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- 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>...") (current)
- 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...") (current)
- 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...") (current)
- 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...") (current)
- 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...") (current)
- 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...") (current)
- 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...") (current)
- 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>...") (current)
- 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...") (current)
- 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...") (current)
- 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.</...") (current)
- 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==") (current)
- 22:25, 15 December 2023 (diff | hist) . . (-270) . . 2023 SSMO Team Round Problems/Problem 13 (current)
- 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...") (current)
- 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...")
- 22:25, 15 December 2023 (diff | hist) . . (+352) . . N 2023 SSMO Team Round Problems/Problem 2 (Created page with "==Problem== A plane and a car start both move northward. The car moves northbound at 60 miles per hour. The plane moves northeast and increases in altitude at an angle of <mat...") (current)
- 22:25, 15 December 2023 (diff | hist) . . (+172) . . N 2023 SSMO Team Round Problems/Problem 1 (Created page with "==Problem== Let <math>(a, b, c, d)</math> be a permutation of <math>(2, 0, 2, 3)</math>. Find the largest possible value of <math>a^b + b^c + c^d + d^a</math> ==Solution==")
- 22:24, 15 December 2023 (diff | hist) . . (+1,656) . . N 2023 SSMO Team Round Problems/Problem 15 (Created page with "==Problem== Consider a piece of paper in the shape of a regular pentagon with sidelength <math>2.</math> We fold it in half. We then fold it such that the vertices of the long...") (current)
- 22:22, 15 December 2023 (diff | hist) . . (+1,087) . . N 2023 SSMO Accuracy Round Problems/Problem 9 (Created page with "==Problem== Consider a <math>2023 \times 2023</math> grid called <math>A = P_{2023}</math>. We take one of the four smaller <math>2022 \times 2022</math> grids located in <mat...") (current)
- 22:22, 15 December 2023 (diff | hist) . . (+741) . . N 2023 SSMO Accuracy Round Problems/Problem 10 (Created page with "==Problem== Let <math>\triangle ABC</math> be a triangle such <math>AB = 13</math>, <math>BC = 14</math>, <math>CA = 15</math>. Let the incircle of <math>\triangle ABC</math>...") (current)
- 22:21, 15 December 2023 (diff | hist) . . (+539) . . N 2023 SSMO Accuracy Round Problems/Problem 7 (Created page with "==Problem== Concentric circles <math>\omega</math> and <math>\omega_1</math> are drawn, with radii <math>3</math> and <math>5,</math> respectively. Chords <math>AB</math> and...") (current)
- 22:21, 15 December 2023 (diff | hist) . . (+679) . . N 2023 SSMO Accuracy Round Problems/Problem 8 (Created page with "==Problem== There is a quadrilateral <math>ABCD</math> inscribed in a circle <math>\omega</math> with center <math>O</math>. In quadrilateral <math>ABCD</math>, diagonal <math...") (current)
- 22:21, 15 December 2023 (diff | hist) . . (+387) . . N 2023 SSMO Accuracy Round Problems/Problem 5 (Created page with "==Problem== Define the <math>\textit{relationship}</math> between two numbers <math>a</math> and <math>b</math> to be <math>\frac{\sigma(ab)}{\sigma(a)\sigma(b)}</math> where...") (current)
- 22:21, 15 December 2023 (diff | hist) . . (+211) . . N 2023 SSMO Accuracy Round Problems/Problem 6 (Created page with "==Problem== Let the roots of <math>P(x) = x^3 - 2023x^2 + 2023^{2023}</math> be <math>p, q, r</math>. Find <cmath>\frac{p^2 + q^2}{p + q} + \frac{q^2 + r^2}{q + r} + \frac{r^2...")
