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• 16:01, 2 May 2025 (diff | hist) . . (+328)‎ . . N 2024 SSMO Relay Round 2 Problems/Problem 3 ‎ (Created page with "==Problem== Let <math>T = TNYWR.</math> A point <math>P</math> is randomly chosen inside the square with vertices <math>A = (0,0), B = (0,T), C = (T,T),</math> and <math>D =...") (current)
• 16:01, 2 May 2025 (diff | hist) . . (+149)‎ . . N 2024 SSMO Relay Round 2 Problems/Problem 2 ‎ (Created page with "==Problem== Let <math>T = TNYWR.</math> If <cmath>a = \sum_{n=1}^{N}n(n+1)(n+2),</cmath> find the last three digits of <math>a.</math> ==Solution==") (current)
• 16:01, 2 May 2025 (diff | hist) . . (+297)‎ . . N 2024 SSMO Relay Round 2 Problems/Problem 1 ‎ (Created page with "==Problem== In a regular hexagon <math>ABCDEF</math>, let <math>X</math> be a point inside the hexagon such that <math>XA=XB=3.</math> If the area of the hexagon is <math>6\s...") (current)
• 16:01, 2 May 2025 (diff | hist) . . (+1)‎ . . 2024 SSMO Relay Round 1 Problems ‎ (current)
• 16:01, 2 May 2025 (diff | hist) . . (+543)‎ . . N 2024 SSMO Relay Round 1 Problems/Problem 3 ‎ (Created page with "==Problem== Let <math>T = TNYWR.</math> In a circle, there are <math>T</math> people. <math>T-2</math> of them have red shoes, and two of them have blue shoes. First, they wi...") (current)
• 16:01, 2 May 2025 (diff | hist) . . (+522)‎ . . N 2024 SSMO Relay Round 1 Problems/Problem 2 ‎ (Created page with "==Problem== Let <math>T = TNYWR.</math> A circular necklace is called <math>interesting</math> if it has <math>T</math> black beads and <math>T</math> white beads. A move con...") (current)
• 16:01, 2 May 2025 (diff | hist) . . (+513)‎ . . N 2024 SSMO Relay Round 1 Problems/Problem 1 ‎ (Created page with "==Problem== Let <math>AD</math> be an altitude of triangle <math>ABC</math> and let <math>DE</math> be an altitude of triangle <math>ACD.</math> If <math>AB=29,CE=9,</math> a...") (current)
• 15:45, 2 May 2025 (diff | hist) . . (+1)‎ . . 2024 SSMO Team Round Problems ‎ (current)
• 15:45, 2 May 2025 (diff | hist) . . (+232)‎ . . N 2024 SSMO Team Round Problems/Problem 14 ‎ (Created page with "==Problem== Let <math>a_1, a_2, \dots, a_7</math> be the roots of the polynomial <cmath>x^7+5x^6+9x^5+x^4+x^3+10x^2+5x+1.</cmath> Find the value of <cmath>\left|\prod_{n=1}^7...") (current)
• 15:45, 2 May 2025 (diff | hist) . . (+346)‎ . . N 2024 SSMO Team Round Problems/Problem 15 ‎ (Created page with "==Problem== In triangle <math>ABC</math> inscribed in circle <math>\omega,</math> let <math>M</math> be the midpoint of <math>BC.</math> Denote <math>P</math> as the intersec...") (current)
• 15:45, 2 May 2025 (diff | hist) . . (+1)‎ . . 2024 SSMO Team Round Problems/Problem 11 ‎ (current)
• 15:45, 2 May 2025 (diff | hist) . . (+446)‎ . . N 2024 SSMO Team Round Problems/Problem 13 ‎ (Created page with "==Problem== In a deck of 54 cards (2 identical jokers, 4 identical cards with <math>1,2,3,\dots,13</math>), each card is dealt to one of 3 people, each having a <math>\frac{1...") (current)
• 15:44, 2 May 2025 (diff | hist) . . (+319)‎ . . N 2024 SSMO Team Round Problems/Problem 11 ‎ (Created page with "==Problem== Let <math>S</math> denote the set of positive divisors of <math>5400.</math> Let <cmath>S_i = \{d \mid d \in S, \, d \equiv i \Mod4\}</cmath> and let <math>s_i</m...")
