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• List of United States middle school mathematics competitions
  ...ath/puzzle competitions for middle schoolers with a focus towards creating a fun and collaborative environment. * [[AMC 8]] hosted by the [[American Mathematics Competitions]] is a very large middle school math contest taken in-school. ([http://www.maa.org
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• List of United States high school mathematics competitions
  * [http://homeschoolmathcontests.com Homeschool Math Contests] has a chart of math contests open to individuals (homeschooled and otherwise), an * [[Mu Alpha Theta]] -- hosts both local and a national competition.
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• MathILy (serious mathematics infused with levity)
  '''{MathILy, MathILy-Er}''' are a pair of intensive 5-week-long residential summer math programs for high sch ...ts for about 7 hours a day total, in a morning and evening shift, six days a week. The lead instructors are mathematicians with Ph.D.s and the apprenti
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• MATHCOUNTS
  ...onal [[mathematics competition]] and [[mathematics coaching]] program that has served millions of middle school students since 1984. Sponsored by the [htt {{Contest Info|name=MATHCOUNTS|region=USA|type=Free Response|difficulty=0.5 - 2.5|breakdown=<u>
  10 KB (1,506 words) - 21:31, 14 May 2024
• ICTM Math Contest
  ...consists of five members who work together on 20 questions for 25 minutes. A school may field as many five member teams as it wishes. The individual com A school team will qualify by taking first place in a region with four or more schools competing.
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• Math books
  * Getting Started is recommended for students grades who are participating in contests like AMC 8/10 and Mathcounts. * Intermediate is recommended for students who can expect to pass the AMC 10/12.
  24 KB (3,177 words) - 12:53, 20 February 2024
• William Lowell Putnam Mathematical Competition
  The '''William Lowell Putnam Mathematical Competition''' is a highly challenging, proof-oriented [[mathematics competition]] for undergra ...own=<u>Problem A/B, 1/2</u>: 7<br><u>Problem A/B, 3/4</u>: 8<br><u>Problem A/B, 5/6</u>: 9}}
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• Physics books
  .../www.amazon.com/exec/obidos/ASIN/0756613647/artofproblems-20 Chaos: Making a New Science] by James Gleick ...le.amazon.com/Dreams-Final-Theory-Steven-Weinberg/dp/0679419233/ Dreams of a Final Theory] by Weinberg
  10 KB (1,410 words) - 13:07, 20 February 2024
• Physics
  <strong>Physics</strong> is a branch of [[science]] that studies the properties of matter, energy, and ma Modern Physics is also a group of different subjects in physics:
  9 KB (1,355 words) - 07:29, 29 September 2021
• AMC historical results
  ...at a consistent number of students qualify for AIME each year, rather than a fixed percentage. Usually, 6000-7000 competitors from the AMC 10 and 12 qua ...ints or higher on the AMC 10. Awarded to students in 10th grade or younger who score 90 points or higher on the AMC 12.
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• United States of America Mathematical Olympiad
  ...tes of America Mathematical Olympiad''' ('''USAMO''') is the third test in a series of exams used to challenge bright students on the path toward choosi ...an Mathematics Competitions]] (AMC). [[Art of Problem Solving]] (AoPS) is a proud sponsor of the AMC and of the recent expansion of USAMO participants
  6 KB (869 words) - 12:52, 20 February 2024
• Joining an ARML team
  ...21-2022. The meetings are currently run online via Zoom. Alabama generally has enough interest to send one team per year to ARML. There are six practices The Arizona ARML team has been organized by [[mathleague.org]] since 2008. More information on parti
  21 KB (3,500 words) - 18:41, 23 April 2024
• Proof writing
  ...nt meaning to how the word is understood by the wider population. Students who spend time studying maths can develop proof-writing skills over time. ...n, accuracy, and clarity. A single word can change the intended meaning of a proof, so it is best to be as precise as possible.
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• USAMO historical results
  ...ct score on the [[USAMO]] has been 42 points for 6 problems. Prior to 1996 a perfect score was 100 points across 5 problems. ...y years, this number was smaller. Starting 2022, the USAMO awarding scheme has been revised to incorporate distinctions of Gold, Silver, Bronze, and HM.
  10 KB (1,317 words) - 08:16, 23 April 2024
• Pigeonhole Principle
  ...ts, the principle may be referred to as the '''Dirichlet box principle'''. A common phrasing of the principle uses balls and boxes and is that if <math> ...nhole principle is as follows: suppose for contradiction that there exists a way to place <math>n</math> balls into <math>k</math> boxes where <math>n>k
  11 KB (1,985 words) - 21:03, 5 August 2023
• Combinatorics
  ...mbers]], and so too methods of solving the [[Rubiks cube]]. Mathematicians who spend their careers studying combinatorics are known as ''combinatorialists ...Inclusion-Exclusion|principle of inclusion-exclusion]]. Combinatorics also has many applications outside of pure mathematics, notably in [[theoretical com
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• Alabama ARML
  ...e [[American Regions Mathematics League]]. Historically, the Alabama team has placed in the top 10 at ARML many times. * In 2006, Alabama came in 15th in the A division.
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• Triangle
  A '''triangle''' is a type of [[polygon]]. {{asy image|<asy>draw((0,1)--(2,0)--(3,2)--cycle);</asy>|right|A triangle.}}
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• Binomial Theorem
  The '''Binomial Theorem''' states that for [[real]] or [[complex]] <math>a</math>, <math>b</math>, and [[non-negative]] [[integer]] <math>n</math>, <center><math>(a+b)^n = \sum_{k=0}^{n}\binom{n}{k}a^{n-k}b^k</math></center>
  5 KB (935 words) - 13:11, 20 February 2024
• Fundamental Theorem of Calculus
  The '''Fundamental Theorem of Calculus''' establishes a link between the two central operations of [[calculus]]: [[derivative|diffe This section is for people who know what [[integral]]s are but don't know the Fundamental Theorem of Calcu
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• Writing scholarships
  ...f '''writing scholarships''' — scholarships granted based primarily upon a submitted essay — is primarily for American students. This list can be r ...be in a creative fundraiser, an inventive new app, series of blog posts on a particular theme, or another idea). The application deadline is 11:59 pm PS
  7 KB (1,039 words) - 18:45, 18 January 2024
• Vector
  ...y, but also most abstractly, a vector is any object which is an element of a given vector space. ...(x\,\,y\,\,z\,\,...)</math>. The set of vectors over a [[field]] is called a [[vector space]].
  7 KB (1,265 words) - 13:22, 14 July 2021
• International Mathematical Olympiad
  ...r, countries from around the world send a team of 6 students to compete in a grueling competition. {{Contest Info|name=IMO |region=International|type=Proof|difficulty=5.5 - 10|breakdown=<u>Probl
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• Modular arithmetic/Intermediate
  ...or <math>a \equiv b</math> (mod <math>n</math>), if the difference <math>{a - b}</math> is divisible by <math>n</math>. ...Z}_n</math> for short). This structure gives us a useful tool for solving a wide range of number-theoretic problems, including finding solutions to [[D
  14 KB (2,317 words) - 19:01, 29 October 2021
• 2006 AMC 12B Problems
  \text {(A) } - 2006 \qquad \text {(B) } - 1 \qquad \text {(C) } 0 \qquad \text {(D) } <math>\text {(A) } - 72 \qquad \text {(B) } - 27 \qquad \text {(C) } - 24 \qquad \text {(D)
  13 KB (2,058 words) - 12:36, 4 July 2023
• 2002 AMC 12B Problems
  ...numbers in the set <math>\{9, 99, 999, 9999, \ldots, 999999999\}</math> is a <math>9</math>-digit number <math>M</math>, all of whose digits are distinc <math>\mathrm{(A)}\ 0
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• 2006 AMC 12B Problems/Problem 19
  ...s. On a family trip his oldest child, who is 9, spots a license plate with a 4-digit number in which each of two digits appears two times. "Look, daddy! \mathrm{(A)}\ 4\qquad\mathrm{(B)}\ 5\qquad\mathrm{(C)}\ 6\qquad\mathrm{(D)}\ 7\qquad\m
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• 1991 AJHSME Problems
  <math>\text{(A)}\ 222,222,222,222 \qquad <math>\text{(A)}\ 4 \qquad \text{(B)}\ 8 \qquad \text{(C)}\ 12 \qquad \text{(D)}\ 16 \qqua
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• Problem solving
  ...but perhaps they were missing something. By the end of MOP, I had learned a somewhat unsettling truth. The others knew fewer tricks than I did, not mor ...have learned also that the formula sheets were fool’s gold – he became a Rhodes scholar.)
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• 2004 AIME I Problems
  The digits of a positive integer <math> n </math> are four consecutive integers in decreasi ...he absolute value of the difference between the greatest element of <math> A </math> and the greatest element of <math> B </math> is 99. Find <math> m.
  9 KB (1,434 words) - 13:34, 29 December 2021
• 1993 AIME Problems
  ...n for office, a candidate made a tour of a country which we assume lies in a plane. On the first day of the tour he went east, on the second day he went \hline \text{number of contestants who caught} \ n \ \text{fish} & 9 & 5 & 7 & 23 & \dots & 5 & 2 & 1 \\
  8 KB (1,275 words) - 06:55, 2 September 2021
• 2001 AIME II Problems
  ...rom left to right, each pair of consecutive digits of <math>N</math> forms a perfect square. What are the leftmost three digits of <math>N</math>? ...y both languages, and let <math>M</math> be the largest number of students who could study both languages. Find <math>M-m</math>.
