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• 14:26, 2 May 2025 (diff | hist) . . (+96)‎ . . N 2023 WSMO Team Round Answer Key ‎ (Created page with "#53 #108 #776 #194 #168 #468 #337 #344 #39 #5 #396 #1643 #7 #3096 #9") (current)
• 14:25, 2 May 2025 (diff | hist) . . (+7,216)‎ . . N 2023 WSMO Team Round Problems ‎ (Created page with "==Problem 1== Bob has a number of pencils. When Bob splits them into groups of 10, he has 3 left over. When he splits them into groups of 12, he has 5 left over. Find the sma...")
• 14:19, 2 May 2025 (diff | hist) . . (+58)‎ . . N 2023 WSMO Accuracy Round Answer Key ‎ (Created page with "#277 #108 #60 #13 #3 #25 #95 #68 #79 #54") (current)
• 14:19, 2 May 2025 (diff | hist) . . (+4,163)‎ . . N 2023 WSMO Accuracy Round Problems ‎ (Created page with "==Problem 1== Let <math>x = \sqrt{69+\sqrt{69+\sqrt{69\dots}}}.</math> Find the value of <math>(2x-1)^2.</math> Solution ==P...") (current)
• 14:18, 2 May 2025 (diff | hist) . . (+8)‎ . . 2023 SSMO Accuracy Round Problems ‎ (current)
• 14:17, 2 May 2025 (diff | hist) . . (0)‎ . . 2023 WSMO Accuracy Round ‎ (current)
• 14:16, 2 May 2025 (diff | hist) . . (+481)‎ . . N 2023 WSMO Tiebreaker Round ‎ (Created page with "'''2023 WSMO Tiebreaker Round''' problems and solutions. The first link contains the full set of test problems. The second link contains the answer key. The rest contain each...") (current)
• 14:15, 2 May 2025 (diff | hist) . . (+1,129)‎ . . N 2023 WSMO Team Round ‎ (Created page with "'''2023 WSMO Team Round''' problems and solutions. The first link contains the full set of test problems. The second link contains the answer key. The rest contain each indivi...") (current)
• 14:15, 2 May 2025 (diff | hist) . . (+891)‎ . . N 2023 WSMO Accuracy Round ‎ (Created page with "'''2023 WSMO Accuracy Round''' problems and solutions. The first link contains the full set of test problems. The second link contains the answer key. The rest contain each in...")
• 14:11, 2 May 2025 (diff | hist) . . (+57)‎ . . N 2023 WSMO Speed Round Answer Key ‎ (Created page with "#6 #40 #74 #13 #31 #16 #6 #2048 #6 #904") (current)
• 10:34, 2 May 2025 (diff | hist) . . (+110)‎ . . 2023 WSMO Speed Round Problems ‎ (current)
• 10:33, 2 May 2025 (diff | hist) . . (+461)‎ . . 2023 WSMO Speed Round Problems ‎
• 10:33, 2 May 2025 (diff | hist) . . (+10)‎ . . 2023 SSMO Speed Round Problems ‎
• 10:32, 2 May 2025 (diff | hist) . . (0)‎ . . 2023 SSMO Speed Round Problems ‎
• 10:30, 2 May 2025 (diff | hist) . . (+3,976)‎ . . N 2023 WSMO Speed Round Problems ‎ (Created page with "==Problem 1== Find the number of square units in the area of the shaded region. <asy> size(4cm); for (int i=0; i<5; ++i) { for (int j=0; j<5; ++j) { dot((i,j)); } } pai...")