• 15:44, 2 May 2025 (diff | hist) . . (+187)‎ . . N 2024 SSMO Team Round Problems/Problem 12 ‎ (Created page with "==Problem== What is the smallest positive integer <math>n</math> with 3 positive prime factors such that for all integers <math>k</math>, <math>k^n \equiv k \pmod n</math>?...") (current)
• 15:44, 2 May 2025 (diff | hist) . . (+233)‎ . . N 2024 SSMO Team Round Problems/Problem 10 ‎ (Created page with "==Problem== The side-lengths of a convex cyclic quadrilateral <math>ABCD</math> are integers and <math>(AB\cdot AD+BC\cdot CD)^2=AC^2\cdot BD^2-72</math>. Find all possible v...") (current)
• 15:44, 2 May 2025 (diff | hist) . . (+271)‎ . . N 2024 SSMO Team Round Problems/Problem 8 ‎ (Created page with "==Problem== Three integers <math>0\le a\le b\le c< 229</math> satisfy the congruence <math>n^3 \equiv 1 \pmod{229}.</math> Given that <math>71^2 - 3</math> and <math>107^2 +...") (current)
• 15:44, 2 May 2025 (diff | hist) . . (+366)‎ . . N 2024 SSMO Team Round Problems/Problem 9 ‎ (Created page with "==Problem== Let <math>ABCDEFGH</math> be an equiangular octagon such that <math>AB=6, BC=8, CD=10, DE=12, EF=6, FG=8, GH=10,</math> and <math>AH=12</math>. The radius of the...") (current)
• 15:44, 2 May 2025 (diff | hist) . . (+170)‎ . . N 2024 SSMO Team Round Problems/Problem 7 ‎ (Created page with "==Problem== Let <math>a</math> and <math>b</math> be real numbers that satisfy <math>a^3+8ab^2=8b^3+4a^2b=375</math>. Find <math>\lfloor ab \rfloor</math>. ==Solution==") (current)
• 15:44, 2 May 2025 (diff | hist) . . (+283)‎ . . N 2024 SSMO Team Round Problems/Problem 6 ‎ (Created page with "==Problem== Let <math>\alpha</math>, <math>\beta</math>, and <math>\gamma</math> be the roots of the polynomial <math>x^3 - 6x^2 - 19x - n</math>. If <math>n</math> is an int...") (current)
• 15:44, 2 May 2025 (diff | hist) . . (+557)‎ . . N 2024 SSMO Team Round Problems/Problem 5 ‎ (Created page with "==Problem== Let <math>ABC</math> be a triangle with <math>AB=AC=5</math> and <math>BC=6</math>. Let <math>\omega_1</math> be the circumcircle of <math>ABC</math> and let <mat...") (current)
• 15:44, 2 May 2025 (diff | hist) . . (+672)‎ . . N 2024 SSMO Team Round Problems/Problem 4 ‎ (Created page with "==Problem== Let <math>ABC</math> be a right triangle with circumcenter <math>O</math> and incenter <math>I</math> such that <math>\angle ABC = 90^{\circ}</math> and <math>\fr...") (current)
• 15:44, 2 May 2025 (diff | hist) . . (+345)‎ . . N 2024 SSMO Team Round Problems/Problem 3 ‎ (Created page with "==Problem== Consider positive integers \(N\) such that when \(N\)'s units digit and leading nonzero digit are removed, what remains is a two-digit perfect square. The average...") (current)
• 15:44, 2 May 2025 (diff | hist) . . (+161)‎ . . N 2024 SSMO Team Round Problems/Problem 2 ‎ (Created page with "==Problem== Find the sum of the three smallest positive integers <math>n</math> where the last two digits of <math>n^4</math> are <math>01</math>. ==Solution==") (current)
• 15:44, 2 May 2025 (diff | hist) . . (+145)‎ . . N 2024 SSMO Team Round Problems/Problem 1 ‎ (Created page with "==Problem== How many ordered triples of positive integers <math>(a, b, c)</math> satisfy the equation <math>2(a^b)^c+1=513</math>? ==Solution==") (current)
• 15:43, 2 May 2025 (diff | hist) . . (+625)‎ . . N 2024 SSMO Accuracy Round Problems/Problem 9 ‎ (Created page with "==Problem== In the game of <math>S</math> - set, there are <math>3^{12}</math> unique cards, each card containing a 12 traits of variants <math>A,B,</math> and <math>C.</math...") (current)
