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- ...inite]] set can be denoted in a variety of ways. The most straightforward representation is simply to write down what the permutation looks like. For example, the ==The Symmetric Group==3 KB (422 words) - 10:01, 25 December 2020
- ...refore the number of sets where there are exactly two 1’s in this binary representation is just <math>\binom {40}{2}</math> because we’re choosing 2 1s to go in A positive integer <math>n</math> has exactly two 1s in its binary representation exactly when <math>n = 2^j + 2^k</math> for <math>j \neq k</math> [[nonnega8 KB (1,283 words) - 18:19, 8 May 2024
- A [[positive integer]] is called ascending if, in its [[decimal representation]], there are at least two digits and each digit is less than any digit to i ...ry. If you have n people and you want to know how many ways you can make a group of any size you could do this <math>2</math> ways. You could count everyone2 KB (336 words) - 04:18, 4 November 2022
- ...-1} = Rx_1+\cdots +Rx_m</math>, and let <math>M_f</math> be the [[matrix]] representation of <math>f</math> with respect to <math>x_1,\ldots,x_m</math>. Then <math>M ...roup. The [[quotient group]] is <math>G/H</math> is then the [[ideal class group]] of <math>R</math>, a object of great importance in algebraic number theor9 KB (1,648 words) - 15:36, 14 October 2017
- ...>S_n</math>, the [[alternating group]] <math>A_n</math>, or the [[dihedral group]] <math>D_n</math>. ...the concept of a '''group action'''. Loosely speaking, a group action of a group <math>G</math> on a set <math>X</math> is an assignment of a bijection <mat5 KB (917 words) - 20:17, 7 September 2008
- ...h>30\%</math> of the group are girls. How many girls were initially in the group? ...by both <math>4</math> and <math>9,</math> and whose base-<math>10</math> representation consists of only <math>4</math>'s and <math>9</math>'s, with at least one o15 KB (2,297 words) - 11:57, 19 February 2020
- ...the number of pairs of different adjacent digits in the binary (base two) representation of <math>n</math>. For example, <math> D(3) = D(11_{2}) = 0 </math>, <math> 4) Extending <math>101001</math> at the first group is impossible. The other four extensions are <math>1001001, 1011001, 1010010 KB (1,552 words) - 20:01, 5 October 2023
- ...math>S</math> be the increasing sequence of positive integers whose binary representation has exactly <math>8</math> ones. Let <math>N</math> be the 1000th number in ...ple each person shakes hands with exactly two of the other people from the group. Let <math>N</math> be the number of ways this handshaking can occur. Consi7 KB (1,228 words) - 11:16, 13 March 2020
- ...ath>n</math> for which <math>\tfrac{1}{n}</math> has the repeating decimal representation <math>0.\overline{ab} = 0.ababab\cdots,</math> with <math>a</math> and <mat A group of <math> 12 </math> pirates agree to divide a treasure chest of gold coins14 KB (2,206 words) - 01:34, 9 September 2024
- ...For how many positive integers <math>b</math> does the base-<math>b</math>-representation of <math>2013</math> end in the digit <math>3</math>? A group of <math>12</math> pirates agree to divide a treasure chest of gold coins a12 KB (1,894 words) - 14:59, 3 January 2024
- ...math> representation of the square of the number whose base <math>b</math> representation is 24, then <math>b</math>, when written in base 10, equals The average (arithmetic mean) age of a group consisting of doctors and lawyers in 40. If the doctors average 35 and the18 KB (2,788 words) - 18:25, 22 August 2024
- 43. <math>\pi</math> is a representation of how many pies Gmaas has eaten. EDIT: The number <math>\pi</math> was cre 44. <math>e</math> is a representation of how many days Gmaas forgot to eat. EDIT: The number <math>e</math> was c69 KB (11,805 words) - 19:49, 18 December 2019
- 43. <math>\pi</math> is a representation of how many pies Almighty Gmaas has eaten. EDIT: The number <math>\pi</mat 44. <math>e</math> is a representation of how many days Almighty Gmaas forgot to eat. EDIT: The number <math>e</ma99 KB (14,096 words) - 22:49, 19 February 2025
- ...the grid-based battlefield. Sometimes abbreviations can be a 2x3 or larger group of characters due to larger units. This does not mean they can be turned. I36 KB (5,897 words) - 18:28, 3 September 2024
- 43. <math>\pi</math> is a representation of how many pies Gmaas has eaten. EDIT: The number <math>\pi</math> was cre 44. <math>e</math> is a representation of how many days Gmaas forgot to eat. EDIT: The number <math>e</math> was c89 KB (15,007 words) - 14:02, 19 February 2025
- 43. <math>\pi</math> is a representation of how many pies Gmaas has eaten. EDIT: The number <math>\pi</math> was cre 44. <math>e</math> is a representation of how many days Gmaas forgot to eat. EDIT: The number <math>e</math> was c69 KB (11,828 words) - 18:26, 3 September 2024