  8 KB (1,282 words) - 21:12, 19 February 2019
• 2006 AMC 10B Problems/Problem 25
  ...s. On a family trip his oldest child, who is 9, spots a license plate with a 4-digit number in which each of two digits appears two times. "Look, daddy! <math> \mathrm{(A) \ } 4\qquad \mathrm{(B) \ } 5\qquad \mathrm{(C) \ } 6\qquad \mathrm{(D) \
  5 KB (878 words) - 14:39, 3 December 2023
• 1993 AIME Problems/Problem 11
  ...Bonnie play this game several times with the stipulation that the loser of a game goes first in the next game. Suppose that Alfred goes first in the fir The probability that the <math>n</math>th flip in each game occurs and is a head is <math>\frac{1}{2^n}</math>. The first person wins if the coin lands
  7 KB (1,058 words) - 20:57, 22 December 2020
• 1998 AIME Problems/Problem 4
  In order for a player to have an odd sum, he must have an odd number of odd tiles: that is ...in <math>\dbinom{4}{2} \cdot \dbinom{2}{2} = 6</math> ways. This gives us a total of <math>10 \cdot 2 \cdot 6 = 120</math> possibilities in which all
  5 KB (917 words) - 02:37, 12 December 2022
• Minnesota ARML
  ...thematics competition]]. All four teams currently compete in ARML Division A, due to the White and Blue teams recently winning awards as top teams in Di Students who finish in the top 10 of the MSHSML regular season meet individual standings
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• 2006 AMC 10B Problems
  <math> \mathrm{(A) \ } -2006\qquad \mathrm{(B) \ } -1\qquad \mathrm{(C) \ } 0\qquad \mathrm{( <math> \mathrm{(A) \ } -72\qquad \mathrm{(B) \ } -27\qquad \mathrm{(C) \ } -24\qquad \mathrm{
  14 KB (2,059 words) - 01:17, 30 January 2024
• Carl Friedrich Gauss
  '''Carl Friedrich Gauss''' was a German [[mathematician]] and [[scientist]] who lived from April 30, 1777 to February 23, 1855. ...prime]]) is [[constructible polygon | constructible]]. He even asked for a 17-gon to be put on his tombstone.
  642 bytes (94 words) - 08:40, 21 August 2009
• Mock MathCounts
  ...s may be sourced from a group of problem writers. Different users may have a different way of participating; some may require signups, while others do n ...l make Mock MATHCOUNTS in any given year, but it's usually a good bet that someone will.
  26 KB (3,265 words) - 21:34, 20 March 2024
• 2007 iTest Problems
  A twin prime pair is a set of two primes <math>(p, q)</math> such that <math>q</math> is <math>2</ <math>\mathrm{(A)}\, 4</math>
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• United States of America Computing Olympiad
  ...Olympiad''' includes a series of seven internet programming contests and a training camp, used to eventually choose the team that will represent the U ...4 problems lasting 4-5 hours. Competitors may participate at any time over a weekend for four hours as long as those hours are continuous.
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• 2001 AMC 8 Problems
  ...class is making a golf trophy. He has to paint <math>300</math> dimples on a golf ball. If it takes him <math>2</math> seconds to paint one dimple, how <math> \mathrm{(A) \ 4 } \qquad \mathrm{(B) \ 6 } \qquad \mathrm{(C) \ 8 } \qquad \mathrm{(D)
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• ELMO
  ...OP]]. Its initials have stood for many things over time, originating from a backronym originally called the "Experimental Lincoln Math Olympiad". The b ..., with an additional 'S' "*, having the same problems as the ELMO but with a new appearance to make it hard to read.
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• Canada/USA Mathcamp
  ...thcamp tends to be relaxed in terms of rules; in fact, Mathcamp officially has only four rules (generally invoking common sense and respect). Students ha ...ines]]. The location rotates around regions of North America, typically on a 3-year cycle.
  4 KB (680 words) - 23:22, 12 April 2021
• 2005 IMO Shortlist Problems/C2
  ...th> persons buy sombreros (directly or indirectly), then that someone wins a free instructional video. Prove that if <math> \displaystyle n </math> per ...l call direct successor of a blossom who is not a blossom him- or her-self a ''bud''.
  3 KB (538 words) - 09:12, 29 August 2011
• LaTeX:Layout
  ...his allows you to use the same code in many source files by just including a single line in each source file. ...font size, which is 10pt by default but can be increased to 11pt or 12pt. A reference on other options for this command can be found [http://www.nada.k
  30 KB (5,171 words) - 10:16, 4 April 2021
• 1998 PMWC Problems
  Find a pair of consecutive Triangular Numbers and the difference between a pair of consecutive Square Numbers whose difference are both <math>11</math ...<math>OB = OA=3</math> cm. <math>\angle BOA</math> is a right angle. <math>A</math> and <math>B</math> are two points on the circumference of circle of
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• 2000 PMWC Problems
  <math>y</math> is a number that has <math>8</math> different factors (including the number <math>1</math> and i Given that <math>A^4=75600\times B</math>. If <math>A</math> and <math>B</math> are positive integers, find the smallest value of
  11 KB (1,713 words) - 22:47, 13 July 2023
• 1999 USAMO Problems/Problem 5
  ...ut producing SOS then the game is a draw. Prove that the second player has a winning strategy. ...uch that <math>\text{min}\,(|l-1|,|l-2000|,|l-k|) > 3</math>, and fills in a S. The first player may again play anywhere, say <math>m</math>. If the sec
  2 KB (433 words) - 13:35, 4 July 2013
• 2001 IMO Problems/Problem 3
  ...e problem that was solved by both the girl and the boy. Show that there is a problem that was solved by at least three girls and at least three boys. ...girl are the holes and the boys are the pigeons, and the guy/pigeon enters a hole/problem which he solved in common with the girl).
  2 KB (453 words) - 07:27, 26 November 2020
• Analysis
  ..."analysis" and what is not. However, one can be pretty sure that something has an analytical flavor every time he or she hears such words as [[limit]], [[ ...lon delta definition of continuity and Cauchy who tried to put calculus on a "firm logical basis."
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• Isaac Newton
  '''Isaac Newton''' (1643 – 1727) was a famous British [[physics|physicist]] and [[mathematician]]. His most famous ...irst, though he made use of rather odd notation. Ironically, Newton earned a knighthood from Queen Anne in 1705 not because of this great discovery, but
  2 KB (391 words) - 13:36, 22 November 2020
• 2000 AMC 12 Problems/Problem 13
  ...ut were never zero. Angela drank a quarter of the total amount of milk and a sixth of the total amount of coffee. How many people are in the family? <math>\text {(A)}\ 3 \qquad \text {(B)}\ 4 \qquad \text {(C)}\ 5 \qquad \text {(D)}\ 6 \qqu
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• 1995 AHSME Problems
  ...7, 83, and 88 on her first three mathematics examinations. If Kim receives a score of 90 on the fourth exam, then her average will <math> \mathrm{(A) \ \text{remain the same} } \qquad \mathrm{(B) \ \text{increase by 1} } \qq
  17 KB (2,387 words) - 22:44, 26 May 2021
• 1997 PMWC Problems
  ...represent a single digit. Different letters represent different digits but a box can represent any digit. What does the five-digit number <math>\mathrm{ ...&\Box\\ \hline &\Box &\Box & 9 &\Box\\ \Box &\Box &\Box & 7 &\\ \hline H & A & P & P & Y\end{array} </cmath>
  15 KB (2,057 words) - 19:13, 10 March 2015
• 1959 AHSME Problems
  Each edge of a cube is increased by <math>50</math>%. The percent of increase of the surfa <math>\textbf{(A)}\ 50 \qquad\textbf{(B)}\ 125\qquad\textbf{(C)}\ 150\qquad\textbf{(D)}\ 300
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• 2007 AMC 8 Problems
  <math>\textbf{(A)}\ 9 \qquad\textbf{(B)}\ 10 \qquad\textbf{(C)}\ 11 \qquad\textbf{(D)}\ 12 \ ...f the number of students who preferred spaghetti to the number of students who preferred manicotti?
  12 KB (1,800 words) - 20:01, 8 May 2023
• 2002 AMC 12B Problems/Problem 17
  ...st as Andy's mower. If they all start to mow their lawns at the same time, who will finish first? <math>\mathrm{(A)}\ \text{Andy}
  2 KB (380 words) - 15:00, 17 August 2023
• 2008 AMC 10B Problems
  A basketball player made <math>5</math> baskets during a game. Each basket was worth either <math>2</math> or <math>3</math> points. <math>\mathrm{(A)}\ 2\qquad\mathrm{(B)}\ 3\qquad\mathrm{(C)}\ 4\qquad\mathrm{(D)}\ 5\qquad\m
  12 KB (1,838 words) - 16:52, 7 October 2022
• 2008 AMC 12B Problems
  A basketball player made <math>5</math> baskets during a game. Each basket was worth either <math>2</math> or <math>3</math> points. <math>\textbf{(A)}\ 2 \qquad \textbf{(B)}\ 3 \qquad \textbf{(C)}\ 4 \qquad \textbf{(D)}\ 5 \
  14 KB (2,199 words) - 13:43, 28 August 2020
• Minority Introduction to Engineering and Science
  ...ploring careers in science, engineering, and entrepreneurship. Despite the name, the program is open to all participant. ...roduction to Engineering) Program. The MITE program was created as part of a national effort sponsored by the then Engineers' Council for Professional D
  2 KB (272 words) - 19:01, 25 November 2022
• 2008 AIME I Problems/Problem 12
  ...hour will be four car lengths behind the back of the car in front of it.) A photoelectric eye by the side of the road counts the number of cars that pa ...t). Then the length of each unit is <math>4(n + 1)</math>. To maximize, in a unit, the CAR comes first, THEN the empty space. So at time zero, the car i
  4 KB (669 words) - 18:35, 8 October 2023
• 1990 APMO Problems
  ...h>, how many non-similar triangles are there in which <math>AEGF</math> is a cyclic quadrilateral? ...the products of <math>a_1, a_2, \dots , a_n</math> taken <math>k</math> at a time. Show that
  2 KB (364 words) - 23:07, 12 September 2016
• 2008 AMC 10A Problems/Problem 15
  <math>\mathrm{(A)}\ 120\qquad\mathrm{(B)}\ 130\qquad\mathrm{(C)}\ 140\qquad\mathrm{(D)}\ 150 ...n find a similar equation for Han, who drove <math>D + 70</math> miles, at a rate of <math>R+5</math>, for <math>T+1</math> hours, giving us <math>D + 7
  6 KB (1,033 words) - 15:19, 1 July 2021
• 2008 USAMO Problems/Problem 6
  ...mber of ways that the mathematicians may be split between the two rooms is a power of two (i.e., is of the form <math>2^k</math> for some positive integ ...e [[vector space]] of all such functions. Define the linear operator <math>A : V \to V</math> as
  13 KB (2,414 words) - 14:37, 11 July 2016
• Mathleague.org
  mathleague.org's test format can best be described as a hybrid between the [[MATHCOUNTS]] and [[ARML]] formats. mathleague.org als {{Contest Info|name=mathleague.org Tests|region=Mostly USA with international participation|typ
  5 KB (801 words) - 12:47, 23 September 2023
• Sylow Theorems
  ...most important results in the field. They are named for P. Ludwig Sylow, who published their proof in 1872. :'''Theorem.''' Every finite group contains a [[Sylow p-subgroup |Sylow <math>p</math>-subgroup]].