- 22:21, 15 December 2023 (diff | hist) . . (+264) . . N 2023 SSMO Accuracy Round Problems/Problem 3 (Created page with "==Problem== Suppose that <math>a, b, c</math> are real numbers such <cmath> \begin{align*} a + b - c &= 4 \\ a^2 + b^2 + c^2 &= 14 \\ a^3 + b^3 - c^3 &= 34 \\ \end...") (current)
- 22:21, 15 December 2023 (diff | hist) . . (+483) . . N 2023 SSMO Accuracy Round Problems/Problem 4 (Created page with "==Problem== In square <math>ABCD,</math> point <math>E</math> is selected on diagonal <math>AC.</math> Let <math>F</math> be the intersection of the circumcircles of triangles...") (current)
- 22:21, 15 December 2023 (diff | hist) . . (+487) . . N 2023 SSMO Accuracy Round Problems/Problem 1 (Created page with "==Problem== Mr. Sammy proposes a Hamburger Proclamation, which has <math>500</math> lines, divided into paragraphs of <math>5</math> lines each. It takes him <math>23</math> s...") (current)
- 22:21, 15 December 2023 (diff | hist) . . (+283) . . N 2023 SSMO Accuracy Round Problems/Problem 2 (Created page with "==Problem== Suppose that the average of all <math>n</math>-digit palindromes is denoted by <math>P_{n}</math> and the average of all <math>n</math>-digit numbers is denoted by...") (current)
- 22:19, 15 December 2023 (diff | hist) . . (+13) . . N 2023 SSMO Tiebreaker Round Answer Key (Created page with "#1162 #10 #25") (current)
- 22:19, 15 December 2023 (diff | hist) . . (+12) . . N 2023 SSMO Relay Round 5 Answer Key (Created page with "#25 #321 #22") (current)
- 22:19, 15 December 2023 (diff | hist) . . (+12) . . N 2023 SSMO Relay Round 4 Answer Key (Created page with "#88 #160 #50") (current)
- 22:19, 15 December 2023 (diff | hist) . . (+12) . . N 2023 SSMO Relay Round 3 Answer Key (Created page with "#325 #13 #39") (current)
- 22:19, 15 December 2023 (diff | hist) . . (+13) . . N 2023 SSMO Relay Round 2 Answer Key (Created page with "#119 #1200 #2") (current)
- 22:19, 15 December 2023 (diff | hist) . . (+19) . . N 2023 SSMO Relay Round 1 Answer Key (Created page with "#2022 #16176 #64704") (current)
- 22:18, 15 December 2023 (diff | hist) . . (+74) . . N 2023 SSMO Team Round Answer Key (Created page with "#18 #61952 #101 #36 #1040 #0 #64 #59 #2560 #254 #191 #3073 #9021 #416 #831") (current)
- 22:18, 15 December 2023 (diff | hist) . . (+46) . . N 2023 SSMO Accuracy Round Answer Key (Created page with "#1983 #49 #4 #40 #340 #8092 #506 #98 #16 #2389") (current)
- 22:16, 15 December 2023 (diff | hist) . . (+348) . . N 2021 WSMO Team Round Problems/Problem 14 (Created page with "==Problem== Suppose that <math>x</math> is a complex number such that <math>x+\frac{1}{x}=\frac{\sqrt{6}+\sqrt{2}}{2}</math> and the imaginary part of <math>x</math> is nonneg...") (current)
- 22:16, 15 December 2023 (diff | hist) . . (+361) . . N 2021 WSMO Team Round Problems/Problem 15 (Created page with "==Problem== Let <math>ABCD</math> and <math>DEFG</math> (vertices labelled clockwise) be squares that intersect exactly once and with areas <math>1011^2</math> and <math>69^2<...") (current)
- 22:16, 15 December 2023 (diff | hist) . . (+382) . . N 2021 WSMO Team Round Problems/Problem 12 (Created page with "==Problem== Choose three integers <math>x,y,z</math> randomly and independently from the nonnegative integers. The probability that the sum of the factors of <math>2^x3^y5^z</...") (current)
