User contributions
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- 13:06, 14 December 2023 (diff | hist) . . (+213) . . N 2022 SSMO Team Round Problems/Problem 9 (Created page with "==Problem== Given real numbers <math>a,b,x,y</math> such that <align*> a^2+b^2&=1,\\ x^2+y^2&=1,\\ abxy-\frac{1}{8}&=b^2y^2, </align*> find the sum of all distinct values of <...") (current)
- 13:06, 14 December 2023 (diff | hist) . . (+636) . . N 2022 SSMO Team Round Problems/Problem 8 (Created page with "==Problem== A frog is at <math>0</math> on a number line and wants to go to <math>9</math>. On each turn, if the frog is at <math>n</math>, the frog hops to one of the numbers...") (current)
- 13:06, 14 December 2023 (diff | hist) . . (+373) . . N 2022 SSMO Team Round Problems/Problem 7 (Created page with "==Problem== Let <math>\cos(2A)</math>, <math>\cos(2B)</math>, and <math>\cos(2C)</math> be the not necessarily distinct roots of a monic cubic <math>f</math>. Given that <math...") (current)
- 13:06, 14 December 2023 (diff | hist) . . (+719) . . N 2022 SSMO Team Round Problems/Problem 6 (Created page with "==Problem== Let <math>n</math> be a positive integer, and let <math>x</math> be some variable. Define <math>P_{x,n}</math> as the maximum fraction of elements in the set of th...") (current)
- 13:06, 14 December 2023 (diff | hist) . . (+867) . . N 2022 SSMO Team Round Problems/Problem 5 (Created page with "==Problem== Consider the following rectangle <math>ABCD</math> where <math>BC=8.</math> If<cmath>CD=CT_2, 4T_2P_2=2DP_1=AC, [ADP_1C]=33, \text{ and }[ABP_2C]=34,</cmath>find t...")
- 13:05, 14 December 2023 (diff | hist) . . (+222) . . N 2022 SSMO Team Round Problems/Problem 4 (Created page with "==Problem== Let <math>a_1=2,b_0=3, a_n=\left(a_{n-1}\right)^2,</math> and <math>b_n=\left(b_{n-1}\right)^3.</math> If <math>c_n=a_n+b_n,</math> find the last two digits of <ma...") (current)
- 13:05, 14 December 2023 (diff | hist) . . (+1,011) . . N 2022 SSMO Team Round Problems/Problem 3 (Created page with "==Problem== Let <math>ABCD</math> be an isosceles trapezoid such that <math>AB\parallel CD.</math> Let <math>E</math> be a point on <math>CD</math> such that <math>AB=CE.</mat...")
- 13:05, 14 December 2023 (diff | hist) . . (+897) . . N 2022 SSMO Team Round Problems/Problem 2 (Created page with "==Problem== Consider <math>8</math> marbles in a line, where the color of each marble is either black or white and is randomly chosen. Define the period of a lineup of 8 marbl...") (current)
- 13:05, 14 December 2023 (diff | hist) . . (+506) . . N 2022 SSMO Team Round Problems/Problem 1 (Created page with "==Problem== In triangle <math>ABC</math>, circumcircle <math>\omega</math> is drawn. Let <math>I</math> be the incenter of <math>\triangle{ABC}</math>. Let <math>H_A</math> be...") (current)
- 13:04, 14 December 2023 (diff | hist) . . (0) . . 2022 SSMO Accuracy Round Problems (current)
- 13:04, 14 December 2023 (diff | hist) . . (+328) . . N 2022 SSMO Accuracy Round Problems/Problem 10 (Created page with "==Problem== Let<cmath>S=\sum^{\infty}_{k=5}2^{-10k}\dbinom{2k}{10}.</cmath>Then the value of <math>S</math> can be expressed as <math>\frac mn</math>, where <math>m</math> and...") (current)
- 13:04, 14 December 2023 (diff | hist) . . (+475) . . N 2022 SSMO Accuracy Round Problems/Problem 9 (Created page with "==Problem== The graph <math>\Gamma</math> has <math>52</math> vertices labeled <math>A, A', B, B', \dots, Z, Z'</math>, such that <math>A</math> is not connected to <math>A'</...") (current)
- 13:03, 14 December 2023 (diff | hist) . . (+501) . . N 2022 SSMO Accuracy Round Problems/Problem 8 (Created page with "==Problem== Let <math>ABCD</math> be a trapezoid with <math>AB \parallel CD</math>. Suppose that <math>AD=1</math>, <math>DC=4</math>, <math>CB=2</math>, and <math>AB<CD</math...") (current)
- 13:03, 14 December 2023 (diff | hist) . . (+522) . . N 2022 SSMO Accuracy Round Problems/Problem 7 (Created page with "==Problem== After a robber drives in a car for <math>t</math> (not necessarily integral) minutes, the car goes at <math>120-t</math> miles per hour. Whenever the car's speed d...") (current)
- 13:03, 14 December 2023 (diff | hist) . . (+727) . . N 2022 SSMO Accuracy Round Problems/Problem 6 (Created page with "==Problem== Consider an unfair <math>6</math>-sided die labeled from <math>1</math> to <math>6</math>, such that the probability of rolling a number <math>m</math> is directly...") (current)
- 13:03, 14 December 2023 (diff | hist) . . (+271) . . N 2022 SSMO Accuracy Round Problems/Problem 5 (Created page with "==Problem== Find the number of ordered pairs <math>(a, b)</math>, where <math>1\leq a, b\leq 9</math>, for which the largest integer <math>n</math> that satisfies<cmath>(a-b)^...") (current)