  11 KB (2,071 words) - 12:25, 9 April 2019
• KGS math club
  A group of people on [http://www.gokgs.com Kiseido Go Server] Mathematics roo ...our, or of a less-than-or-equal rank. What is the greatest possible length a parade can reach?
  22 KB (3,358 words) - 15:17, 18 July 2017
• How should I prepare?
  ...' are an excellent resource to help prepare for math contests. They cover a broad range of topics, from algebra to geometry to number theory to combina ...tests to see if the books are on the right level for you. '''Alcumus''' is a good resource even if you do not own any of the AoPS books.
  13 KB (1,926 words) - 11:22, 30 November 2023
• 1998 AHSME Problems
  ...ides of five congruent rectangles is labeled with an integer. In rectangle A, <math>w = 4, x = 1, y = 6, z = 9</math>. In rectangle B, <math>w = 1, x = <math> \mathrm{(A)\ } A \qquad \mathrm{(B) \ }B \qquad \mathrm{(C) \ } C \qquad \mathrm{(D) \ } D
  15 KB (2,222 words) - 10:40, 11 August 2020
• Millennium Problems
  ...set of seven problems for which the [[Clay Mathematics Institute]] offered a US \$7 million prize fund (\$1 million per problem) to celebrate the new mi ...the American John Tate announced the prize: one million dollars to anyone who could solve one of the seven most difficult open problems at the time.
  13 KB (1,969 words) - 17:57, 22 February 2024
• 2008 iTest Problems
  ...s as a Renewable Energy Engineer for the Southern Company, and Hannah runs a lab at Jupiter Falls University where she researches biomass (renewable fue When the Kubiks went on vacation to San Diego last year, they spent a day at the San Diego Zoo.
  71 KB (11,749 words) - 01:31, 2 November 2023
• 2008 iTest Problems/Problem 82
  Tony’s favorite “sport” is a spectator event known as the Super Mega Ultra Galactic Thumbwrestling thumbwrestlers who have dedicated their lives to earning lithe, powerful thumbs, compete to
  2 KB (246 words) - 22:44, 5 January 2023
• For The Win
  ...here you can compete against many players and the Countdown game, which is a head-to-head competition modeled after the [[MATHCOUNTS]]® Countdown round This version of FTW has been deactivated. Visit the new one [[For The Win beta|here]].
  2 KB (282 words) - 02:51, 24 June 2023
• 2002 AMC 10B Problems
  <math> \mathrm{(A) \ } \frac{1}{6}\qquad \mathrm{(B) \ } \frac{1}{3}\qquad \mathrm{(C) \ } \f For the nonzero numbers <math>a, b,</math> and <math>c,</math> define
  10 KB (1,540 words) - 22:53, 19 December 2023
• 1963 IMO Problems/Problem 6
  ...and no two contestants predicted to finish consecutively actually did so. A second prediction had the contestants finishing in the order <math>DAECB</m ...inishers. But (4) has 2 disjoint correctly predicted consecutive finishers who are <math>DA</math> and <math>CB</math>.
  2 KB (249 words) - 14:28, 31 July 2016
• 1985 AJHSME Problems/Problem 7
  ...ath>1</math> through <math>4</math> are shown. All rows begin and end with a white square. The number of black squares in the <math>37\text{th}</math> r <math>\text{(A)}\ 34 \qquad \text{(B)}\ 35 \qquad \text{(C)}\ 36 \qquad \text{(D)}\ 37 \qq
  3 KB (584 words) - 09:23, 10 January 2023
• 1987 AJHSME Problems
  <math>\text{(A)}\ .012 \qquad \text{(B)}\ .066 \qquad \text{(C)}\ .12 \qquad \text{(D)}\ . <math>\text{(A)}\ .008 \qquad \text{(B)}\ .08 \qquad \text{(C)}\ .8 \qquad \text{(D)} 1.25
  12 KB (1,568 words) - 09:35, 31 October 2021
• 2009 AMC 12A Problems/Problem 25
  The first two terms of a sequence are <math>a_1 = 1</math> and <math>a_2 = \frac {1}{\sqrt3}</math>. <math>\textbf{(A)}\ 0\qquad \textbf{(B)}\ 2 - \sqrt3\qquad \textbf{(C)}\ \frac {1}{\sqrt3}\q
  7 KB (990 words) - 07:23, 24 October 2022
• 1987 AJHSME Problems/Problem 17
  Abby, Bret, Carl, and Dana are seated in a row of four seats numbered #1 to #4. Joe looks at them and says: ...h one of Joe's statements is false. Bret is actually sitting in seat #3. Who is sitting in seat #2?
  934 bytes (156 words) - 23:53, 4 July 2013
• Singapore mathematics competitions
  * Singapore Mathematical Olympiad for Primary Schools (SMOPS). Students who perform well in SMOPS may proceed to the Asia-Pacific Mathematics Olympiad ...ned for elementary and middle school students and has been conducted twice a year in March and October since 2016.
  2 KB (282 words) - 03:31, 5 November 2023
• 1964 IMO Problems/Problem 4
  at least three people who write to each other about the same topic. ...sider a complete graph with 6 vertices colored with 2 colors. There exists a monochromatic triangle.
  2 KB (339 words) - 18:00, 7 December 2022
• 1991 AJHSME Problems/Problem 23
  ...are in either band or orchestra or both. The number of males in the band who are NOT in the orchestra is <math>\text{(A)}\ 10 \qquad \text{(B)}\ 20 \qquad \text{(C)}\ 30 \qquad \text{(D)}\ 50 \qq
  1 KB (159 words) - 18:23, 29 December 2022
• 1993 AJHSME Problems
  Which pair of numbers does NOT have a product equal to <math>36</math>? <math>\text{(A)}\ \{ -4,-9\} \qquad \text{(B)}\ \{ -3,-12\} \qquad \text{(C)}\ \left\{ \df
  14 KB (1,797 words) - 11:13, 28 December 2022
• Mock AIME 2 2010 Answer Key
  ...an be easily proved through strong induction. Starting from 2010, which is a multiple of 15, we must first purge 1 lemming. We can then purge 4 lemmings ...atisfies <math>b_1+b_2+\ldots+b_{10}\equiv 0 \pmod{3}</math>, there exists a corresponding <math>(a_1, a_2, \ldots, a_{10})</math> such that <math>a_1+a
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• Getting Started With Python Programming
  ...ing language. The only language that AoPS teaches (as of May 16, 2021) in a class is Python. ...''Intermediate Programming with Python'' students should install Python on a regular computer.
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• 1996 AJHSME Problems
  <math>\text{(A)}\ 2 \qquad \text{(B)}\ 3 \qquad \text{(C)}\ 4 \qquad \text{(D)}\ 5 \qquad ...1 from the number 10, adds 2 to his number, and then doubles the result. Who gets the largest final answer?
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• 1974 IMO Problems
  Three players <math>A, B</math> and <math>C</math> play the following game: On each of three card ...has 9. At the last round <math>B</math> received <math>r</math> counters. Who received <math>q</math> counters on the first round?
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• 1974 IMO Problems/Problem 1
  Three players <math>A, B</math> and <math>C</math> play the following game: On each of three card ...has 9. At the last round <math>B</math> received <math>r</math> counters. Who received <math>q</math> counters on the first round?
  2 KB (418 words) - 15:46, 24 November 2010
• 2004 AMC 8 Problems
  ...ter length represents <math>72</math> kilometers. How many kilometers does a <math>17</math>-centimeter length represent? <math> \textbf{(A)}\ 6\qquad\textbf{(B)}\ 102\qquad\textbf{(C)}\ 204\qquad\textbf{(D)}\ 864\q
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• 2006 AMC 8 Problems
  <math> \textbf{(A)}\ 10\qquad\textbf{(B)}\ 15\qquad\textbf{(C)}\ 16\qquad\textbf{(D)}\ 17\qqu <math> \textbf{(A)}\ 1\qquad\textbf{(B)}\ 6\qquad\textbf{(C)}\ 13\qquad\textbf{(D)}\ 19\qquad
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• 2011 AMC 12A Problems/Problem 17
  \textbf{(A)}\ \frac{3}{5} \qquad pair A=(0,0), B=(3,0), C=(0,4);
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• Introduction to Programming Week 2
  Computers work with data, which might be a number, a piece of text, or a true/false value. ...n]] are either [[integer]]s or [[floating point number]]s. Unlike humans, who use base 10, computers store numbers in binary (base 2), which may lead to
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• AoPS Moderators
  ...f Problem Solving]] website is a non-administrator user who has powers for a particular forum which non-moderators don't. When a user is a moderator, their username shows up in green.
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• 1999 AMC 8 Problems
  <math>\text{(A)} \div \qquad \text{(B)}\ \times \qquad \text{(C)} + \qquad \text{(D)}\ - \ What is the degree measure of the smaller angle formed by the hands of a clock at 10 o clock?
