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• 12:10, 14 December 2023 (diff | hist) . . (+470)‎ . . N 2022 SSMO Relay Round 2 Problems/Problem 3 ‎ (Created page with "==Problem== Let <math>T =</math> TNYWR. Let <math>a+b = \lfloor \sqrt{T} \rfloor</math>. If <math>a^5 + b^5 = 15</math>, then <math>ab</math> has two possible values. The abso...") (current)
• 12:10, 14 December 2023 (diff | hist) . . (+382)‎ . . N 2022 SSMO Relay Round 2 Problems/Problem 2 ‎ (Created page with "==Problem== Let <math>T=</math> TNYWR. Suppose that the monic quadratic <math>f(x)</math> is tangent to the function <math>g(x)=|x+2|-T</math> at two points, when graphed on t...") (current)
• 12:10, 14 December 2023 (diff | hist) . . (+648)‎ . . N 2022 SSMO Relay Round 2 Problems/Problem 1 ‎ (Created page with "==Problem== Let <math>P</math> be a randomly selected point on a circle, and let <math>A</math> be a randomly selected point inside the same circle. A dilation centered at <ma...") (current)
• 12:09, 14 December 2023 (diff | hist) . . (+291)‎ . . N 2022 SSMO Relay Round 1 Problems/Problem 3 ‎ (Created page with "==Problem== Let <math>T=</math> TNYWR. Now, let <math>ABC</math> a triangle such that <math>AB=T,</math> <math>AC=100</math>, and <math>\angle{ABC}=36^{\circ}.</math> Find the...") (current)
• 12:09, 14 December 2023 (diff | hist) . . (+564)‎ . . N 2022 SSMO Relay Round 1 Problems/Problem 2 ‎ (Created page with "==Problem== Let <math>T=</math> TNYWR. Now, let <math>\ell</math> and <math>m</math> have equations <math>y=(2+\sqrt{3})x+16</math> and <math>y=\frac{x\sqrt{3}}{3}+20,</math>...") (current)
• 12:09, 14 December 2023 (diff | hist) . . (+227)‎ . . N 2022 SSMO Relay Round 1 Problems/Problem 1 ‎ (Created page with "==Problem== Suppose <math>a, b, c</math> are distinct digits where <math>a \not= 0</math> such that <math>\left(\overline{abc}\right)^2 = \overline{bad00}</math> where <math>d...") (current)
• 12:09, 14 December 2023 (diff | hist) . . (-68)‎ . . 2022 SSMO Team Round Problems/Problem 5 ‎ (current)
• 12:08, 14 December 2023 (diff | hist) . . (+18)‎ . . 2022 SSMO Team Round Problems/Problem 3 ‎ (current)
• 12:08, 14 December 2023 (diff | hist) . . (+8)‎ . . 2022 SSMO Team Round Problems/Problem 14 ‎ (current)
• 12:07, 14 December 2023 (diff | hist) . . (+859)‎ . . N 2022 SSMO Team Round Problems/Problem 15 ‎ (Created page with "==Problem== Consider two externally tangent circles <math>\omega_1</math> and <math>\omega_2</math> with centers <math>O_1</math> and <math>O_2</math>. Suppose that <math>\ome...") (current)
• 12:07, 14 December 2023 (diff | hist) . . (+782)‎ . . N 2022 SSMO Team Round Problems/Problem 14 ‎ (Created page with "==Problem== On a hot summer day, three little piggies decide to play with water balloons. The three piggies travel to a 200-floor parking garage each armed with exactly one wa...")
• 12:07, 14 December 2023 (diff | hist) . . (+607)‎ . . N 2022 SSMO Team Round Problems/Problem 13 ‎ (Created page with "==Problem== In regular hexagon <math>ABCDEF</math> with side length 1, an electron starts at point <math>A</math>. When the electron hits an edge, it reflects off of it, with...") (current)
• 12:07, 14 December 2023 (diff | hist) . . (+743)‎ . . N 2022 SSMO Team Round Problems/Problem 12 ‎ (Created page with "==Problem== Regular pentagon <math>ABCDE</math> is inscribed in circle <math>\omega_1</math> with radius <math>5\sqrt{5}</math>. Circle <math>\omega_2</math> is the reflection...") (current)
• 12:07, 14 December 2023 (diff | hist) . . (+186)‎ . . N 2022 SSMO Team Round Problems/Problem 11 ‎ (Created page with "==Problem== Find the number of solutions to <math>a^3+36ab+64=27b^3,</math> where <math>a</math> is an integer, <math>b</math> is a real number, and <math>|b|\le 50</math>. =...") (current)
• 12:06, 14 December 2023 (diff | hist) . . (+151)‎ . . N 2022 SSMO Team Round Problems/Problem 10 ‎ (Created page with "==Problem== If <math>p, q, r</math> are the roots of the polynomial <math>x^3-2x^2-4</math>, find<cmath>(p^3+qr)(q^3+pr)(r^3+pq).</cmath> ==Solution==")
• 12:06, 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)
• 12:06, 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)
• 12:06, 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)
• 12:06, 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)
• 12:06, 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...")
• 12:05, 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)
• 12:05, 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...")
• 12:05, 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)
• 12:05, 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)
• 12:04, 14 December 2023 (diff | hist) . . (0)‎ . . 2022 SSMO Accuracy Round Problems ‎ (current)
• 12:04, 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)
• 12:04, 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)
• 12:03, 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)
• 12:03, 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)
• 12:03, 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)
• 12:03, 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)
• 12:03, 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)
• 12:02, 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)
• 12:02, 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)
• 12:02, 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)
• 12:01, 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)
• 12:01, 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)
• 12:01, 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)
• 12:01, 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)
• 12:01, 14 December 2023 (diff | hist) . . (+2)‎ . . 2021 WSMO Team Round/Problem 11 ‎ (current)
• 12:00, 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")
• 12:00, 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)
• 12:00, 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)
• 12:00, 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)
• 11:59, 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)
• 11:58, 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)
• 11:56, 14 December 2023 (diff | hist) . . (+40)‎ . . 2023 SSMO Accuracy Round ‎ (current)
• 11:56, 14 December 2023 (diff | hist) . . (+40)‎ . . 2023 SSMO Team Round ‎
• 11:56, 14 December 2023 (diff | hist) . . (+40)‎ . . 2023 SSMO Speed Round ‎ (current)
• 11:55, 14 December 2023 (diff | hist) . . (+40)‎ . . 2022 SSMO Relay Round 4 ‎ (current)

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