- 13:03, 14 December 2023 (diff | hist) . . (+362) . . N 2022 SSMO Accuracy Round Problems/Problem 4 (Created page with "==Problem== A monic polynomial <math>f</math> has real roots <math>r,s,t.</math> A monic polynomial <math>g</math> has roots <math>r^3,s^3,t^3.</math> Given that the minimum p...") (current)
- 13:02, 14 December 2023 (diff | hist) . . (+501) . . N 2022 SSMO Accuracy Round Problems/Problem 3 (Created page with "==Problem== Let <math>A=(6,3,2), B=(2,-9,-6),</math> and <math>O=(0,0,0).</math> Suppose that <math>D</math> is a point in space such that <math>OD</math> bisects <math>\angle...") (current)
- 13:02, 14 December 2023 (diff | hist) . . (+486) . . N 2022 SSMO Accuracy Round Problems/Problem 2 (Created page with "==Problem== Consider a cone with radius <math>5</math> and height <math>12</math>, and a point <math>P</math> in the same plane as the base of the cone, but a distance of <mat...") (current)
- 13:02, 14 December 2023 (diff | hist) . . (+284) . . N 2022 SSMO Accuracy Round Problems/Problem 1 (Created page with "==Problem== Consider a bijective function (meaning each element in the domain maps to a distinct element in the range) <math>f:S\rightarrow S,</math> where <math>S=\{1, 2, 3,...") (current)
- 13:01, 14 December 2023 (diff | hist) . . (+335) . . N 2021 WSMO Team Round/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)
- 13:01, 14 December 2023 (diff | hist) . . (+323) . . N 2021 WSMO Team Round/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)
- 13:01, 14 December 2023 (diff | hist) . . (+418) . . N 2021 WSMO Team Round/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)
- 13:01, 14 December 2023 (diff | hist) . . (+357) . . N 2021 WSMO Team Round/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)
- 13:01, 14 December 2023 (diff | hist) . . (+2) . . 2021 WSMO Team Round/Problem 11 (current)
- 13:00, 14 December 2023 (diff | hist) . . (+161) . . N 2021 WSMO Team Round/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>) ==Solution")
- 13:00, 14 December 2023 (diff | hist) . . (+359) . . N 2021 WSMO Team Round/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)
- 13:00, 14 December 2023 (diff | hist) . . (+724) . . N 2021 WSMO Team Round/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)
- 13:00, 14 December 2023 (diff | hist) . . (+371) . . N 2021 WSMO Team Round/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...") (current)
- 12:59, 14 December 2023 (diff | hist) . . (+418) . . N 2021 WSMO Team Round/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...") (current)
- 12:58, 14 December 2023 (diff | hist) . . (+468) . . N 2021 WSMO Accuracy Round Problems/Problem 8 (Created page with "==Problem== 20 unit spheres are stacked in a triangular pyramid formation, such that the first layer has 1 sphere, the second layer has 3 spheres, the third layer has 6 sphere...") (current)
- 12:56, 14 December 2023 (diff | hist) . . (+40) . . 2023 SSMO Team Round
- 12:56, 14 December 2023 (diff | hist) . . (+40) . . 2023 SSMO Accuracy Round (current)
- 12:56, 14 December 2023 (diff | hist) . . (+40) . . 2023 SSMO Speed Round (current)
- 12:55, 14 December 2023 (diff | hist) . . (+40) . . 2022 SSMO Relay Round 4 (current)
- 12:55, 14 December 2023 (diff | hist) . . (+40) . . 2022 SSMO Relay Round 3 (current)
- 12:55, 14 December 2023 (diff | hist) . . (+40) . . 2022 SSMO Relay Round 5 (current)
- 12:55, 14 December 2023 (diff | hist) . . (+40) . . 2022 SSMO Relay Round 2 (current)
- 12:55, 14 December 2023 (diff | hist) . . (+40) . . 2022 SSMO Relay Round 1 (current)
- 12:55, 14 December 2023 (diff | hist) . . (+40) . . 2022 SSMO Team Round (current)
- 12:55, 14 December 2023 (diff | hist) . . (+40) . . 2022 SSMO Accuracy Round (current)
- 12:54, 14 December 2023 (diff | hist) . . (+40) . . 2022 SSMO Speed Round (current)
- 12:54, 14 December 2023 (diff | hist) . . (+25) . . SMO Problem Archive (current)
- 12:53, 14 December 2023 (diff | hist) . . (+40) . . 2021 WSMO Speed Round (current)
- 12:53, 14 December 2023 (diff | hist) . . (+40) . . 2021 WSMO Team Round (current)
- 12:53, 14 December 2023 (diff | hist) . . (+40) . . 2021 WSMO Accuracy Round (current)
- 12:52, 14 December 2023 (diff | hist) . . (+40) . . 2022 SSMO Tiebreaker Round (current)
- 12:52, 14 December 2023 (diff | hist) . . (+481) . . N 2023 SSMO Tiebreaker Round (Created page with "'''2023 SSMO 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)
- 12:52, 14 December 2023 (diff | hist) . . (-53) . . SMO Problem Archive
- 12:51, 14 December 2023 (diff | hist) . . (-2) . . SMO Problem Archive
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