  17 KB (2,394 words) - 19:51, 8 May 2023
• Rhode Island MathCounts
  Due to its small size, Rhode Island has no chapters. Instead, students progress straight to the state competition f ...lowed by lunch. After lunch, the team round takes place, and then there is a brief waiting period until the countdown round competitors are announced. A
  9 KB (1,234 words) - 08:31, 2 May 2024
• 2003 AMC 10B Problems
  <math>\textbf{(A)} -1 \qquad\textbf{(B)} -\frac{2}{3} \qquad\textbf{(C)} \frac{2}{3} \qquad\ ...<math> \ </math><math>1</math> more than a pink pill, and Al's pills cost a total of <math> \ </math><math>546</math> for the two weeks. How much does
  15 KB (2,166 words) - 21:17, 16 February 2021
• Reaper
  There is a log for Reaper game 77 (and possibly for future ones too). The chance of a multiplier (seen below) is about 10%, while the chance of an octuple reap i
  4 KB (795 words) - 16:11, 1 April 2023
• 2003 AMC 8 Problems
  Jamie counted the number of edges of a cube, Jimmy counted the numbers of corners, and Judy counted the number of <math>\mathrm{(A)}\ 12 \qquad\mathrm{(B)}\ 16 \qquad\mathrm{(C)}\ 20 \qquad\mathrm{(D)}\ 22
  16 KB (2,236 words) - 12:02, 19 February 2024
• 1999 AMC 8 Problems/Problem 6
  ...Bo and Coe have more than Moe. Jo has more than Moe, but less than Bo. Who has the least amount of money? <math> \text{(A)}\ \text{Bo}\qquad\text{(B)}\ \text{Coe}\qquad\text{(C)}\ \text{Flo}\qquad\
  903 bytes (171 words) - 21:17, 30 October 2016
• 2005 CEMC Gauss (Grade 7) Problems
  = Part A: Each correct answer is worth 5 points = <math>\text{(A)}\ 1 \qquad \text{(B)}\ 2 \qquad \text{(C)}\ 3 \qquad \text{(D)}\ 4 \qquad
  16 KB (2,317 words) - 03:54, 24 October 2014
• 2011 IMO Problems/Problem 1
  ...which <math>a_i +a_j</math> divides <math>s_A</math>. Find all sets <math>A</math> of four distinct positive integers which achieve the largest possibl ...+a_3)+(a_2+a_1) = s_A \ge 0</math>, so again <math>(a_2, a_4)</math> isn't a good couple. We have in total 6 couples. So <math>n_A \leq 6-2=4</math>.
  9 KB (1,718 words) - 23:08, 26 June 2014
• 2006 Indonesia MO Problems/Problem 4
  ...awn. The first player who cannot move anymore loses the game. Which player has the winning strategy? Explain the strategy. {{Indonesia MO box|year=2006|num-b=3|num-a=5}}
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• 1999 AMC 8 Problems/Problem 19
  ...are baking Bonnie's Best Bar Cookies this year. Their recipe, which makes a pan of 15 cookies, lists these items: <math>1\frac{1}{2}</math> cups flour, ...e enough pans of cookies to supply 216 cookies. There are 8 tablespoons in a stick of butter. How many sticks of butter will be needed? (Some butter may
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• Arthur Benjamin
  ...isc series ''Mathemagics''. This series has 5 The Great Courses videos. He has also written the book ''The Magic Of Math''.
  644 bytes (110 words) - 14:57, 24 June 2020
• 2003 AMC 8 Problems/Problem 18
  ...viting only the following: all of her friends and all of those classmates who are friends with at least one of her friends. How many classmates will not pair a=(102,256), b=(68,131), c=(162,101), d=(134,150);
  2 KB (250 words) - 22:17, 5 January 2024
• BBCode:Tutorial
  ...tag too. The closing tag is the same as the opening tag except that it has a / symbol at the front. For example, the tag [/b] is code for "stop making t Below are some of the most commonly used BBCode tags around AoPS forums. For a comprehensive list of all BBCode tags, see [[List of BBCodes|List of BBCode
  10 KB (1,680 words) - 19:26, 5 April 2023
• 2003 AMC 8 Problems/Problem 16
  ...and <math>2</math> back passenger seat. Bonnie and Carlo are the only ones who know how to drive the car. How many possible seating arrangements are there <math> \textbf{(A)}\ 2\qquad\textbf{(B)}\ 4\qquad\textbf{(C)}\ 6\qquad\textbf{(D)}\ 12\qquad\
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• 2003 AMC 8 Problems/Problem 17
  ...dren listed below are from two families of three siblings each. Each child has blue or brown eyes and black or blond hair. Children from the same family h <math>\textbf{(A)}\ \text{Nadeen and Austin}\qquad\textbf{(B)}\ \text{Benjamin and Sue}\qqua
  2 KB (265 words) - 23:23, 22 March 2022
• Mathtime Version 1 Issue 2
  ...e the positive integer <math>n</math> such that <math>n^2+20n+40</math> is a perfect square. (Proposed by djmathman) ...atest possible integer value of <math>n</math> such that <math>75^n</math> has less than <math>1000</math> distinct positive divisors? (Proposed by djmath
  15 KB (2,444 words) - 21:46, 1 January 2012
• 1989 AHSME Problems
  <math> \textrm{(A)}\ -7\qquad\textrm{(B)}\ -2\qquad\textrm{(C)}\ 0\qquad\textrm{(D)}\ 1\qquad <math> \textrm{(A)}\ \frac{1}5\qquad\textrm{(B)}\ \frac{1}4\qquad\textrm{(C)}\ \frac{2}7\qqua
  15 KB (2,247 words) - 13:44, 19 February 2020
• 2012 AMC 12B Problems/Problem 14
  ...</math>. Let <math>N</math> be the smallest initial number that results in a win for Bernardo. What is the sum of the digits of <math>N</math>? <math> \textbf{(A)}\ 7\qquad\textbf{(B)}\ 8\qquad\textbf{(C)}\ 9\qquad\textbf{(D)}\ 10\qquad\
  3 KB (463 words) - 09:46, 24 April 2024
• 2012 AMC 10B Problems
  Each third-grade classroom at Pearl Creek Elementary has 18 students and 2 rabbits. How many more students than rabbits are there i <math> \textbf{(A)}\ 48\qquad\textbf{(B)}\ 56\qquad\textbf{(C)}\ 64\qquad\textbf{(D)}\ 72\qqu
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• 2012 AMC 12B Problems
  Each third-grade classroom at Pearl Creek Elementary has 18 students and 2 pet rabbits. How many more students than rabbits are ther <math> \textbf{(A)}\ 48\qquad\textbf{(B)}\ 56\qquad\textbf{(C)}\ 64\qquad\textbf{(D)}\ 72\qqu
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• University of Northern Colorado Math Contest
  This is a list of all UNC Math Contests in the AoPSWiki. Users are encouraged to pos The contest consists of two rounds. Each round is a paper and pencil exam with about 9-12 problems. Students compete individual
  2 KB (336 words) - 15:09, 2 January 2020
• 2012 AMC 10B Problems/Problem 18
  ...en at random from this population and gets a positive test result actually has the disease. Which of the following is closest to <math>p</math>? <math>\textbf{(A)}\ \frac{1}{98}\qquad\textbf{(B)}\ \frac{1}{9}\qquad\textbf{(C)}\ \frac{1}{
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• Epsilon Camp
  ...ds who are passionate about math to professional mathematics, and to build a supportive community of peers and families. ...experience to immerse the campers in a rich mathematical culture, creating a community of like-minded peers and faculty.
  4 KB (538 words) - 15:27, 6 January 2023
• 2012 AIME I Problems
  ...s with three not necessarily distinct digits, <math>abc</math>, with <math>a \neq 0</math> and <math>c \neq 0</math> such that both <math>abc</math> and ...h> miles per hour, respectively. The first time Butch and Sundance meet at a milepost, they are <math>n</math> miles from Dodge, and they have been trav
  10 KB (1,617 words) - 14:49, 2 June 2023
• 2012 AIME I Problems/Problem 7
  At each of the sixteen circles in the network below stands a student. A total of <math>3360</math> coins are distributed among the sixteen students pair A = (0,0);
  6 KB (1,058 words) - 01:49, 25 November 2023
• 2012 AIME II Problems
  ...science. There are two male and two female professors in each department. A committee of six professors is to contain three men and three women and mus ...tially heading south, and Cao bikes in a straight line across the field to a point <math>D</math> on the south edge of the field. Cao arrives at point <
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• 2012 AIME II Problems/Problem 14
  ...two handshaking arrangements different if and only if at least two people who shake hands under one arrangement do not shake hands under the other arrang ...consider reflections as separate entities. Thus, each of the three cases has <math>\dfrac{(3-1)!}{2}=1</math> arrangements. Therefore, for this case, t
  6 KB (1,098 words) - 14:18, 7 July 2023
• 2017 AMC 8 Problems
  <math>\textbf{(A) }2+0+1+7\qquad\textbf{(B) }2 \times 0 +1+7\qquad\textbf{(C) }2+0 \times 1 Alicia, Brenda, and Colby were the candidates in a recent election for student president. The pie chart below shows how the vo
  12 KB (1,771 words) - 21:13, 20 January 2024
• Mock AIME I 2012 Problems
  A circle of maximal area is inscribed in the region bounded by the graph of < A permutation of the numbers <math>\{2</math>, <math>3</math>, <math>4</math>
  7 KB (1,309 words) - 11:13, 8 April 2012
• Mock AIME I 2012 Problems/Problem 13
  ...lowed to subtract 1 at any time. The loser is the person who must subtract a number from itself and get zero. Let <math>S</math> be the set of all posit ...e have <math>p \mid n - p</math> and so <math>n - p</math> is even but not a power of <math>2</math>. By induction, all such positions are wins for the
  2 KB (445 words) - 17:43, 7 April 2012
• 2006 SMT/General Problems
  After a cyclist has gone <math> \frac{2}{3} </math> of his route, he gets a flat tire. Finishing on foot, he spends twice as long walking as he did rid A customer enters a supermarket. The probability that the customer buys bread is <math> 0.60 </
  10 KB (1,477 words) - 16:02, 27 May 2012
• 2012 AMC 12B Problems/Problem 16
  <math> \textbf{(A)}\ 108\qquad\textbf{(B)}\ 132\qquad\textbf{(C)}\ 671\qquad\textbf{(D)}\ 846 Let the ordered triple <math>(a,b,c)</math> denote that <math>a</math> songs are liked by Amy and Beth, <math>b</math> songs by Beth and Jo
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• 1999 USAMO Problems
  (a) every square that does not contain a checker shares a side with one that does; ...ven squares, such that every two consecutive squares of the sequence share a side.
