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- 22:30, 15 December 2023 (diff | hist) . . (+448) . . N 2023 SSMO Tiebreaker Round Problems/Problem 3 (Created page with "==Problem== For <math>n\geq4,</math> let <math>a_n</math> be the maximum possible value of <math>P(n+1)</math> given that <math>P(x)</math> is a <math>n</math> degree monic po...") (current)
- 22:30, 15 December 2023 (diff | hist) . . (+338) . . N 2023 SSMO Tiebreaker Round Problems/Problem 2 (Created page with "==Problem== Let <math>P(x) = x^3 + 3ax^2 + 3bx + (a+b)</math> be a real polynomial with nonnegative and nonzero real roots <math>p, q, r</math>. Suppose that <cmath>(p + 1)^3...")
- 22:30, 15 December 2023 (diff | hist) . . (+276) . . N 2023 SSMO Tiebreaker Round Problems/Problem 1 (Created page with "==Problem== 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 is c...") (current)
- 22:30, 15 December 2023 (diff | hist) . . (+320) . . N 2023 SSMO Relay Round 5 Problems/Problem 3 (Created page with "==Problem== Let <math>T=</math> TNYWR. Suppose that <math>x^2+y^2 = N.</math> Find the remainder when the expected value of the square of the maximum value <math>ax+by</math>...") (current)
- 22:30, 15 December 2023 (diff | hist) . . (+194) . . N 2023 SSMO Relay Round 5 Problems/Problem 2 (Created page with "==Problem== Let <math>T=</math> TNYWR. Let <math>a_n = \text{lcm} \{1, 2, \dots n\}</math> for positive integers <math>n</math>.Compute <cmath>\sum_{i=1}^N a_i \pmod {720}.</c...") (current)
- 22:30, 15 December 2023 (diff | hist) . . (+386) . . N 2023 SSMO Relay Round 5 Problems/Problem 1 (Created page with "==Problem== 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 <ma...") (current)
- 22:29, 15 December 2023 (diff | hist) . . (+489) . . N 2023 SSMO Relay Round 4 Problems/Problem 3 (Created page with "==Problem== Let <math>T=</math> TNYWR. <math>N+1</math> numbers are chosen from the set <math>\{1,2,3,\dots,N+1\}</math> with replacement. If the probability that the median o...") (current)
- 22:29, 15 December 2023 (diff | hist) . . (+486) . . N 2023 SSMO Relay Round 4 Problems/Problem 2 (Created page with "==Problem== Let <math>T=</math> TNYWR. Let <math>n = \left\lfloor\sqrt{N}\right\rfloor.</math> Suppose that <math>N</math> points are chosen on the sides of a triangle with ar...") (current)
- 22:29, 15 December 2023 (diff | hist) . . (+523) . . N 2023 SSMO Relay Round 4 Problems/Problem 1 (Created page with "==Problem== 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>\fr...") (current)
- 22:29, 15 December 2023 (diff | hist) . . (+2,269) . . N 2023 SSMO Relay Round 3 Problems/Problem 3 (Created page with "==Problem== Let <math>T=</math> TNYWR. Let <math>n = N+1.</math> A spray painter has a paint gun that paints all areas within a radius of <math>2.</math> The spray painter wal...") (current)
- 22:29, 15 December 2023 (diff | hist) . . (+499) . . N 2023 SSMO Relay Round 3 Problems/Problem 2 (Created page with "==Problem== Let <math>T=</math> TNYWR. In triangle <math>ABC</math> with circumradius and inradius having lengths <math>R</math> and <math>r,</math> respectively. Given that...") (current)
- 22:29, 15 December 2023 (diff | hist) . . (+592) . . N 2023 SSMO Relay Round 3 Problems/Problem 1 (Created page with "==Problem== 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>A,...") (current)
- 22:29, 15 December 2023 (diff | hist) . . (+397) . . N 2023 SSMO Relay Round 2 Problems/Problem 3 (Created page with "==Problem== Let <math>T=</math> TNYWR. In a committee of <math>2023</math> people, <math>N</math> are scientists and the rest are builders. In order to make a building, <math>...") (current)
- 22:29, 15 December 2023 (diff | hist) . . (+307) . . N 2023 SSMO Relay Round 2 Problems/Problem 2 (Created page with "==Problem== Let <math>T=</math> TNYWR. Suppose that <math>L = \left\lfloor\sqrt{N}\right\rfloor</math> points are evenly spaced around the circle. Find the number of ways to s...") (current)
- 22:28, 15 December 2023 (diff | hist) . . (+263) . . N 2023 SSMO Relay Round 2 Problems/Problem 1 (Created page with "==Problem== 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 \ap...") (current)
- 22:28, 15 December 2023 (diff | hist) . . (+180) . . N 2023 SSMO Relay Round 1 Problems/Problem 3 (Created page with "==Problem== Let <math>T=</math> TNYWR. Find the number of solutions to the equation <cmath>\sec^{N} (Nx) - \tan^{N}(Nx) = 1</cmath> such <math>0 \le x \le \pi</math> ==Solut...") (current)
- 22:28, 15 December 2023 (diff | hist) . . (+195) . . N 2023 SSMO Relay Round 1 Problems/Problem 2 (Created page with "==Problem== Let <math>T=</math> TNYWR. Let <math>a_0 = 3, a_1 = 1, a_2 = N</math>, and let <math>a_n = a_{n-1} - \frac{a_{n-3}}{8}</math>. Find <cmath>\sum_{i=0}^\infty a_i.</...") (current)
- 22:28, 15 December 2023 (diff | hist) . . (+125) . . N 2023 SSMO Relay Round 1 Problems/Problem 1 (Created page with "==Problem== Compute the remainder when <math>2022^{2021^{2020^{\dots}}}</math> is divided by <math>2023</math>. ==Solution==") (current)
- 22:25, 15 December 2023 (diff | hist) . . (-270) . . 2023 SSMO Team Round Problems/Problem 13 (current)
- 22:25, 15 December 2023 (diff | hist) . . (+224) . . N 2023 SSMO Team Round Problems/Problem 14 (Created page with "==Problem== Find the sum of all perfect squares of the form <math>2p^3 - 5p^2q + q^2</math> where <math>p</math> and <math>q</math> are positive integers such <math>p</math> i...") (current)
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