- 22:16, 15 December 2023 (diff | hist) . . (+443) . . N 2021 WSMO Team Round Problems/Problem 13 (Created page with "==Problem== Square <math>BCDE</math> is drawn outside of equilateral triangle <math>ABC.</math> Regular hexagon <math>DEFGHI</math> is drawn outside of square <math>BCDE.</mat...") (current)
- 22:16, 15 December 2023 (diff | hist) . . (+196) . . N 2021 WSMO Team Round Problems/Problem 10 (Created page with "==Problem== The minimum possible value of <cmath>\sqrt{m^2+n^2}+\sqrt{3m^2+3n^2-6m+12n+15}</cmath> can be expressed as <math>a.</math> Find <math>a^2.</math> ''Proposed by pi...") (current)
- 22:16, 15 December 2023 (diff | hist) . . (+190) . . N 2021 WSMO Team Round Problems/Problem 11 (Created page with "==Problem== Find the remainder when <cmath>\sum_{x+y+z\leq10}\frac{(x+y+z)!}{x!y!z!}</cmath> is divided by <math>100</math>. (<math>x,y,z\geq 0</math>) ''Proposed by pinkpig'...") (current)
- 22:16, 15 December 2023 (diff | hist) . . (+384) . . N 2021 WSMO Team Round Problems/Problem 9 (Created page with "==Problem== In triangle <math>ABC,</math> points <math>D</math> and <math>E</math> trisect side <math>BC</math> such that <math>D</math> is closer to <math>C</math> than <math...") (current)
- 22:16, 15 December 2023 (diff | hist) . . (+749) . . N 2021 WSMO Team Round Problems/Problem 7 (Created page with "==Problem== A frog makes one hop every minute on the first quadrant of the coordinate plane (this means that the frog's <math>x</math> and <math>y</math> coordinates are posit...") (current)
- 22:16, 15 December 2023 (diff | hist) . . (+454) . . N 2021 WSMO Team Round Problems/Problem 8 (Created page with "==Problem== Isaac, Gottfried, Carl, Euclid, Albert, Srinivasa, René, Adihaya, and Euler sit around a round table (not necessarily in that order). Then, Hypatia takes a seat....") (current)
- 22:16, 15 December 2023 (diff | hist) . . (+812) . . N 2021 WSMO Team Round Problems/Problem 6 (Created page with "==Problem== Suppose that regular dodecagon <math>ABCDEFGHIJKL</math> has side length <math>5.</math> The area of the shaded region can be expressed as <math>a+b\sqrt{c},</math...") (current)
- 22:16, 15 December 2023 (diff | hist) . . (+25) . . 2021 WSMO Team Round Problems/Problem 5 (current)
- 22:16, 15 December 2023 (diff | hist) . . (+25) . . 2021 WSMO Team Round Problems/Problem 3 (current)
- 22:16, 15 December 2023 (diff | hist) . . (+27) . . 2021 WSMO Team Round Problems/Problem 4 (current)
- 22:12, 15 December 2023 (diff | hist) . . (+25) . . 2021 WSMO Team Round Problems/Problem 2 (current)
- 22:12, 15 December 2023 (diff | hist) . . (+26) . . 2021 WSMO Team Round Problems/Problem 1 (current)
- 22:11, 15 December 2023 (diff | hist) . . (+371) . . N 2021 WSMO Team Round Problems/Problem 5 (Created page with "==Problem== Two runners are running at different speeds. The first runner runs at a consistent 12 miles per hour. The second runner runs at <math>t+4</math> miles per hour, wh...")
- 22:08, 15 December 2023 (diff | hist) . . (+507) . . N 2021 WSMO Team Round Problems/Problem 4 (Created page with "==Problem== Consider a triangle <math>A_1B_1C_1</math> satisfying <math>A_1B_1=3,B_1C_1=3\sqrt{3},A_1C_1=6</math>. For all successive triangles <math>A_nB_nC_n</math>, we have...")
- 22:07, 15 December 2023 (diff | hist) . . (+418) . . N 2021 WSMO Team Round Problems/Problem 3 (Created page with "==Problem== Farmer Sam has <math>n</math> dollars. He knows that this is exactly enough to buy either 50 pounds of grass and 32 ounces of hay or 96 ounces of grass and 24 poun...")
