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• 11:43, 9 September 2025 (diff | hist) . . (+204)‎ . . N 2025 SSMO Relay Round 2 Problems/Problem 1 ‎ (Created page with "==Problem== Let <math>(p,q,r)</math> be the real solution to following system: <cmath>\begin{align*} pq &= 20 \\ qr &= 25 \\ r+p &= 9. \end{align*}</cmath> Compute <math>p^2+...") (current)
• 11:42, 9 September 2025 (diff | hist) . . (+204)‎ . . N 2025 SSMO Relay Round 1 Problems/Problem 2 ‎ (Created page with "==Problem== Let <math>T = TNYWR.</math> A positive integer is called \textit{zro} if more than half of its digits are <math>0</math>. Find the sum of the first <math>T^2</mat...") (current)
• 11:42, 9 September 2025 (diff | hist) . . (+194)‎ . . N 2025 SSMO Relay Round 1 Problems/Problem 3 ‎ (Created page with "==Problem== Let <math>T = TNYWR.</math> Positive integers <math>m</math> and <math>n</math> satisfy <math>m^2-n^2 = T</math>. What is the least possible value of <math>m+n</m...") (current)
• 11:42, 9 September 2025 (diff | hist) . . (+270)‎ . . N 2025 SSMO Relay Round 1 Problems/Problem 1 ‎ (Created page with "==Problem== Let <math>x_1, x_2, \ldots, x_7</math> be distinct integers such that the mean of <math>\{x_i,x_{i+1},x_{i+2}\}</math> is an integer for all integers <math>1\le i...") (current)
• 11:41, 9 September 2025 (diff | hist) . . (+590)‎ . . 2025 SSMO Relay Round 1 Problems ‎ (current)
• 11:41, 9 September 2025 (diff | hist) . . (+1,745)‎ . . N 2025 SSMO Relay Round 5 Problems ‎ (Created page with "==Problem 1== The numbers <math>17</math> and <math>25</math> are written on a blackboard. Every second, if the number <math>n</math> is currently written on the blackboard,...") (current)
• 11:40, 9 September 2025 (diff | hist) . . (+1,516)‎ . . N 2025 SSMO Relay Round 4 Problems ‎ (Created page with "==Problem 1== Call a positive integer <i>chuzzed</i> if the sum of the digits in its binary representation is equal to the units digit of its base-<math>10</math> representat...") (current)
• 11:40, 9 September 2025 (diff | hist) . . (+1,245)‎ . . N 2025 SSMO Relay Round 3 Problems ‎ (Created page with "==Problem 1== Michael, Nico, and Jackson are splitting a <math>100</math> dollar bill. Michael's favorite number is <math>3,</math> so he insists on paying a positive amount...") (current)
• 11:39, 9 September 2025 (diff | hist) . . (+1,365)‎ . . N 2025 SSMO Relay Round 2 Problems ‎ (Created page with "==Problem 1== Let <math>(p,q,r)</math> be the real solution to following system: <cmath>\begin{align*} pq &= 20 \\ qr &= 25 \\ r+p &= 9. \end{align*}</cmath> Compute <math>p^...") (current)
• 11:37, 9 September 2025 (diff | hist) . . (+217)‎ . . N 2025 SSMO Relay Round 1 Problems ‎ (Created page with "==Problem 1== Solution ==Problem 2== Solution ==Problem 3== 2025 SSMO R...")
