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• 21:18, 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)
• 21:18, 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)
• 21:16, 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)
• 21:16, 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)
• 21:16, 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)
• 21:16, 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)
• 21:16, 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)
• 21:16, 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)
• 21:16, 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)
• 21:16, 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)
• 21:16, 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)
• 21:16, 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)
• 21:16, 15 December 2023 (diff | hist) . . (+25)‎ . . 2021 WSMO Team Round Problems/Problem 5 ‎ (current)
• 21:16, 15 December 2023 (diff | hist) . . (+25)‎ . . 2021 WSMO Team Round Problems/Problem 3 ‎ (current)
• 21:16, 15 December 2023 (diff | hist) . . (+27)‎ . . 2021 WSMO Team Round Problems/Problem 4 ‎ (current)
• 21:12, 15 December 2023 (diff | hist) . . (+25)‎ . . 2021 WSMO Team Round Problems/Problem 2 ‎ (current)
• 21:12, 15 December 2023 (diff | hist) . . (+26)‎ . . 2021 WSMO Team Round Problems/Problem 1 ‎ (current)
• 21:11, 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...")
• 21:08, 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...")
• 21:07, 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...")
• 21:07, 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...")
• 21:06, 15 December 2023 (diff | hist) . . (-1)‎ . . 2021 WSMO Team Round Problems/Problem 1 ‎
• 21:06, 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...")
• 20:48, 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)
• 20:36, 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)
• 20:35, 15 December 2023 (diff | hist) . . (0)‎ . . 2023 SSMO Relay Round 3 Problems ‎ (current)
• 20:35, 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)
• 20:34, 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...")
• 20:33, 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)
• 20:32, 15 December 2023 (diff | hist) . . (+1)‎ . . 2023 SSMO Relay Round 1 Problems ‎ (current)
• 20:32, 15 December 2023 (diff | hist) . . (+5)‎ . . 2023 SSMO Relay Round 1 Problems ‎
• 20:32, 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...")
• 20:30, 15 December 2023 (diff | hist) . . (-37)‎ . . 2023 SSMO Team Round Problems ‎
• 20:26, 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...")
• 20:21, 15 December 2023 (diff | hist) . . (+290)‎ . . 2023 SSMO Team Round ‎ (current)
• 20:20, 15 December 2023 (diff | hist) . . (+1)‎ . . 2023 SSMO Accuracy Round Problems ‎
• 20:20, 15 December 2023 (diff | hist) . . (+5)‎ . . 2023 SSMO Accuracy Round Problems ‎
• 20:19, 15 December 2023 (diff | hist) . . (-133)‎ . . 2023 SSMO Accuracy Round Problems ‎
• 20:16, 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...")
• 18:42, 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)
• 18:42, 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)
• 12:13, 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)
• 12:13, 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)
• 12:12, 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)
• 12:11, 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)
• 12:11, 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)
• 12:11, 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)
• 12:11, 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)
• 12:11, 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)
• 12:10, 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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