• 15:43, 2 May 2025 (diff | hist) . . (+449)‎ . . N 2024 SSMO Accuracy Round Problems/Problem 8 ‎ (Created page with "==Problem== <math>ABCD</math> is a convex cyclic quadrilateral with <math>AB = 2, BC = 5, CD = 10,</math> and <math>AD = 11.</math> Let <math>W, Y, X,</math> and <math>Z</mat...") (current)
• 15:43, 2 May 2025 (diff | hist) . . (+631)‎ . . N 2024 SSMO Accuracy Round Problems/Problem 10 ‎ (Created page with "==Problem== Bobby is spinning a rigged wheel with three sections labeled <math>A,B,</math> and <math>C.</math> Two integers <math>0\leq x,y\leq 50</math> are chosen randomly...") (current)
• 15:43, 2 May 2025 (diff | hist) . . (+172)‎ . . N 2024 SSMO Accuracy Round Problems/Problem 7 ‎ (Created page with "==Problem== Find the value of <math>a+b+c+d</math> given \begin{align*} a^2+d^2 &= b^2+c^2 = 361,\\ ac+bd &= 247,\text{ and }\\ ab+cd &= 570.\\ \end{align*} ==Solution==") (current)
• 15:42, 2 May 2025 (diff | hist) . . (+352)‎ . . N 2024 SSMO Accuracy Round Problems/Problem 6 ‎ (Created page with "==Problem== Three six-sided dice are rolled. Then, the product of the three numbers on the top faces in calculated. If the probability of getting the product that is not a pe...") (current)
• 15:42, 2 May 2025 (diff | hist) . . (+367)‎ . . N 2024 SSMO Accuracy Round Problems/Problem 5 ‎ (Created page with "==Problem== Let <math>ABCD</math> be a convex quadrilateral such that <math>\angle ABC = 120^\circ</math> and <math>\angle ADC = 60^\circ</math>. If <math>AB = BC = CD = 5</m...") (current)
• 15:42, 2 May 2025 (diff | hist) . . (+501)‎ . . N 2024 SSMO Accuracy Round Problems/Problem 2 ‎ (Created page with "==Problem== Equilateral triangle <math>N</math> is inscribed within circle <math>O</math>. A smaller equilateral triangle <math>P</math> is inscribed within <math>N</math> su...") (current)
• 15:42, 2 May 2025 (diff | hist) . . (+514)‎ . . N 2024 SSMO Accuracy Round Problems/Problem 4 ‎ (Created page with "==Problem== Right triangle <math>ABC</math> has a right angle at <math>C</math> and hypotenuse <math>1</math>. Let points <math>D</math> and <math>E</math> lie on <math>AC</m...") (current)
• 15:42, 2 May 2025 (diff | hist) . . (+297)‎ . . N 2024 SSMO Accuracy Round Problems/Problem 3 ‎ (Created page with "==Problem== Three distinct random integers <math>a</math>, <math>b</math>, and <math>c</math> are selected so that <math>1 \le a, b, c \le 10</math>. Let the probability that...") (current)
• 15:42, 2 May 2025 (diff | hist) . . (+237)‎ . . N 2024 SSMO Accuracy Round Problems/Problem 1 ‎ (Created page with "==Problem== Let a time of day be three-full if exactly three of its digits are <math>3</math>s when displayed on a <math>12</math>-hour clock in the <math>hh:mm:ss</math> for...") (current)
• 15:42, 2 May 2025 (diff | hist) . . (+171)‎ . . N 2024 SSMO Speed Round Problems/Problem 10 ‎ (Created page with "==Problem== Let <math>a_1, a_2, \dots a_{14}</math> be the roots of <math>(x^7-x^3+2)^2=0</math>. Find the value of <math>\prod_{i=1}^{14} (a_i^7+1)</math>. ==Solution==")
• 15:41, 2 May 2025 (diff | hist) . . (+182)‎ . . N 2024 SSMO Speed Round Problems/Problem 9 ‎ (Created page with "==Problem== Let <math>a, b, c,</math> and <math>d</math> be positive integers such that <math>abcd = a+b+c+d</math>. Find the maximum possible value of <math>a</math>. ==Sol...")