• 11:36, 9 September 2025 (diff | hist) . . (+423)‎ . . N 2025 SSMO Relay Round 5 ‎ (Created page with "'''2025 SSMO Relay Round 5''' problems and solutions. The first link contains the full set of test problems. The rest contain each individual problem and its solution. *202...") (current)
• 11:36, 9 September 2025 (diff | hist) . . (+423)‎ . . N 2025 SSMO Relay Round 4 ‎ (Created page with "'''2025 SSMO Relay Round 4''' problems and solutions. The first link contains the full set of test problems. The rest contain each individual problem and its solution. *202...") (current)
• 11:36, 9 September 2025 (diff | hist) . . (+423)‎ . . N 2025 SSMO Relay Round 3 ‎ (Created page with "'''2025 SSMO Relay Round 3''' problems and solutions. The first link contains the full set of test problems. The rest contain each individual problem and its solution. *202...") (current)
• 11:36, 9 September 2025 (diff | hist) . . (+423)‎ . . N 2025 SSMO Relay Round 2 ‎ (Created page with "'''2025 SSMO Relay Round 2''' problems and solutions. The first link contains the full set of test problems. The rest contain each individual problem and its solution. *202...") (current)
• 11:36, 9 September 2025 (diff | hist) . . (+423)‎ . . N 2025 SSMO Relay Round 1 ‎ (Created page with "'''2025 SSMO Relay Round 1''' problems and solutions. The first link contains the full set of test problems. The rest contain each individual problem and its solution. *202...") (current)
• 11:35, 9 September 2025 (diff | hist) . . (+291)‎ . . N 2025 SSMO Relay Rounds ‎ (Created page with "'''2025 SSMO Relay Rounds''' problems and solutions. The following 5 links contain problems and solutions for the 5 relay rounds in the 2024 SSMO. *2025 SSMO Relay Round 1...") (current)
• 11:35, 9 September 2025 (diff | hist) . . (+14)‎ . . N 2025 SSMO Tiebreaker Round Answer Key ‎ (Created page with "#51 #674 #1616") (current)
• 11:34, 9 September 2025 (diff | hist) . . (+210)‎ . . N 2025 SSMO Tiebreaker Round Problems/Problem 3 ‎ (Created page with "==Problem== Find the number of functions <math>f:\{1, 2, 3, 4, 5, 6, 7, 8\} \to \{1, 2, 3, 4\}</math> such that <math>f(2f(x)) = f(x)</math> for all <math>x \in \{1, 2, 3, 4,...") (current)
• 11:34, 9 September 2025 (diff | hist) . . (+171)‎ . . N 2025 SSMO Tiebreaker Round Problems/Problem 2 ‎ (Created page with "==Problem== Determine the largest positive integer <math>n</math> satisfying <cmath>\frac{\sqrt{n+1} - \sqrt{n}}{\sqrt{n+2026} - \sqrt{n+2025}} > 2.</cmath> ==Solution==") (current)
• 11:34, 9 September 2025 (diff | hist) . . (+1,126)‎ . . N 2025 SSMO Tiebreaker Round Problems/Problem 1 ‎ (Created page with "==Problem== In a triangular grid, each cell must contain exactly one number such that: * Each cell in the bottom row contains either <math>0</math> or <math>1</math>. * Each...") (current)
• 11:34, 9 September 2025 (diff | hist) . . (+1,655)‎ . . N 2025 SSMO Tiebreaker Round Problems ‎ (Created page with "==Problem 1== In a triangular grid, each cell must contain exactly one number such that: * Each cell in the bottom row contains either <math>0</math> or <math>1</math>. * Eac...") (current)
• 11:33, 9 September 2025 (diff | hist) . . (+482)‎ . . N 2025 SSMO Tiebreaker Round ‎ (Created page with "'''2025 SSMO Tiebreaker Round''' problems and solutions. The first link contains the full set of test problmems. The second link contains the answer key. The rest contain each...") (current)
• 11:33, 9 September 2025 (diff | hist) . . (+61)‎ . . N 2025 SSMO Team Round Answer Key ‎ (Created page with "#32 #4 #64 #1 #7 #121 #69 #36 #832 #54 #271 #659 #71 #60 #901") (current)
• 11:32, 9 September 2025 (diff | hist) . . (+846)‎ . . N 2025 SSMO Team Round Problems/Problem 15 ‎ (Created page with "==Problem== The circles <math>\omega_1</math> and <math>\omega_2</math> have radii <math>8</math> and <math>7</math>, respectively, and intersect at points <math>A</math> and...") (current)
• 11:32, 9 September 2025 (diff | hist) . . (+197)‎ . . N 2025 SSMO Team Round Problems/Problem 14 ‎ (Created page with "==Problem== Find the number of ordered triples of positive integers <math>(a,b,c)</math> such that <math>a+b+c=305</math> and <math>ab+bc+ca</math> is a multiple of <math>305...") (current)
• 11:32, 9 September 2025 (diff | hist) . . (+679)‎ . . N 2025 SSMO Team Round Problems/Problem 13 ‎ (Created page with "==Problem== Let <math>S</math> be the set of all ordered quintuples of integers <math>(x_1,x_2,x_3,x_4,x_5)</math> satisfying <math>0 \le x_1\le x_2\le x_3\le x_4 \le x_5\le...") (current)