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• 2004 AMC 8 Problems/Problem 18
  ...th> points, Dave <math>11</math> points, and Ellen <math>17</math> points. Who hits the region worth <math>6</math> points? <math>\textbf{(A)}\ \text{Alice}\qquad \textbf{(B)}\ \text{Ben}\qquad \textbf{(C)}\ \text{Ci
  2 KB (262 words) - 11:53, 23 March 2020
• 2013 AMC 12B Problems
  On a particular January day, the high temperature in Lincoln, Nebraska, was <mat <math>\textbf{(A)}\ -13 \qquad \textbf{(B)}\ -8 \qquad \textbf{(C)}\ -5 \qquad \textbf{(D)}\
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• 2013 AIME II Problems
  ...\text{B}</math>, and <math>\text{C}</math> are digits. Find <math>100\text{A}+10\text{B}+\text{C}</math>. Positive integers <math>a</math> and <math>b</math> satisfy the condition
  8 KB (1,402 words) - 12:17, 13 March 2020
• 2013 AIME II Problems/Problem 1
  ...\text{B}</math>, and <math>\text{C}</math> are digits. Find <math>100\text{A}+10\text{B}+\text{C}</math>. ...0</math> metric minutes in a day. The ratio of normal to metric minutes in a day is <math>\frac{1440}{1000}</math>, which simplifies to <math>\frac{36}{
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• 2014 AMC 10A Problems
  {{AMC10 Problems|year=2014|ab=A}} <math> \textbf{(A)}\ 3\qquad\textbf{(B)}\ 8\qquad\textbf{(C)}\ \frac{25}{2}\qquad\textbf{(D)}
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• 2014 AMC 10A Problems/Problem 11
  A customer who intends to purchase an appliance has three coupons, only one of which may be used: For which of the following listed prices will coupon <math>1</math> offer a greater price reduction than either coupon <math>2</math> or coupon <math>3
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• Camp-euclid
  ...are active researchers. Students will be assigned into groups; each group has mentors assigned to it. There are 4 hours per week of seminar meetings and
  560 bytes (86 words) - 17:33, 11 August 2014
• 2014 AMC 12A Problems
  {{AMC12 Problems|year=2014|ab=A}} <math> \textbf{(A)}\ 3\qquad\textbf{(B)}\ 8\qquad\textbf{(C)}\ \frac{25}{2}\qquad\textbf{(D)}
  12 KB (1,863 words) - 19:04, 11 April 2024
• 1990 AHSME Problems
  <math>\textbf{(A)}\ \pm\frac{1}{2}\qquad\textbf{(B)}\ \pm 1\qquad\textbf{(C)}\ \pm 2\qquad\t <math>\textbf{(A) } -16\qquad
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• 1975 AHSME Problems
  <math>\textbf{(A)}\ 3/4 \qquad <math>\textbf{(A)}\ \text{all }m\qquad
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• Utah Math Olympiad
  This is a list of all UMO exams in the AoPSWiki. Users are encouraged to post additi ...h 7 points. Partial credit will be awarded for significant progress toward a correct solution.
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• 2013 UMO Problems
  (a) Show that you can retrace the diagram without lifting up your pencil using Alice and Carl play the following game using a square sheet of paper. On each turn, the player makes
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• 2013 UMO Problems/Problem 5
  Cooper and Malone take turns replacing <math>a</math>, <math>b</math>, and <math>c</math> in the equation below with real <cmath>P(x) = x^3 + ax^2 + bx + c.</cmath> Once a coefficient has been replaced, no one can choose to
  638 bytes (103 words) - 15:27, 14 October 2014
• 2014 UNC) Math Contest II Problems
  The Duchess had a child on May 1st every two years until she had five children. This year the is a perfect square: <math>1 + 3 + 5 + 7 + 9 = 25</math>. How old will the young
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• 2014 UNCO Math Contest II Problems/Problem 10
  The March Hare invites <math>11</math> guests to a tea party. He randomly cake. The guests decide to play a game. Each one tries to guess
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• 2014 UNCO Math Contest II Problems
  The Duchess had a child on May 1st every two years until she had five children. This year the is a perfect square: <math>1 + 3 + 5 + 7 + 9 = 25</math>. How old will the young
  7 KB (1,228 words) - 15:10, 20 August 2020
• 2005 CEMC Gauss (Grade 7) Problems/Problem 7
  Karen has just been chosen the new “Math Idol”. A total of <math>1,480,000</math> votes were cast and Karen received <math>83 <math>\text{(A)}\ 830,000 \qquad \text{(B)}\ 1,228,400 \qquad \text{(C)}\ 1,100,000 \qquad
  638 bytes (88 words) - 01:45, 23 October 2014
• 2016 AMC 12A Problems
  {{AMC12 Problems|year=2016|ab=A}} <math>\textbf{(A)}\ 99\qquad\textbf{(B)}\ 100\qquad\textbf{(C)}\ 110\qquad\textbf{(D)}\ 121\
  15 KB (2,348 words) - 17:20, 19 January 2024
• KGS math club/solution 11 26
  ...blicly known list and says that her short list is one of these four pairs. A picks one pair as her real short list and picks the three remaining pairs r If the short list of B is among the pairs A announced, B can tell A that they have the same short list and that they do not know the murderer.
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• 2015 AMC 10A Problems
  {{AMC10 Problems|year=2015|ab=A}} <math> \textbf{(A)}\ -125\qquad\textbf{(B)}\ -120\qquad\textbf{(C)}\ \frac{1}{5}\qquad\textbf
  12 KB (1,887 words) - 18:52, 14 May 2024
• 2015 AMC 12A Problems
  {{AMC12 Problems|year=2015|ab=A}} <math> \textbf{(A)}\ -125\qquad\textbf{(B)}\ -120\qquad\textbf{(C)}\ \frac{1}{5}\qquad\textbf
  13 KB (2,117 words) - 12:33, 24 August 2023
• 2015 AMC 10A Problems/Problem 22
  ...l eight people flip their coins and those who flip heads stand while those who flip tails remain seated. What is the probability that no two adjacent peop <math>\textbf{(A)}\dfrac{47}{256}\qquad\textbf{(B)}\dfrac{3}{16}\qquad\textbf{(C) }\dfrac{49
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• 2015 AMC 10B Problems
  <math> \textbf{(A) } -2 \qquad\textbf{(B) } \dfrac{1}{16} \qquad\textbf{(C) } \dfrac{7}{4} \q Marie does three equally time-consuming tasks in a row without taking breaks. She begins the first task at 1:00 PM and finishe
  14 KB (2,247 words) - 11:38, 26 March 2024
• 2015 AMC 12B Problems
  <math>\textbf{(A)}\; -2 \qquad\textbf{(B)}\; \dfrac{1}{16} \qquad\textbf{(C)}\; \dfrac{7}{4} Marie does three equally time-consuming tasks in a row without taking breaks. She begins the first task at 1:00 PM and finishe
  13 KB (2,064 words) - 13:39, 1 October 2022
• 2015 AMC 12B Problems/Problem 22
  .... One person is seated in each chair. Each person gets up and sits down in a chair that is not the same and is not adjacent to the chair he or she origi <math>\textbf{(A)}\; 14 \qquad\textbf{(B)}\; 16 \qquad\textbf{(C)}\; 18 \qquad\textbf{(D)}\;
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• Oklahoma MathCounts
  ...n as regionals. There are five distinct regions. Each region competes on a certain date. Eastern region has been eliminated in 2015. It is uncertain about their existence in the futu
  4 KB (452 words) - 19:17, 9 February 2024
• 2015 AIME I Problems/Problem 15
  ...nd <math>c</math> is not divisible by the square of any prime. Find <math>a+b+c</math>. label(rpic,"$A$",(-3,3*sqrt(3),0),W);
  9 KB (1,407 words) - 19:37, 17 February 2024
• OSSM Awesome Contest
  ...ring Day) is a middle school math contest opened to 6th-8th grade students who lives in Oklahoma. ...dents combined are able to advance towards round 2. In addition, students who have won an award in round 2 in the past (not necessarily the year directly
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• 2015 AMC 8 Problems/Problem 22
  ...number of students per row each day. However, on June 13, they cannot find a new way of organizing the students. What is the smallest possible number of <math>\textbf{(A) } 21 \qquad \textbf{(B) } 30 \qquad \textbf{(C) } 60 \qquad \textbf{(D) }
  2 KB (394 words) - 23:39, 23 January 2024
• 2015 AMC 8 Problems
  ...feet long and <math>9</math> feet wide? (There are <math>3</math> feet in a yard.) <math>\textbf{(A) }12\qquad\textbf{(B) }36\qquad\textbf{(C) }108\qquad\textbf{(D) }324\qquad
  16 KB (2,322 words) - 14:04, 2 February 2024
• 2016 AMC 12A Problems/Problem 11
  ...g, <math>65</math> students who cannot dance, and <math>29</math> students who cannot act. How many students have two of these talents? <math>\textbf{(A)}\ 16\qquad\textbf{(B)}\ 25\qquad\textbf{(C)}\ 36\qquad\textbf{(D)}\ 49\qqu
  2 KB (336 words) - 22:05, 19 October 2016
• Gmaas
  ...is not older than he is because Gmaas is infinity years old. EDIT EDIT: He has now ...ke and reciprocated the fee," you must pay <math>1,000,000</math> to solve a problem using the Games theorem. You wouldn't waste that much money to solv
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• 2006 iTest Problems
  <math>\mathrm{(A)}\, 8</math> <math>\mathrm{(A)}\, 15\quad\mathrm{(B)}\, \frac{40}{3}</math>
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• Jason Batterson
  ...his experience to write the book Competition Math for Middle School, which has been used by thousands of middle-school students to improve their problem-s
  840 bytes (123 words) - 13:41, 21 May 2016
• Customizing Blogs with CSS
  ...uter language used to improve the user interface of websites designed with a mark up language (most notably HTML). CSS changes websites from globs of h The best way to see what CSS is is to see a website without it. Here is a site we all know and love, the AoPS home page....without CSS:
  1 KB (178 words) - 22:20, 15 December 2016
• CSS and HTML fundamentals
  ...ages, headings, bold text, lists, images, and basically all the content of a page with HTML. ...layout, size, and much more! In order to use CSS, however, you must know a little bit about HTML.
