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• 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...")
• 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...")
• 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...")
• 21:35, 15 December 2023 (diff | hist) . . (0)‎ . . 2023 SSMO Relay Round 3 Problems ‎
• 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>...")
• 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...")
• 21:32, 15 December 2023 (diff | hist) . . (+1)‎ . . 2023 SSMO Relay Round 1 Problems ‎
• 21:32, 15 December 2023 (diff | hist) . . (+5)‎ . . 2023 SSMO Relay Round 1 Problems ‎

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