• 10:24, 2 May 2025 (diff | hist) . . (+852)‎ . . N 2023 WSMO Speed Round ‎ (Created page with "'''2023 WSMO Speed Round''' problems and solutions. The first link contains the full set of test problems. The second link contains the answer key. The rest contain each indiv...") (current)
• 10:24, 2 May 2025 (diff | hist) . . (+118)‎ . . SMO Problem Archive ‎
• 21:16, 18 February 2025 (diff | hist) . . (+11)‎ . . m 2023 SSMO Team Round Problems ‎ (→‎Problem 13)
• 21:16, 18 February 2025 (diff | hist) . . (-1)‎ . . m 2023 SSMO Team Round Problems ‎ (→‎Problem 13)
• 22:30, 15 December 2023 (diff | hist) . . (+448)‎ . . N 2023 SSMO Tiebreaker Round Problems/Problem 3 ‎ (Created page with "==Problem== For <math>n\geq4,</math> let <math>a_n</math> be the maximum possible value of <math>P(n+1)</math> given that <math>P(x)</math> is a <math>n</math> degree monic po...") (current)
• 22:30, 15 December 2023 (diff | hist) . . (+338)‎ . . N 2023 SSMO Tiebreaker Round Problems/Problem 2 ‎ (Created page with "==Problem== Let <math>P(x) = x^3 + 3ax^2 + 3bx + (a+b)</math> be a real polynomial with nonnegative and nonzero real roots <math>p, q, r</math>. Suppose that <cmath>(p + 1)^3...")
• 22:30, 15 December 2023 (diff | hist) . . (+276)‎ . . N 2023 SSMO Tiebreaker Round Problems/Problem 1 ‎ (Created page with "==Problem== From the phrase "Summer Solstice", how many ways are there to make a 4 letter "word" such that the second and third letters aren't spaces and the first letter is c...") (current)
• 22:30, 15 December 2023 (diff | hist) . . (+320)‎ . . N 2023 SSMO Relay Round 5 Problems/Problem 3 ‎ (Created page with "==Problem== Let <math>T=</math> TNYWR. Suppose that <math>x^2+y^2 = N.</math> Find the remainder when the expected value of the square of the maximum value <math>ax+by</math>...")
• 22:30, 15 December 2023 (diff | hist) . . (+194)‎ . . N 2023 SSMO Relay Round 5 Problems/Problem 2 ‎ (Created page with "==Problem== Let <math>T=</math> TNYWR. Let <math>a_n = \text{lcm} \{1, 2, \dots n\}</math> for positive integers <math>n</math>.Compute <cmath>\sum_{i=1}^N a_i \pmod {720}.</c...")
• 22:30, 15 December 2023 (diff | hist) . . (+386)‎ . . N 2023 SSMO Relay Round 5 Problems/Problem 1 ‎ (Created page with "==Problem== Let <math>S_n</math> be the set of all rational numbers of the form <math>0.\overline{a_1a_2a_3\dots a_n},</math> where <math>n</math> is an integer satisfying <ma...")
• 22:29, 15 December 2023 (diff | hist) . . (+489)‎ . . N 2023 SSMO Relay Round 4 Problems/Problem 3 ‎ (Created page with "==Problem== Let <math>T=</math> TNYWR. <math>N+1</math> numbers are chosen from the set <math>\{1,2,3,\dots,N+1\}</math> with replacement. If the probability that the median o...")
• 22:29, 15 December 2023 (diff | hist) . . (+486)‎ . . N 2023 SSMO Relay Round 4 Problems/Problem 2 ‎ (Created page with "==Problem== Let <math>T=</math> TNYWR. Let <math>n = \left\lfloor\sqrt{N}\right\rfloor.</math> Suppose that <math>N</math> points are chosen on the sides of a triangle with ar...")
• 22:29, 15 December 2023 (diff | hist) . . (+523)‎ . . N 2023 SSMO Relay Round 4 Problems/Problem 1 ‎ (Created page with "==Problem== Martha starts out with the number <math>7</math> on her calculator, which has three buttons that multiply the current number by <math>\frac{1}{2}</math>, <math>\fr...") (current)
• 22:29, 15 December 2023 (diff | hist) . . (+2,269)‎ . . N 2023 SSMO Relay Round 3 Problems/Problem 3 ‎ (Created page with "==Problem== Let <math>T=</math> TNYWR. Let <math>n = N+1.</math> A spray painter has a paint gun that paints all areas within a radius of <math>2.</math> The spray painter wal...")
