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  • ...f the left end, resulting in a <math>256</math> by <math>1</math> strip of quadruple thickness. This process is repeated <math>8</math> more times. After the la
    6 KB (899 words) - 19:58, 12 May 2022
  • ...cide with and lie on top of the left end, resulting in a 256 by 1 strip of quadruple thickness. This process is repeated 8 more times. After the last fold, the
    9 KB (1,410 words) - 04:05, 20 February 2019
  • ...math>b\longrightarrow b+1</math>, etc. and this will still produce a valid quadruple. This means, that we can fix <math>a=1</math>, and then just repeatedly add Case 1: <math>b=2</math>, <math>c=94</math>. This produces the quadruple <math>(1,2,94,95)</math>, which indeed works.
    8 KB (1,343 words) - 15:27, 19 December 2023
  • ...d-b\cdot c</math> is odd? (For example, <math>(0,3,1,1)</math> is one such quadruple, because <math>0\cdot 1-3\cdot 1 = -3</math> is odd.)
    13 KB (1,968 words) - 17:05, 23 November 2024
  • ...can have at most 4 edges coming out of it. For each point, assign it the [[quadruple]]: <math>(a,b,c,d)</math> where <math>a</math>, <math>b</math>, <math>c</ma ...for which <math>a</math> is minimal (i.e. out of all maximal elements in a quadruple, choose the one with the least maximal element). We have that <math>4a \ge
    10 KB (1,878 words) - 13:56, 30 June 2021
  • ...case solves to <math>(e,f,g,h)=(25,21,7,15)</math>, which gives us a valid quadruple <math>(a,b,c,d)=(24,20,6,14)</math>, and we have <math>a-d=24-14 =\boxed{10
    2 KB (298 words) - 12:01, 18 September 2023
  • Brent has goldfish that quadruple (become four times as many) every month, and Gretel has goldfish that doubl
    13 KB (1,880 words) - 12:35, 19 February 2020
  • Define an ordered quadruple of integers <math>(a, b, c, d)</math> as interesting if <math>1 \le a<b<c<d ...th> represents its value and <math>x</math> is a place holder. Clearly the quadruple is interesting if there are more place holders between <math>c</math> and <
    9 KB (1,535 words) - 00:28, 16 January 2023
  • Define an ordered quadruple of integers <math>(a, b, c, d)</math> as ''interesting'' if <math>1 \le a<b
    8 KB (1,301 words) - 07:43, 11 October 2020
  • Brent has goldfish that quadruple (become four times as many) every month, and Gretel has goldfish that doubl Brent starts with <math>4</math> goldfish and they quadruple each month, giving us <math>y=4\cdot 4^{x}</math> or <math>y=2^{2x+2}</math
    2 KB (264 words) - 10:26, 27 June 2023
  • ...or is added to its numerator and to its denominator and find one that will quadruple.
    10 KB (1,477 words) - 15:02, 27 May 2012
  • Call a quadruple <math>(w, x, y, z)</math> of positive integers <math>n</math>-plausible if
    15 KB (2,452 words) - 02:03, 4 July 2020
  • ...of time given, Ina will run twice the distance of Eve, and Paul would run quadruple the distance of Eve. Let's consider the time it takes for Paul to meet Eve:
    3 KB (516 words) - 02:25, 16 January 2023
  • The cross-ratio be <i><b>projective invariant</b></i> of a quadruple of collinear points, so
    10 KB (1,660 words) - 20:26, 1 December 2024
  • ...d-b\cdot c</math> is odd? (For example, <math>(0,3,1,1)</math> is one such quadruple, because <math>0\cdot 1-3\cdot 1 = -3</math> is odd.)
    6 KB (1,044 words) - 21:35, 4 November 2024
  • ...th <math>6</math> as a factor, triple count any case with <math>12</math>, quadruple count any case with <math>24</math>, etc.
    19 KB (2,881 words) - 04:58, 18 September 2024
  • Basic ordered quadruple & P(i) & D(i) \ \hline
    4 KB (690 words) - 13:32, 6 January 2021
  • ...ve a bad case. We shall keep track of all the "bad" cases. For Case 1, any quadruple that includes <math>{d = 0}</math> is "bad". So no restrictions upon <math>
    16 KB (2,769 words) - 18:11, 28 December 2024
  • Given any ordered quadruple <math>(a'_1, a'_2, a'_3, a'_4)</math> in modulo <math>m,</math> it follows \textbf{Ordered Quadruple} & \textbf{Sum Modulo }\boldsymbol{m} \ [0.5ex]
    11 KB (1,687 words) - 23:04, 28 April 2023
  • A quadruple <math>(a, b, c, d)</math> of distinct integers is said to be <math>\textit{
    10 KB (1,887 words) - 11:25, 16 December 2024

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