problem == ...r this point it must continue to repeat. Thus, in particular <math>a_{j + 6} = a_j</math> for all <math>j</math>, and so repeating this <math>n</math>
    2 KB (410 words) - 13:37, 1 May 2022
  • == Problem == ...> (since we know <math>a</math> is positive). Thus <math>c = 6^3 - 3\cdot 6 = \boxed{198}</math>.
    1 KB (205 words) - 18:58, 10 March 2024
  • == Problem == f.p=fontsize(6);
    11 KB (1,722 words) - 09:49, 13 September 2023
  • == Problem == ...th>\dbinom{6}{0} + \dbinom{6}{1} + \dbinom{6}{2} + \dbinom{6}{3} + \dbinom{6}{4}=57</math> of its subsets have at most four elements (the number of subs
    2 KB (364 words) - 19:41, 1 September 2020
  • == Problem == ...first 16 triangular numbers, which evaluates to <math>\frac{(16)(17)(18)}{6} = \boxed{816}</math>.
    6 KB (872 words) - 16:51, 9 June 2023
  • == Problem == pathpen = black; pointpen = black +linewidth(0.6); pen s = fontsize(10);
    11 KB (1,850 words) - 18:07, 11 October 2023
  • == Problem == ...ctorization]] of <math>1000000 = 2^65^6</math>, so there are <math>(6 + 1)(6 + 1) = 49</math> divisors, of which <math>48</math> are proper. The sum of
    3 KB (487 words) - 20:52, 16 September 2020
  • == Problem == ...owever, we must change it back to base 10 for the answer, which is <math>3^6 + 3^5 + 3^2 = 729 + 243 + 9 = \boxed {981}</math>.
    5 KB (866 words) - 00:00, 22 December 2022
  • == Problem == The key to this problem is to realize that <math>n+10 \mid n^3 +1000</math> for all <math>n</math>.
    2 KB (338 words) - 19:56, 15 October 2023
  • == Problem == <center><math>2x_1+x_2+x_3+x_4+x_5=6</math></center>
    1 KB (212 words) - 16:25, 17 November 2019
  • == Problem == ...tan x \cdot \tan y = \frac{\tan x + \tan y}{30} = \frac{25}{30} = \frac{5}{6}</math>
    3 KB (545 words) - 23:44, 12 October 2023
  • == Problem == ...sqrt{7}\right)\left(\sqrt{5}-\sqrt{6}+\sqrt{7}\right)\left(-\sqrt{5}+\sqrt{6}+\sqrt{7}\right).</cmath>
    3 KB (460 words) - 00:44, 5 February 2022
  • == Problem == &= (x(x-6) + 18)(x(x+6)+18),
    7 KB (965 words) - 10:42, 12 April 2024
  • == Problem == ...that <math>(n + \frac{1}{1000})^3 = n^3 + \frac{3}{10^3} n^2 + \frac{3}{10^6} n + \frac{1}{10^9}</math>. For a given value of <math>n</math>, if <math>(
    4 KB (673 words) - 19:48, 28 December 2023
  • == Problem == ...or large factors of <math>2\cdot 3^{11}</math> which are less than <math>3^6</math>. The largest such factor is clearly <math>2\cdot 3^5 = 486</math>;
    3 KB (418 words) - 18:30, 20 January 2024
  • == Problem == ...ains a [[point]] <math>P</math> for which <math>PA = 10</math>, <math>PB = 6</math>, and <math>\angle APB = \angle BPC = \angle CPA</math>. Find <math>
    1 KB (200 words) - 18:44, 5 February 2024
  • == Problem == Since <math>91n - 104k < n + k</math>, <math>k > \frac{6}{7}n</math>. Also, <math>0 < 91n - 104k</math>, so <math>k < \frac{7n}{8}</
    2 KB (393 words) - 16:59, 16 December 2020
  • == Problem == {{AIME box|year=1987|num-b=6|num-a=8}}
    3 KB (547 words) - 22:54, 4 April 2016

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