• 15:41, 2 May 2025 (diff | hist) . . (+658)‎ . . N 2024 SSMO Speed Round Problems/Problem 7 ‎ (Created page with "==Problem== Let <math>S</math> denote the set of all ellipses centered at the origin and with axes <math>AB</math> and <math>CD</math> where <math>A=(-x,0),B=(x,0),C=(0,-y),<...") (current)
• 15:41, 2 May 2025 (diff | hist) . . (+550)‎ . . N 2024 SSMO Speed Round Problems/Problem 8 ‎ (Created page with "==Problem== Bob has two coins; one is fair, and one lands on heads with a probability of <math>\frac{2}{3}.</math> Bob chooses a random coin and flips it twice. Alice watches...") (current)
• 15:41, 2 May 2025 (diff | hist) . . (+337)‎ . . N 2024 SSMO Speed Round Problems/Problem 6 ‎ (Created page with "==Problem== There are <math>4</math> people and <math>4</math> houses. Each person independently randomly chooses a house to live in. The expected number of inhabited houses...")
• 15:41, 2 May 2025 (diff | hist) . . (+299)‎ . . N 2024 SSMO Speed Round Problems/Problem 5 ‎ (Created page with "==Problem== Let <math>\triangle ABC</math> and <math>\triangle ADC</math> be right triangles, such that <math>\angle ABC = \angle ADC = 90^\circ</math>. Given that <math>\ang...") (current)
• 15:41, 2 May 2025 (diff | hist) . . (+576)‎ . . N 2024 SSMO Speed Round Problems/Problem 4 ‎ (Created page with "==Problem== Sam wants to read the \textit{Harry Potter} and \textit{Warriors} books. There are 7 \textit{Harry Potter }books that must be read in a specific order, and there...") (current)
• 15:41, 2 May 2025 (diff | hist) . . (+221)‎ . . N 2024 SSMO Speed Round Problems/Problem 3 ‎ (Created page with "==Problem== The polynomial <math>x^3 - 15x^2 + 4x + 4</math> has distinct real roots <math>r</math>, <math>s</math>, and <math>t</math>. Find the value of <cmath>\left|(r^2 +...")
• 15:40, 2 May 2025 (diff | hist) . . (+328)‎ . . N 2024 SSMO Speed Round Problems/Problem 2 ‎ (Created page with "==Problem== Gracie's students play with some toys. When 4 or 5 students are present, the toys can be equally distributed to everyone. However, when there are only 3 students,...") (current)
• 15:40, 2 May 2025 (diff | hist) . . (+97)‎ . . N 2024 SSMO Speed Round Problems/Problem 1 ‎ (Created page with "==Problem== Find the sum of the distinct prime factors of <math>2024^2 - 1</math>. ==Solution==")
• 15:39, 2 May 2025 (diff | hist) . . (+232)‎ . . N 2023 WSMO Tiebreaker Round Problems/Problem 3 ‎ (Created page with "==Problem== Let <math>S</math> be the set of all values of <math>a</math> such that the area of a triangle with side lengths <math>5, 7, a</math> is a positive integer. Find...") (current)
• 15:39, 2 May 2025 (diff | hist) . . (+108)‎ . . N 2023 WSMO Tiebreaker Round Problems/Problem 2 ‎ (Created page with "==Problem== If <math>x^3+y^3=76895, x<y</math> and <math>x+y=65,</math> find <math>xy.</math> ==Solution==") (current)
• 15:39, 2 May 2025 (diff | hist) . . (+90)‎ . . N 2023 WSMO Tiebreaker Round Problems/Problem 1 ‎ (Created page with "==Problem== Find the number of factors of <math>24 ^ {6} - 20 ^ {6}.</math> ==Solution==") (current)
• 15:38, 2 May 2025 (diff | hist) . . (+684)‎ . . N 2023 WSMO Team Round Problems/Problem 14 ‎ (Created page with "==Problem== Consider quadrilateral <math>ABCD</math> with circumcircle centered at <math>O</math>. Given <math>AB=2<CD</math>, the circumcircle of <math>\triangle{ABO}</math>...") (current)
• 15:38, 2 May 2025 (diff | hist) . . (+613)‎ . . N 2023 WSMO Team Round Problems/Problem 13 ‎ (Created page with "==Problem== Gerry the Squirrel is at a corner of a <math>9\times9</math> grid. 1 acorn <math>A_1</math> is placed. There are four coins placed randomly on the <math>9\times 9...") (current)
• 15:38, 2 May 2025 (diff | hist) . . (+638)‎ . . N 2023 WSMO Team Round Problems/Problem 12 ‎ (Created page with "==Problem== Consider parabola <math>\mathcal P</math> pointing upwards with vertex at the origin of the Cartesian plane. Denote the focus of it as <math>F</math> and the dire...") (current)

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