- 22:07, 15 December 2023 (diff | hist) . . (+253) . . N 2021 WSMO Team Round Problems/Problem 2 (Created page with "==Problem== Bobby has some pencils. When he tries to split them into 5 equal groups, he has 2 left over. When he tries to split them into groups of 8, he has 6 left over. What...")
- 22:06, 15 December 2023 (diff | hist) . . (-1) . . 2021 WSMO Team Round Problems/Problem 1
- 22:06, 15 December 2023 (diff | hist) . . (+324) . . N 2021 WSMO Team Round Problems/Problem 1 (Created page with "==Problem== How many ways are there to pick a three-letter word using only letters from "Winter Solstice" such that the word is a capital letter followed by two lowercase lett...")
- 21:48, 15 December 2023 (diff | hist) . . (+1,211) . . N 2023 SSMO Tiebreaker Round Problems (Created page with "==Problem 1== 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 i...") (current)
- 21:36, 15 December 2023 (diff | hist) . . (+1,040) . . N 2023 SSMO Relay Round 5 Problems (Created page with "==Problem 1== 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...") (current)
- 21:35, 15 December 2023 (diff | hist) . . (0) . . 2023 SSMO Relay Round 3 Problems (current)
- 21:35, 15 December 2023 (diff | hist) . . (+1,638) . . N 2023 SSMO Relay Round 4 Problems (Created page with "==Problem 1== 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>...") (current)
- 21:34, 15 December 2023 (diff | hist) . . (+3,500) . . N 2023 SSMO Relay Round 3 Problems (Created page with "==Problem 1== 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...")
- 21:33, 15 December 2023 (diff | hist) . . (+1,107) . . N 2023 SSMO Relay Round 2 Problems (Created page with "==Problem 1== 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...") (current)
- 21:32, 15 December 2023 (diff | hist) . . (+1) . . 2023 SSMO Relay Round 1 Problems (current)
- 21:32, 15 December 2023 (diff | hist) . . (+5) . . 2023 SSMO Relay Round 1 Problems
- 21:32, 15 December 2023 (diff | hist) . . (+634) . . N 2023 SSMO Relay Round 1 Problems (Created page with "==Problem 1== Compute the remainder when <math>2022^{2021^{2020^{\dots}}}</math> is divided by <math>2023</math>. Solution ==P...")
- 21:30, 15 December 2023 (diff | hist) . . (-37) . . 2023 SSMO Team Round Problems
- 21:26, 15 December 2023 (diff | hist) . . (+7,970) . . N 2023 SSMO Team Round Problems (Created page with "==Problem 1== Let <math>(a, b, c, d)</math> be a permutation of <math>(2, 0, 2, 3)</math>. Find the largest possible value of <math>a^b + b^c + c^d + d^a</math> 2022 SSMO...")
- 21:21, 15 December 2023 (diff | hist) . . (+290) . . 2023 SSMO Team Round (current)
- 21:20, 15 December 2023 (diff | hist) . . (+1) . . 2023 SSMO Accuracy Round Problems
- 21:20, 15 December 2023 (diff | hist) . . (+5) . . 2023 SSMO Accuracy Round Problems
- 21:19, 15 December 2023 (diff | hist) . . (-133) . . 2023 SSMO Accuracy Round Problems
- 21:16, 15 December 2023 (diff | hist) . . (+5,770) . . N 2023 SSMO Accuracy Round Problems (Created page with "==Problem 1== Mr. Sammy proposes a Hamburger Proclamation, which has <math>500</math> lines, divided into paragraphs of <math>5</math> lines each. It takes him <math>23</math...")