• 22:29, 15 December 2023 (diff | hist) . . (+499)‎ . . N 2023 SSMO Relay Round 3 Problems/Problem 2 ‎ (Created page with "==Problem== Let <math>T=</math> TNYWR. In triangle <math>ABC</math> with circumradius and inradius having lengths <math>R</math> and <math>r,</math> respectively. Given that...")
• 22:29, 15 December 2023 (diff | hist) . . (+592)‎ . . N 2023 SSMO Relay Round 3 Problems/Problem 1 ‎ (Created page with "==Problem== In triangle <math>ABC</math> with <math>AB=13,AC=14,BC=15</math>, circles <math>\omega_1,\omega_2,</math> and <math>\omega_3</math> are drawn, centered at <math>A,...") (current)
• 22:29, 15 December 2023 (diff | hist) . . (+397)‎ . . N 2023 SSMO Relay Round 2 Problems/Problem 3 ‎ (Created page with "==Problem== Let <math>T=</math> TNYWR. In a committee of <math>2023</math> people, <math>N</math> are scientists and the rest are builders. In order to make a building, <math>...")
• 22:29, 15 December 2023 (diff | hist) . . (+307)‎ . . N 2023 SSMO Relay Round 2 Problems/Problem 2 ‎ (Created page with "==Problem== Let <math>T=</math> TNYWR. Suppose that <math>L = \left\lfloor\sqrt{N}\right\rfloor</math> points are evenly spaced around the circle. Find the number of ways to s...")
• 22:28, 15 December 2023 (diff | hist) . . (+263)‎ . . N 2023 SSMO Relay Round 2 Problems/Problem 1 ‎ (Created page with "==Problem== Consider the cubic polynomial <math>P(x)=ax^3+bx^2+cx+d</math>, where <math>a,b,c,d</math> are single-digit integers, which has roots of approximately <cmath>x \ap...") (current)
• 22:28, 15 December 2023 (diff | hist) . . (+180)‎ . . N 2023 SSMO Relay Round 1 Problems/Problem 3 ‎ (Created page with "==Problem== Let <math>T=</math> TNYWR. Find the number of solutions to the equation <cmath>\sec^{N} (Nx) - \tan^{N}(Nx) = 1</cmath> such <math>0 \le x \le \pi</math> ==Solut...")
• 22:28, 15 December 2023 (diff | hist) . . (+195)‎ . . N 2023 SSMO Relay Round 1 Problems/Problem 2 ‎ (Created page with "==Problem== Let <math>T=</math> TNYWR. Let <math>a_0 = 3, a_1 = 1, a_2 = N</math>, and let <math>a_n = a_{n-1} - \frac{a_{n-3}}{8}</math>. Find <cmath>\sum_{i=0}^\infty a_i.</...")
• 22:28, 15 December 2023 (diff | hist) . . (+125)‎ . . N 2023 SSMO Relay Round 1 Problems/Problem 1 ‎ (Created page with "==Problem== Compute the remainder when <math>2022^{2021^{2020^{\dots}}}</math> is divided by <math>2023</math>. ==Solution==")
• 22:25, 15 December 2023 (diff | hist) . . (-270)‎ . . 2023 SSMO Team Round Problems/Problem 13 ‎
• 22:25, 15 December 2023 (diff | hist) . . (+224)‎ . . N 2023 SSMO Team Round Problems/Problem 14 ‎ (Created page with "==Problem== Find the sum of all perfect squares of the form <math>2p^3 - 5p^2q + q^2</math> where <math>p</math> and <math>q</math> are positive integers such <math>p</math> i...") (current)
• 22:25, 15 December 2023 (diff | hist) . . (+799)‎ . . N 2023 SSMO Team Round Problems/Problem 13 ‎ (Created page with "==Problem== Let <math>D(n)</math> denote the product of all divisors of <math>n</math> Let <math>P(i,j)</math> denote the set of all integers that are both a multiple of <math...")
