User contributions
(newest | oldest) View (newer 50 | older 50) (20 | 50 | 100 | 250 | 500)
- 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)
- 13:10, 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)
- 13:10, 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)
- 13:10, 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)
- 13:09, 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)
- 13:09, 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)
- 13:09, 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)
- 13:09, 14 December 2023 (diff | hist) . . (-68) . . 2022 SSMO Team Round Problems/Problem 5 (current)
- 13:08, 14 December 2023 (diff | hist) . . (+18) . . 2022 SSMO Team Round Problems/Problem 3 (current)
- 13:08, 14 December 2023 (diff | hist) . . (+8) . . 2022 SSMO Team Round Problems/Problem 14 (current)
- 13:07, 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)
- 13:07, 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...")
- 13:07, 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)
- 13:07, 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)
- 13:07, 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)
- 13:06, 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==")
(newest | oldest) View (newer 50 | older 50) (20 | 50 | 100 | 250 | 500)