  7 KB (1,174 words) - 21:20, 14 November 2016
• 2017 AMC 10A Problems/Problem 19
  ...o sit next to Eric. How many ways are there for the five of them to sit in a row of <math>5</math> chairs under these conditions? <math> \textbf{(A)}\ 12\qquad\textbf{(B)}\ 16\qquad\textbf{(C)}\ 28\qquad\textbf{(D)}\ 32\qqu
  7 KB (1,196 words) - 01:31, 31 January 2023
• 2017 AMC 10A Problems/Problem 6
  ...the multiple choice questions right on the upcoming exam would receive an A on the exam. Which one of these statements necessarily follows logically? ...ultiple choice questions right.}\\\textbf{(E)}\ \text{If Lewis received an A, then he got at least one of the multiple choice questions right.}</math>
  3 KB (485 words) - 16:50, 5 August 2022
• 2017 AMC 10A Problems/Problem 8
  ...</math> people who know no one. People who know each other hug, and people who do not know each other shake hands. How many handshakes occur within the gr <math>\textbf{(A)}\ 240\qquad\textbf{(B)}\ 245\qquad\textbf{(C)}\ 290\qquad\textbf{(D)}\ 480
  3 KB (494 words) - 12:47, 19 October 2021
• 2017 AMC 10A Problems
  {{AMC10 Problems|year=2017|ab=A}} <math>\textbf{(A)}\ 70\qquad\textbf{(B)}\ 97\qquad\textbf{(C)}\ 127\qquad\textbf{(D)}\ 159\q
  15 KB (2,285 words) - 18:02, 28 October 2023
• 2017 AMC 12A Problems
  {{AMC12 Problems|year=2017|ab=A}} <math>\textbf{(A)}\ 8\qquad\textbf{(B)}\ 11\qquad\textbf{(C)}\ 12\qquad\textbf{(D)}\ 13\qqua
  15 KB (2,418 words) - 16:58, 7 November 2022
• 2017 AMC 10B Problems
  ...ded <math>11</math>. Then she switched the digits of the result, obtaining a number between <math>71</math> and <math>75</math>, inclusive. What was Mar <math>\textbf{(A)}\ 11\qquad\textbf{(B)}\ 12\qquad\textbf{(C)}\ 13\qquad\textbf{(D)}\ 14\qqu
  12 KB (1,930 words) - 20:23, 9 September 2022
• 2017 AMC 10B Problems/Problem 13
  <math>\textbf{(A)}\ 1\qquad\textbf{(B)}\ 2\qquad\textbf{(C)}\ 3\qquad\textbf{(D)}\ 4\qquad\t ...</math> classes is the total number of extra classes taken by the students who take <math>2</math> or <math>3</math> classes. Since we know that there are
  8 KB (1,283 words) - 13:26, 31 December 2023
• 2017 AMC 12B Problems
  ...te of <math>2</math> comic books per month. LaShawn's collection currently has <math>10</math> comic books in it, and he is adding to his collection at th <math>\textbf{(A)}\ 1\qquad\textbf{(B)}\ 4\qquad\textbf{(C)}\ 5\qquad\textbf{(D)}\ 20\qquad\
  15 KB (2,343 words) - 18:26, 25 December 2020
• 2017 AMC 12B Problems/Problem 22
  ...the probability that, at the end of the fourth round, each of the players has four coins? <math>\textbf{(A)}\quad \dfrac{7}{576} \qquad \qquad \textbf{(B)}\quad \dfrac{5}{192} \qquad
  12 KB (1,935 words) - 11:37, 16 December 2023
• 2017 AIME I Problems/Problem 7
  ...ere <math>a</math> and <math>b</math> are nonnegative integers with <math>a + b \leq 6</math>. Find the remainder when <math>S</math> is divided by <ma ...inom{6}{b} \binom{6}{c}</math> over all <math>a,b,c</math> such that <math>a+b+c=6</math>. Consider an array of 18 dots, with 3 columns of 6 dots each.
  8 KB (1,348 words) - 19:51, 29 January 2024
• 2017 AMC 8 Problems/Problem 24
  ...cember 31, 2016. On how many days during the next year did she not receive a phone call from any of her grandchildren? <math>\textbf{(A) }78\qquad\textbf{(B) }80\qquad\textbf{(C) }144\qquad\textbf{(D) }146\qquad
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• MathCON
  MathCON is a nonprofit national mathematics organization recognized for its annual stude About 1 percent of students who participate in the online competition will advance to finals in Chicago, IL
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• British Mathematical Olympiad
  ...ional math competition held in the United Kingdom. Solvers who score over a certain threshold in the Senior Mathematical Challenge are automatically en Participants who submit a solution with the highest quality in BMO 2 can earn the Christopher Bradley
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• 2018 AMC 10B Problems/Problem 18
  ...x children will occupy the second and third rows in the van, each of which has three seats. To avoid disruptions, siblings may not sit right next to each <math>\textbf{(A)} \text{ 60} \qquad \textbf{(B)} \text{ 72} \qquad \textbf{(C)} \text{ 92}
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• 2018 AMC 10B Problems/Problem 10
  pair A =origin; draw(E1--M--H--E1--A--B--E1--F--B--M--C--G--H);
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• 1960 AHSME Problems/Problem 17
  The formula <math>N=8 \times 10^{8} \times x^{-3/2}</math> gives, for a certain group, the number of individuals whose income exceeds <math>x</math <math>\textbf{(A)}\ 10^4\qquad
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• Basic Programming With Python
  (Note: This is a really long article. To learn the most from this article, you need to read Note that this article has lots of program examples. It is recommended (but not required) to try these
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• 2007 iTest Problems/Ultimate Question
  ...the [[2007 iTest]], but with the T-values substituted. This is for people who want to work on the problems without having to solve the previous problems. ...th <math>2^{2007}+1</math> terms. If the integer <math>2004</math> appears a total of <math>N</math> times among these <math>2^{2007}+1</math> terms, fi
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• Infinity
  ...ver end. The first use of infinity was during Ancient Greek by Anaximander who referred to it as "apeiron". The symbol, <math>\infty</math> was first used
  454 bytes (71 words) - 01:38, 6 July 2018
• 2008 iTest Problems/Problem 56
  ...osts of renewable energy resources. "How much more does it really cost for a family like ours to switch entirely to renewable energy?" ...landfill gas. We pay that premium ourselves, but some families operate on a tighter budget, or don't understand the alternatives yet."
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• 2008 iTest Problems/Problem 63
  ...hnology companies for a venture capital firm. Other possibilities also tug a little at Michael for different reasons. ...the bats, to the other bat, then back to her starting point. He smiles for a moment, then keeps jogging. If Michael’s work is correct, what distance d
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• 2006 Indonesia MO Problems
  ...ath> be positive integers. If <math> 30|a+b+c</math>, prove that <math> 30|a^5+b^5+c^5</math>. ...he set of all triangles <math> ABC</math> which have property: <math> \tan A,\tan B,\tan C</math> are positive integers. Prove that all triangles in <ma
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• 2008 iTest Problems/Problem 71
  ..._iTest_Problems/Problem_13 a problem] she really likes, partly because she has never worked one like it before: Joshua is the kind of mathematical explorer who likes to alter problems, make them harder, or generalize them. So, he propo
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• 2018 AMC 8 Problems
  An amusement park has a collection of scale models, with ratio <math>1 : 20</math>, of buildings an <math>\textbf{(A) }14\qquad\textbf{(B) }15\qquad\textbf{(C) }16\qquad\textbf{(D) }18\qquad\t
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• 2008 iTest Problems/Problem 70
  ...some snorkling gear, Joshua walks back to the beach where Alexis works on a mural in the sand beside where they drew out symbol lists. Joshua walks dir "You're a square, Josh."
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• 2018 AMC 8 Problems/Problem 3
  ...a multiple of 7 that person leaves the circle and the counting continues. Who is the last one present in the circle? <math>\textbf{(A) } \text{Arn}\qquad\textbf{(B) }\text{Bob}\qquad\textbf{(C) }\text{Cyd}\qqu
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• 2018 AMC 8 Problems/Problem 20
  In <math>\triangle ABC,</math> a point <math>E</math> is on <math>\overline{AB}</math> with <math>AE=1</math pair A,B,C,DD,EE,FF;
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• Eric Wu
  ...ot from [[North Carolina mathematics competitions|North Carolina]] who has a Texas Pin from Luke Robitaille<br \>
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• 2016 UMO Problems
  ...st wins. A sample game is described below. If both players play optimally, who will win? pair A=(1,0),B=(1/2,sqrt(3)/2),C=(-1/2,sqrt(3)/2),D=(-1,0),E=(-1/2,-sqrt(3)/2),E=(
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• 2019 AMC 10B Problems/Problem 22
  ...nd that is the end of the first round of play. In the second round Rashaan has no money to give, but Sylvia and Ted might choose each other to give their <math>\textbf{(A) } \frac{1}{7} \qquad\textbf{(B) } \frac{1}{4} \qquad\textbf{(C) } \frac{1}
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• 2019 AMC 10B Problems
  <math>\textbf{(A) } \frac{5}{8} \qquad \textbf{(B) } \frac{4}{5} \qquad \textbf{(C) } \frac{ ...h>n-2</math> is prime." Which of the following values of <math>n</math> is a counterexample to this statement?