• 22:25, 15 December 2023 (diff | hist) . . (+653)‎ . . N 2023 SSMO Team Round Problems/Problem 12 ‎ (Created page with "==Problem== Let <math>T</math> be the set of rationals of the form <math>\frac{a}{2^b}</math> for nonnegative <math>a</math> and <math>b</math>. Define the function <math>f \c...") (current)
• 22:25, 15 December 2023 (diff | hist) . . (+390)‎ . . N 2023 SSMO Team Round Problems/Problem 11 ‎ (Created page with "==Problem== Let <math>ABCD</math> be a cyclic quadrilateral such that <math>AC</math> is the diameter. Let <math>P</math> be the orthocenter of <math>ABD</math>. Define <math>...") (current)
• 22:25, 15 December 2023 (diff | hist) . . (+464)‎ . . N 2023 SSMO Team Round Problems/Problem 10 ‎ (Created page with "==Problem== There exists a lane of infinite cars. Each car has a <math>\frac{1}{3}</math> chance of being high quality and a <math>\frac{2}{3}</math> chance of being low quali...") (current)
• 22:25, 15 December 2023 (diff | hist) . . (+468)‎ . . N 2023 SSMO Team Round Problems/Problem 8 ‎ (Created page with "==Problem== Three rabbits run away from the origin at the same speed and constant velocity such that the angle between any two rabbits' directions is <math>120^\circ</math>. A...")
• 22:25, 15 December 2023 (diff | hist) . . (+369)‎ . . N 2023 SSMO Team Round Problems/Problem 9 ‎ (Created page with "==Problem== Let <math>B</math>, <math>K</math>, and <math>R</math> be the total number of possible moves for a bishop, knight, or rook from any position of a <math>9</math> by...") (current)
• 22:25, 15 December 2023 (diff | hist) . . (+379)‎ . . N 2023 SSMO Team Round Problems/Problem 7 ‎ (Created page with "==Problem== Let <math>S = \{1, 2, 3, 4, \cdots, 23\}</math> and let there be randomly chosen sets <math>A, B, C</math> where <math>A, B, C \subseteq S</math>. The probability...") (current)
• 22:25, 15 December 2023 (diff | hist) . . (+534)‎ . . N 2023 SSMO Team Round Problems/Problem 5 ‎ (Created page with "==Problem== Joshy is playing a game with a dartboard that has two sections. If Joshy hits the first section, he gets <math>20</math> points, and if he hits the second section,...") (current)
• 22:25, 15 December 2023 (diff | hist) . . (+353)‎ . . N 2023 SSMO Team Round Problems/Problem 6 ‎ (Created page with "==Problem== Suppose that <math>a,b,c</math> are positive reals satisfying<cmath>(a^3+4)(b^3+6)(c^3+8) = 8(a+b+c)^3.</cmath> Find the sum of all possible values of <math>\frac{...") (current)
• 22:25, 15 December 2023 (diff | hist) . . (+132)‎ . . N 2023 SSMO Team Round Problems/Problem 4 ‎ (Created page with "==Problem== Find the sum of values for prime <math>p</math> such that <math>p \mid (2023^{p^2}+(p-1)!+2^{p^4}).</math> ==Solution==") (current)
• 22:25, 15 December 2023 (diff | hist) . . (+588)‎ . . N 2023 SSMO Team Round Problems/Problem 3 ‎ (Created page with "==Problem== Let <math>ABC</math> be a triangle such that <math>AB=4\sqrt{2}, BC=5\sqrt{2},</math> and <math>AC=\sqrt{82}.</math> Let <math>\omega</math> be the circumcircle of...")

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