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• Inequality
  For two [[number]]s <math>a</math> and <math>b</math>: ...b</math>, <math>b<a</math>, and vice versa. The same applies to the latter two signs: if and only if <math>a\ge b</math>, <math>b\le a</math>, and vice ve
  12 KB (1,806 words) - 05:07, 19 June 2024
• 2003 AMC 12A Problems
  The sum of the two 5-digit numbers <math>AMC10</math> and <math>AMC12</math> is <math>123422</ ...likely. Object <math>B</math> starts at <math>(5,7)</math> and each of its steps is either to the left or down, both equally likely. Which of the following
  13 KB (1,955 words) - 20:06, 19 August 2023
• 2006 AMC 12B Problems/Problem 18
  ...h> is even. It can easily be shown that each location that satisfies these two conditions is indeed reachable.
  2 KB (354 words) - 15:57, 28 December 2020
• Problem solving
  ...There were over 200 students in the course, and we quickly separated into two groups. One group understood that all we would be taught could largely be d =Main Steps=
  6 KB (1,039 words) - 16:43, 30 July 2018
• 2005 AIME I Problems/Problem 10
  ...a smaller value of <math>p+q</math>, which is provable by following these steps over again) (alternatively, we could use the [[Shoelace Theorem]]). We can ...lt is the equation <math>|980 - 56p| = 140</math>. Solve this equation for two possible answers <math>p = 15, 20</math>. Plugging into <math>q = -5p + 107
  5 KB (852 words) - 20:23, 4 October 2023
• 2004 AIME I Problems/Problem 2
  ...an of set <math>B</math> is <math>0.5</math>, which means that the "middle two" integers of set <math>B</math> are <math>0</math> and <math>1</math>. The Solving for <math>f+l</math>, we find the sum of the two terms is <math>4</math>.
  8 KB (1,437 words) - 20:53, 19 May 2023
• 1987 AIME Problems
  What is the largest possible distance between two points, one on the sphere of radius 19 with center <math>(-2,-10,5),</math> ...king (in steps per unit time) is three times Bob's walking speed, how many steps are visible on the escalator at a given time? (Assume that this value is co
  6 KB (869 words) - 14:34, 22 August 2023
• 1995 AIME Problems
  ...o sides of square <math>S_{i+1},</math> are the perpendicular bisectors of two adjacent sides of square <math>S_{i+2}.</math> The total area enclosed by ...the probability that the object reaches <math>(2,2)</math> in six or fewer steps. Given that <math>p</math> can be written in the form <math>m/n,</math> wh
  6 KB (1,000 words) - 23:25, 26 March 2024
• 1985 AIME Problems/Problem 12
  Two solutions follow from here: ...}</math> and add them up before dividing by <math>3^7</math>. Here we have two ways to proceed:
  19 KB (3,128 words) - 20:38, 23 July 2024
• 1987 AIME Problems/Problem 10
  ...king (in steps per unit time) is three times Bob's walking speed, how many steps are visible on the escalator at a given time? (Assume that this value is co Let the total number of steps be <math>x</math>, the speed of the escalator be <math>e</math> and the spe
  7 KB (1,187 words) - 15:21, 27 January 2024
• 1995 AIME Problems/Problem 3
  ...the probability that the object reaches <math>(2,2)</math> in six or fewer steps. Given that <math>p</math> can be written in the form <math>m/n,</math> wh ...mber of steps for the object to reach <math>(2,2)</math>, so the number of steps the object may have taken is either <math>4</math> or <math>6</math>.
  3 KB (602 words) - 22:15, 16 June 2019
• 2000 AIME I Problems/Problem 15
  ...ve <math>d_{1537} = 1537 - 2 = 1535</math>. <math>2000 - 1537 = 463</math> steps remain. So, <math>d_{2000} = d_{1537} - 463 = 1072</math>. Finally, there a ...gh all of the <math>2000</math> cards initially in the deck once, in round two, you would go through all <math>1000</math> cards initially in the deck onc
  15 KB (2,673 words) - 18:16, 6 January 2024
• 2001 AIME I Problems/Problem 15
  ...o that each face contains a different number. The [[probability]] that no two consecutive numbers, where <math>8</math> and <math>1</math> are considered It follows that an octagon cannot have two successive long diagonals. Also notice that an octagonal path can jump from
  11 KB (1,836 words) - 20:08, 26 August 2024
• 2003 AIME II Problems/Problem 13
  ...x of an equilateral triangle. On each move, it randomly selects one of the two vertices where it is not currently located, and crawls along a side of the ...for the ant to return to the original vertex, the net number of clockwise steps must be a multiple of 3, i.e., <math>\#CW - \#CCW \equiv 0 \pmod{3}</math>.
  15 KB (2,406 words) - 22:56, 23 November 2023
• 2002 AIME II Problems/Problem 8
  ...tively, you could use the equation above and proceed with one of the other two solutions listed. ...ath> because we need to find the smallest skipped integer. The rest of the steps are the same as Solution 1.
  6 KB (908 words) - 13:22, 14 July 2023
• 2005 AMC 10B Problems/Problem 24
  Let <math>x</math> and <math>y</math> be two-digit integers such that <math>y</math> is obtained by reversing the digits The first steps are the same as Solution 1. Let <math>x = 10a+b, y = 10b+a</math>, where w
  5 KB (845 words) - 18:23, 17 September 2023
• P versus NP
  ...me. The <math>P</math> versus <math>NP</math> question asks whether these two classes are the same, or whether there are problems in <math>NP</math> that ...] and [[mathematics]]. The most common measurements are [[time]] (how many steps it takes to solve a problem as a function of input, usually expressed with
  6 KB (1,104 words) - 14:11, 25 October 2017
• Asymptote: Advanced Configuration
  There are two things that Asymptote users commonly would like to do with their figures: m ...d to <tt>C:\Program Files</tt> on your computer, you can use the following steps to get MikTeX to see Asymptote:
  12 KB (1,931 words) - 12:53, 26 January 2020
• 2007 AIME I Problems
  ...tain time, one of these three persons is exactly halfway between the other two. At that time, find the distance in feet between the start of the walkway ...math>O_2</math> lie in the exterior of the triangle and are the centers of two circles with equal radii. The circle with center <math>O_1</math> is tange
  7 KB (1,218 words) - 14:28, 11 July 2022
• 2007 AIME I Problems/Problem 2
  ...tain time, one of these three persons is exactly halfway between the other two. At that time, find the [[distance]] in feet between the start of the walk
  2 KB (301 words) - 07:09, 4 November 2022

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