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• 16:02, 2 May 2025 (diff | hist) . . (+321)‎ . . N 2024 SSMO Relay Round 4 Problems/Problem 2 ‎ (Created page with "==Problem== Let <math>T = TNYWR.</math> Regular octagon <math>OLYMPIAD</math> is perfectly inscribed within Circle <math>Q</math>. Circle <math>Q</math> has area <math>T\pi</...")
• 16:02, 2 May 2025 (diff | hist) . . (+309)‎ . . N 2024 SSMO Relay Round 4 Problems/Problem 1 ‎ (Created page with "==Problem== Freddy the Frog can jump <math>1</math> unit right or up. He is at <math>(1,1)</math> and wants to get to <math>(7, 4)</math>. However, he is scared of points <ma...")
• 16:02, 2 May 2025 (diff | hist) . . (+556)‎ . . N 2024 SSMO Relay Round 3 Problems/Problem 3 ‎ (Created page with "==Problem== Let <math>T = TNYWR-1.</math> Riley and Boris are playing a game on a <math>T\times T</math> grid of dots. The game alternates turns and starts with Riley. Each t...")
• 16:02, 2 May 2025 (diff | hist) . . (+154)‎ . . N 2024 SSMO Relay Round 3 Problems/Problem 2 ‎ (Created page with "==Problem== Let <math>T = TNYWR.</math> Find the greatest odd integer <math>n</math> for which <math>n^2+(T-1)n</math> is a perfect square. ==Solution==")
• 16:02, 2 May 2025 (diff | hist) . . (+496)‎ . . N 2024 SSMO Relay Round 3 Problems/Problem 1 ‎ (Created page with "==Problem== Alice and Bob on the second floor of the building right next to the escalator moving upwards. Alice and Bob each run at 200 steps per minute and the escalator is...")
• 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 =...")
• 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==")
• 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...")
• 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...")
• 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...")
• 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...")
• 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...")
• 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...")
• 15:45, 2 May 2025 (diff | hist) . . (+1)‎ . . 2024 SSMO Team Round Problems/Problem 11 ‎
• 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...")
• 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>?...")
• 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...")
• 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 +...")
• 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...")
• 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==")
• 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...")
• 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...")
• 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...")
• 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...")
• 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==")
• 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==")
• 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...")
• 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...")
• 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...")
• 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...")
• 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...")
• 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...")
• 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...")
• 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...")
• 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...")
• 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),<...")
• 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...")
• 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...")
• 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...")
• 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,...")
• 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...")

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