- 19:42, 15 December 2023 (diff | hist) . . (+348) . . N 2022 SSMO Tiebreaker Round Problems/Problem 2 (Created page with "==Problem== Let <math>P(x) = x^3 - 7x^2 + 9x - 2</math>. If <math>P(x) = (x - a)^3 + b(x - a) + c</math> where <math>a, b, c</math> are real numbers, then the value of <math>a...") (current)
- 19:42, 15 December 2023 (diff | hist) . . (+250) . . N 2022 SSMO Tiebreaker Round Problems/Problem 1 (Created page with "==Problem== For all positive integers <math>n,</math> let <math>S(n)</math> denote the least positive integer <math>x</math> such that <math>n+x</math> is a palindrome. Find t...") (current)
- 13:13, 14 December 2023 (diff | hist) . . (+377) . . N 2022 SSMO Relay Round 5 Problems/Problem 3 (Created page with "==Problem== Let <math>T=</math> TNYWR, and let <math>a_k=\text{cis}\left(\frac{k\pi}{T+1}\right)</math>. Suppose that<cmath>\sum_{k=1}^{T+1} \frac{|a_{2k}+a_{2k+2}-a_{2k-1+T}|...") (current)
- 13:13, 14 December 2023 (diff | hist) . . (+389) . . N 2022 SSMO Relay Round 5 Problems/Problem 2 (Created page with "==Problem== Let <math>T=</math> TNYWR, and let <math>S=\{a_1,a_2,\dots,a_{2022}\}</math> be a sequence of 2022 positive integers such that <math>a_1\le a_2\le \cdots \le a_{20...") (current)
- 13:12, 14 December 2023 (diff | hist) . . (+350) . . N 2022 SSMO Relay Round 5 Problems/Problem 1 (Created page with "==Problem== Consider an <math>8\times 8</math> chessboard with a knight in one of the center squares. The knight may move in an <math>L</math>-shaped fashion, going two square...") (current)
- 13:11, 14 December 2023 (diff | hist) . . (+255) . . N 2022 SSMO Relay Round 4 Problems/Problem 3 (Created page with "==Problem== Let <math>T=</math> TNYWR. If <math>f(1)=1</math>, <math>f(2)=12</math>, and<cmath>f(n+2)=12f(n+1)-20f(n)</cmath>for all positive integers <math>n</math>, find the...") (current)
- 13:11, 14 December 2023 (diff | hist) . . (+286) . . N 2022 SSMO Relay Round 4 Problems/Problem 2 (Created page with "==Problem== The roots of <math>f(x)=x^3+5x+8</math> are <math>r_1,r_2,r_3.</math> Let <math>g_n(x)</math> be a polynomial with roots <math>r_1+n, r_2+n,r_3+n.</math> If<cmath>...") (current)
- 13:11, 14 December 2023 (diff | hist) . . (+830) . . N 2022 SSMO Relay Round 4 Problems/Problem 1 (Created page with "==Problem== On any given day, there is a <math>70\%</math> chance that a robot will find a new organism, a <math>20\%</math> chance it will find an already discovered organism...") (current)
- 13:11, 14 December 2023 (diff | hist) . . (+273) . . N 2022 SSMO Relay Round 3 Problems/Problem 3 (Created page with "==Problem== Let <math>T=</math> TNYWR. Let <math>f(x)</math> be a polynomial of degree 10, such that <math>f(i)=i</math> for all <math>i=1,2,\dots,10</math> and <math>f(11) =T...") (current)
- 13:11, 14 December 2023 (diff | hist) . . (+292) . . N 2022 SSMO Relay Round 3 Problems/Problem 2 (Created page with "==Problem== Let <math>T=</math> TNYWR. In cyclic quadrilateral <math>ABCD,</math> <math>\angle{BAD}=60^{\circ},</math> and <math>BC=CD=T.</math> If <math>AB</math> is a positi...") (current)
- 13:10, 14 December 2023 (diff | hist) . . (+413) . . N 2022 SSMO Relay Round 3 Problems/Problem 1 (Created page with "==Problem== Let <math>f:\mathbb Z\rightarrow\mathbb Z</math> be a function such that <math>f(0)=0</math> and <math>f\left(|x^2-4|\right)=0</math> if <math>f(x)=0</math>. Moreo...") (current)
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