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• 2019 AMC 10B Problems/Problem 25
  ...ength <math>19</math> are there that begin with a <math>0</math>, end with a <math>0</math>, contain no two consecutive <math>0</math>s, and contain no <math>\textbf{(A) }55\qquad\textbf{(B) }60\qquad\textbf{(C) }65\qquad\textbf{(D) }70\qquad\t
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• 2019 AMC 10B Problems/Problem 18
  ...from home and a point <math>B</math> kilometers from home. What is <math>|A-B|</math>? <math>\textbf{(A) } \frac{2}{3} \qquad \textbf{(B) } 1 \qquad \textbf{(C) } 1 \frac{1}{5} \q
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• 2019 AMC 12B Problems
  <math>\textbf{(A) } \frac{5}{8} \qquad \textbf{(B) } \frac{4}{5} \qquad \textbf{(C) } \frac{ ...h>n-2</math> is prime." Which of the following values of <math>n</math> is a counterexample to this statement?
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• 2019 AMC 12B Problems/Problem 13
  ...1,2,3....</math> What is the probability that the red ball is tossed into a higher-numbered bin than the green ball?<br> <math>\textbf{(A) } \frac{1}{4} \qquad\textbf{(B) } \frac{2}{7} \qquad\textbf{(C) } \frac{1}
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• Gmaasology
  ...dy of [[Gmaas]]. [[Gmaas]] is one of only two known living beings who have a Ph.D. in [[Gmaasology]], with the other being Sseraj, Gmaas's human. [[Gmaa [[Gmaasology]] has existed for much of human history. Here are a selection of historical events related to [[Gmaas]] and [[Gmaasology]] unti
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• 2006 Indonesia MO Problems/Problem 6
  ...e area, apply for a new phone number. What is the chance that Mr. Edy gets a phone number which consists of at most five different digits? The two eights has seven spots available, so there are <math>\tfrac{7 \cdot 6}{2} = 21</math>
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• 2020 AMC 8 Problems/Problem 6
  ...cars in front of Aaron. At least one person sat between Karen and Darren. Who sat in the middle car? <math>\textbf{(A) }\text{Aaron} \qquad \textbf{(B) }\text{Darren} \qquad \textbf{(C) }\text{
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• Gods Fighting Sim
  - There may now be a weekly tax deduction. The tax is decided by the guild that is occupying the - If the guild is run in a dictatorship, a oligarchy, a monarchy, or a democracy, the leader or representative will decide the tax.
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• Rubiks cube
  ...isting the numbers of combinations for various sized cubes. There’s also a javascript calculator in case you want to figure it out for larger sizes. ...manageable number. If you fiddle with the 2x2x2 cube randomly, eight hours a day continuously, you’ll solve it by pure chance roughly two or three tim
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• Administrators
  ...strator on the Art of Problem Solving website is a user who has powers for a particular forum which [[moderators]] and regular users don't. When a user is an administrator, their username shows up in red. This only happens
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• GMAAS
  ...page! Since the old one ([[Gmaas]]) was locked, the [[User:Piphi|piphi]] has restored it in the form of this page! We thank him greatly. ...͍̓̎̀͊͝s̶̤̯̤͇͚͍͍͒̓̅̅̎͊̑̎͘, but none shall speak his name, as it is unworthy for any mortal to even gaze their eyes upon Almighty Gma
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• 2019 AMC 8 Problems/Problem 11
  ...uage class. How many eighth graders take ''only'' a math class and ''not'' a foreign language class? <math>\textbf{(A) }16\qquad\textbf{(B) }53\qquad\textbf{(C) }31\qquad\textbf{(D) }39\qquad\t
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• 2019 AMC 8 Problems/Problem 23
  <math>\textbf{(A) }10\qquad\textbf{(B) }11\qquad\textbf{(C) }12\qquad\textbf{(D) }13\qquad\t ...}{7} + 15 = 45</math>, and thus, the other seven players would have scored a total of <math>56-45 = \boxed{\textbf{(B)} 11}</math>. (We see that this wo
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• 2019 AMC 8 Problems/Problem 24
  pair A,B,C,DD,EE,FF; A = (1.2,1.7);
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• 2000 SMT/Advanced Topics Problems
  How many different ways are there to paint the sides of a tetrahedron with exactly 4 colors? Each side ...ight)^{6}+\left(\frac{-1-i\sqrt{3}}{2}\right)^{6}</math> to the form <math>a+bi</math>
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• 2021 HMC 10
  ...B=\frac{9}{10}</math> and <math>C=\frac{12}{25}</math>. The value of <math>A+B+C</math> can be expressed as <math>\frac{m}{n}</math> in the simplest for <math>\textbf{(A)} ~177 \qquad\textbf{(B)} ~178 \qquad\textbf{(C)} ~179 \qquad\textbf{(D)} ~
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• 2024 AIME II Problems
  ...n exactly three of these things. Find the number of residents of Aimeville who own all four of these things. A list of positive integers has the following properties:
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• 2022 AMC 10A Problems
  {{AMC10 Problems|year=2022|ab=A}} <math>\textbf{(A)}\ \frac{31}{10}\qquad\textbf{(B)}\ \frac{49}{15}\qquad\textbf{(C)}\ \frac{
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• Online Physics Olympiad
  ...rgraduate students in university may also participate, but they will be in a separate division and are not able to qualify for prizes. On the submission portal, each contestant has three times to submit their answer. Note that correct answers will immediat
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• AMC 12C 2020
  <math>\mathrm{(A) \ } -10\qquad \mathrm{(B) \ } -3\qquad \mathrm{(C) \ } 5\qquad \mathrm{(D) ...th> plane in the shape of a circle, centered at <math>(5, 6)</math> with a a radius of <math>8</math>. The area that is in the field but above the line
  9 KB (1,450 words) - 18:33, 21 April 2020
• Mathcounts Week/Countdown Round
  The moderator would ask a pre-arranged state level countdown question. The first 30 answers (mainly, ...receiving hundreds of instantaneous replies. As such, the score contained a lot of randomness.
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• IvyZen Scholarship Program
  IvyZen has helped students craft unique and compelling themes covering a diverse area of interests such as social entrepreneurship, applied math, AI Over the years, they’ve come across many students who cannot afford their services. But they’ve taken on many such students in
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• 2021 AIME I Problems/Problem 13
  ...pectively, intersect at distinct points <math>A</math> and <math>B</math>. A third circle <math>\omega</math> is externally tangent to both <math>\omega <font color=red><b>Claim.</b></font color> <math>DPEQ</math> is a harmonic quadrilateral.
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• WorldWarZ
  ...at matters at the moment. The task at hand is the only thing that matters, a search to find individuals more trained than him. So, let us continue.
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• 2021 AMC 10B Problems
  <math>\textbf{(A)} ~9 \qquad\textbf{(B)} ~10 \qquad\textbf{(C)} ~18 \qquad\textbf{(D)} ~19 \ <math>\textbf{(A)} ~0 \qquad\textbf{(B)} ~4\sqrt{3}-6 \qquad\textbf{(C)} ~6 \qquad\textbf{(D
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• 2022 AIME I Problems/Problem 13
  ...orm <math>0.\overline{abcd},</math> where at least one of the digits <math>a,</math> <math>b,</math> <math>c,</math> or <math>d</math> is nonzero. Let < Make cases by factors of <math>x</math>. (A venn diagram of cases would be nice here.)
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• 2022 AIME II Problems
  ...25}</math> of the people at the concert. Find the minimum number of adults who could have been at the concert after the bus arrived. Azar, Carl, Jon, and Sergey are the four players left in a singles tennis tournament. They are randomly assigned opponents in the semi
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• 2021 Fall AMC 10B Problems
  <math>(\textbf{A})\: 10{,}000\qquad(\textbf{B}) \: 10{,}010\qquad(\textbf{C}) \: 10{,}110\qq <math>\textbf{(A)}\: 4\qquad\textbf{(B)} \: 6\qquad\textbf{(C)} \: 8\qquad\textbf{(D)} \: 10
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• 2021 Fall AMC 12B Problems/Problem 20
  A cube is constructed from <math>4</math> white unit cubes and <math>4</math> <math>\textbf{(A)}\ 7 \qquad\textbf{(B)}\ 8 \qquad\textbf{(C)}\ 9 \qquad\textbf{(D)}\
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• 2020 AMC 8 Problems
  Luka is making lemonade to sell at a school fundraiser. His recipe requires <math>4</math> times as much water a <math>\textbf{(A) } 6\qquad\textbf{(B) } 8\qquad\textbf{(C) } 12\qquad\textbf{(D) } 18\qquad
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• 2021 AMC 12B Problems
  <math>\textbf{(A) }9 \qquad \textbf{(B) }10 \qquad \textbf{(C) }18 \qquad \textbf{(D) }19 \q At a math contest, <math>57</math> students are wearing blue shirts, and another
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• 2020 AMC 8 Problems/Problem 23
  <math>\textbf{(A) }120 \qquad \textbf{(B) }150 \qquad \textbf{(C) }180 \qquad \textbf{(D) }2 ...ds, then the other two students must each receive <math>1</math> award; if a student receives <math>2</math> awards, then another student must also rece
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• Georgeooga-Harryooga Theorem
  ...ath>\frac{(a-b)!(a-b+1)!}{(a-2b+1)!}</math> ways to arrange the objects in a line. ...ath>1</math>, <math>2</math>, <math>3</math>, ..., <math>a-1</math>, <math>a</math>. Let the last <math>b</math> objects be the ones we can't have toget
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• Peru mathematics competitions
  ...mpiada Nacional Escolar de Matemática) is a mathematical competition that has been held annually since 2004, organized by the Ministry of Education of Pe In addition, the three students who obtain the highest scores for each level (regardless of their category) in
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• 2022 AMC 12A Problems
  {{AMC12 Problems|year=2022|ab=A}} <math>\textbf{(A)}\ \frac{31}{10}\qquad\textbf{(B)}\ \frac{49}{15}\qquad\textbf{(C)}\ \frac{
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• Harvey
  ...l, this is a page dedicated to the "man", the myth, the "man" and the myth who carries Richard Rusczyk, HARVEY! ...the inspiration for Harvey because he is in the acknowledgements and has a name similar to Harvey.
  642 bytes (102 words) - 22:15, 30 January 2024
• Time (Python)
  ...module is a module that allows [[Python]] to perform specific actions for a limited time. When using the Time module, remember to type this tells Python to pause for a specific amount of time before continuing. Python will also print any prin
  925 bytes (158 words) - 15:18, 6 May 2024
• 2021 AMC 12B Problems/Problem 22
  ...ps possibly creating new walls. The walls are one brick tall. For example, a set of walls of sizes <math>4</math> and <math>2</math> can be changed into ...wins. For which starting configuration is there a strategy that guarantees a win for Beth?
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• 2021 AIME II Problems/Problem 11
  ...s, that some number in <math>S</math> was divisible by <math>6</math>, and a different number in <math>S</math> was divisible by <math>7</math>. The tea ...reen. By the least common multiple, we obtain cycles: If <math>n</math> is a possible maximum value of <math>S,</math> then <math>n+42</math> must be an
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• Advanced Gmaasology
  ...based on a manuscript by the creator of An Introduction to Gmaasology and has been reproduced here. It was published in <math>1321</math>, if the date is ...ver been before, but few properly know about it. In fact, of the 'experts' who claim to know about it, the majority are, in fact, frauds. Gmaasological ex
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• 2022 AIME II Problems/Problem 2
  Azar, Carl, Jon, and Sergey are the four players left in a singles tennis tournament. They are randomly assigned opponents in the semi Let <math>A</math> be Azar, <math>C</math> be Carl, <math>J</math> be Jon, and <math>S<
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• 2021 Fall AMC 10B Problems/Problem 20
  ...e players in this game. What is the probability that Hugo's first roll was a <math>5,</math> given that he won the game? <math>(\textbf{A})\: \frac{61}{216}\qquad(\textbf{B}) \: \frac{367}{1296}\qquad(\textbf{C})
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• 2021 Fall AMC 10B Problems/Problem 10
  ...multiply your number by <math>100</math> and add my number, the result is a perfect square. " What is the sum of the two numbers drawn from the hat? <math>\textbf{(A) }27\qquad\textbf{(B) }37\qquad\textbf{(C) }47\qquad\textbf{(D) }57\qquad\t
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• 2021 Fall AMC 10B Problems/Problem 11
  A regular hexagon of side length <math>1</math> is inscribed in a circle. Each minor arc of the circle determined by a side of the hexagon is reflected over that side. What is the area of the re
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• AMC 10 2021 (Mock) Problems
  ...2021,<math> and </math>A + C - B = 2022,<math> what is the value of </math>A + B + C - 2020 - 2021 - 2022<math>? </math>\mathrm{(A) \ } 0\qquad \mathrm{(B) \ } 2020\qquad \mathrm{(C) \ } 2021\qquad \mathrm{
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• Technodoggo
  Technodoggo is a <math>12</math>-year old doggo who considers himself Californian though he lives in Nevada. He qualified for A He got <math>2</math> medals as a full-scorer from the Noetic Math Contest and got <math>2</math>nd place in
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• 2022 AMC 8 Problems
  ...h Team designed a logo shaped like a multiplication symbol, shown below on a grid of 1-inch squares. What is the area of the logo in square inches? <math>\textbf{(A) } 10 \qquad \textbf{(B) } 12 \qquad \textbf{(C) } 13 \qquad \textbf{(D) }
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• The Mani-Cretin Mathematical Examinations
  The Mani-Celadin Mathematical Examinations refer to a series of secondary school mathematics competitions hosted by the Mani-Cela ...reasoning skills needed for different science subjects, and be engaged in a process of creative thinking. The problems on the PSC can mostly be solved
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• Crusade
  ...century, which was initiated by the alien and primordial entity Tharizdun who entered the marterial universe, resulting in the destruction of the interne ...mongst the hundreds for a suitable host are considered reasonable. This is a universe that preaches the expendability of the individual. Only the leader
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• Kiwibird52
  ...oys piano, creative writing, and bubble tea. He has two cats, a piano, and a sister (Crazypenguin84). He is currently learning how to write CSS and Java
  587 bytes (108 words) - 19:24, 14 September 2022
• Forum4Ever1
  ...t the rights to the name, and created Forum4Every1. This forum turned into a failure, and is now known as [DEAD] Forum4Every1. Please see Always Thinkin Forum4Every1 v1.4 has had a rocky start, due to multiple reasons. [list=1]
  952 bytes (158 words) - 04:16, 15 September 2022
• 2023 AMC 8 Problems
  <math>\textbf{(A)}\ 0 \qquad \textbf{(B)}\ 6 \qquad \textbf{(C)}\ 10 \qquad \textbf{(D)}\ 18 A square piece of paper is folded twice into four equal quarters, as shown be
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• 2022 AMC 10A Problems/Problem 12
  response, either a lie or the truth, but each subsequent statement has the opposite "Are you a truth-teller?" The principal gave a piece of candy to each of the <math>22</math>
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• 2022 AMC 10B Problems/Problem 23
  ...ve direction, using up <math>t_n</math> minutes. If the total elapsed time has exceeded <math>1</math> minute during the <math>n</math>th step, she stops <math>\textbf{(A) }\frac{1}{3} \qquad \textbf{(B) }\frac{1}{2} \qquad \textbf{(C) }\frac{2}{
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• 2023 AMC 8 Problems/Problem 8
  ...s for the players. The numbers <math>1</math> and <math>0</math> represent a win or loss, respectively. For example, Lola won five matches and lost the <math>\textbf{(A)}\ \texttt{000101} \qquad \textbf{(B)}\ \texttt{001001} \qquad \textbf{(C)}
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• 2012 EGMO Problems
  Let <math>ABC</math> be a triangle with circumcentre <math>O</math>. The points <math>D,E,F</math> li ...h> rows and <math>n</math> columns can be filled with real numbers in such a manner that for any two different rows <math>\left[ {{a_1},{a_2},\ldots,{a_
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• 2017 EGMO Problems
  ...</math>.Prove that the points <math>M,N,A</math> and <math>C</math> lie on a circle. ...tive integers <math>\mathbb{Z}_{>0}</math> with <math>k</math> colours and a function <math>f:\mathbb{Z}_{>0}\to \mathbb{Z}_{>0}</math> with the followi
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• 2023 AMC 8 Problems/Problem 14
  ...ld like to cover the package with a large number of stamps. Suppose he has a collection of <math>5</math>-cent, <math>10</math>-cent, and <math>25</math <math>\textbf{(A)}\ 45 \qquad \textbf{(B)}\ 46 \qquad \textbf{(C)}\ 51 \qquad \textbf{(D)}\
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• 2023 AMC 8 Problems/Problem 15
  ...oday, after walking <math>5</math> blocks, Viswam discovers he has to make a detour, walking <math>3</math> blocks of equal length instead of <math>1</m draw((0,0)--(5,0)--(5,1)--(6,1)--(6,0)--(10.1,0),deepblue+linewidth(1.25)); //Who even noticed
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• 2023 AIME I Problems/Problem 1
  ...random order. The probability that every man stands diametrically opposite a woman is <math>\frac{m}{n},</math> where <math>m</math> and <math>n</math> ...<math>10\cdot8\cdot6\cdot4\cdot2</math> ways to place the five men each in a man-woman diameter. Finally, there are <math>9!</math> ways to place the ni
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• 2023 AIME II Problems/Problem 7
  ...erty that no four vertices colored the same color are the four vertices of a rectangle. same color are the four vertices of a rectangle''.
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• 2023 AIME II Problems/Problem 10
  ...cells of a <math>2 \times 6</math> grid so that for any two cells sharing a side, the difference between the numbers in those cells is not divisible by ...ly 1 configuration for the rightmost pair to be set after the leftmost one has been placed.
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• 2016 Mathcounts State Sprint Problems
  ...a+b}</math>. What is the value of <math>5@3</math>? Express your answer as a common fraction. A bag contains <math>4</math> blue, <math>5</math> green and <math>3</math> r
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• Insiders bet more on Fizz a social network that has now bubbled up at 80 college campuses
  Fizz, a burgeoning social network established by two Stanford dropouts, captured th Fizz operates on a distinct model that invites individuals with a Stanford email address to join its network, allowing them to contribute and
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• Xarcade! (c)
  Xarcade!© is a forum founded by AlienGirl05 that emerged in early 2022. It has since then, through amazing dedication, become one of the top game forums t ...3, a lot of the forum's most influential members joined, such as bpan2021, who joined early March, 2022, and is now the forum's co-owner. adrastea, awesom
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• Know the Facts: Gmaas
  ...e contributors section. WARNING: Security details will be checking once in a while, so please edit this page appropriately! ..., though his godly power can turn him into anything, he just prefers to be a cat. As you read on, you will discover more things about him then you will
  88 KB (14,928 words) - 13:54, 29 April 2024
• 2000 OIM Problems/Problem 5
  There is a pile of 2000 stones. Two players take turns removing stones, alternately, a ...ayer who cannot make a valid play on his turn loses. Find which player has a winning strategy and find it.
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• 2017 OIM Problems/Problem 5
  ...e integer <math>n</math>, all its positive integer divisors are written in a blackboard. Ana and Beto play the following game: ...Beto wins. If Ana has the first turn, find for each <math>n</math> who has a winning strategy.
  746 bytes (128 words) - 14:46, 14 December 2023
• Alex
  ...s he neat and organized. later in the b5 books he becomes a director he is a well-known character
  140 bytes (27 words) - 20:22, 13 March 2024
• 2005 iTest Problems
  Carrie, Miranda, Charlotte, and Samantha are sitting at a table with <math>5</math> numbered chairs (numbered <math>1</math> through ...her teacher just couldn’t contain her applause, and awarded an automatic A to her for the rest of the year.
  25 KB (3,738 words) - 10:53, 23 April 2024