• 11:32, 9 September 2025 (diff | hist) . . (+291)‎ . . N 2025 SSMO Team Round Problems/Problem 12 ‎ (Created page with "==Problem== Let <math>a_n=(4+3\sqrt2)^n</math> for all nonnegative integers <math>n</math>. Let <cmath>\sum_{k=0}^\infty\frac{\lfloor a_k\rfloor}{10^k}=\frac{m}{n},</cmath> w...") (current)
• 11:32, 9 September 2025 (diff | hist) . . (+568)‎ . . N 2025 SSMO Team Round Problems/Problem 11 ‎ (Created page with "==Problem== Squares <math>s_1,</math> <math>s_2,</math> and <math>s_3</math> with side lengths <math>9,</math> <math>17,</math> and <math>10,</math> respectively, lie inside...") (current)
• 11:32, 9 September 2025 (diff | hist) . . (+381)‎ . . N 2025 SSMO Team Round Problems/Problem 10 ‎ (Created page with "==Problem== Anna has a three term arithmetic sequence of integers. She divides each term of her sequence by a positive integer <math>n>1</math>, and tells Bob that the three...") (current)
• 11:32, 9 September 2025 (diff | hist) . . (+382)‎ . . N 2025 SSMO Team Round Problems/Problem 9 ‎ (Created page with "==Problem== Pairwise distinct integers <math>a,</math> <math>b,</math> <math>c,</math> and <math>d</math> satisfy the system of equations <cmath>\begin{align*} ab &= cd \\ a...") (current)
• 11:32, 9 September 2025 (diff | hist) . . (+268)‎ . . N 2025 SSMO Team Round Problems/Problem 8 ‎ (Created page with "==Problem== Adam has a fair coin with a <math>2</math> written on one side and a <math>3</math> written on the other. What is the expected number of times Adam needs to flip...") (current)
• 11:32, 9 September 2025 (diff | hist) . . (+420)‎ . . N 2025 SSMO Team Round Problems/Problem 6 ‎ (Created page with "==Problem== The rhombus <math>PQRS</math> has side length <math>3</math>. The point <math>X</math> lies on segment <math>PR</math> such that line <math>QX</math> is perpendic...") (current)
• 11:32, 9 September 2025 (diff | hist) . . (+347)‎ . . N 2025 SSMO Team Round Problems/Problem 7 ‎ (Created page with "==Problem== Let <math>n</math> be the largest integer such that <math>20!^{25!} + 25!^{20!}</math> is divisible by <math>2025^n</math>. The value of <math>n</math> can be wri...") (current)
• 11:32, 9 September 2025 (diff | hist) . . (+143)‎ . . N 2025 SSMO Team Round Problems/Problem 5 ‎ (Created page with "==Problem== Bob rolls a fair six-sided die until he rolls an even number. What is the expected sum of all the numbers he rolled? ==Solution==") (current)
• 11:31, 9 September 2025 (diff | hist) . . (+330)‎ . . N 2025 SSMO Team Round Problems/Problem 4 ‎ (Created page with "==Problem== Let <math>P(x) = x^2 - ax + b</math> be a quadratic with nonzero real coefficients. Given that <math>P(a)</math> and <math>P(-b)</math> are roots of <math>P(x),</...") (current)
• 11:31, 9 September 2025 (diff | hist) . . (+436)‎ . . N 2025 SSMO Team Round Problems/Problem 3 ‎ (Created page with "==Problem== A rectangle is divided as shown into nine smaller rectangles. The areas of the five smallest rectangles are <math>1,</math> <math>2,</math> <math>3,</math> <math>...") (current)
• 11:30, 9 September 2025 (diff | hist) . . (+174)‎ . . N 2025 SSMO Team Round Problems/Problem 2 ‎ (Created page with "==Problem== Nonnegative integers <math>a</math> and <math>b</math> satisfy <math>a!+b^4 = 16a+41</math>. Find the sum of all possible values of <math>b</math>. ==Solution==") (current)
• 11:30, 9 September 2025 (diff | hist) . . (+280)‎ . . N 2025 SSMO Team Round Problems/Problem 1 ‎ (Created page with "==Problem== There are <math>N</math> solutions <math>(a,b,c)</math> to <math>a + b^2 + c = 2025,</math> where <math>a</math> and <math>b</math> are positive integers and <mat...") (current)
• 11:30, 9 September 2025 (diff | hist) . . (+6,412)‎ . . N 2025 SSMO Team Round Problems ‎ (Created page with "==Problem 1== There are <math>N</math> solutions <math>(a,b,c)</math> to <math>a + b^2 + c = 2025,</math> where <math>a</math> and <math>b</math> are positive integers and <m...") (current)
• 11:27, 9 September 2025 (diff | hist) . . (+1,130)‎ . . N 2025 SSMO Team Round ‎ (Created page with "'''2025 SSMO Team Round''' problems and solutions. The first link contains the full set of test problmems. The second link contains the answer key. The rest contain each indiv...") (current)
• 11:27, 9 September 2025 (diff | hist) . . (-2)‎ . . 2025 SSMO Accuracy Round Problems ‎
• 11:27, 9 September 2025 (diff | hist) . . (-2)‎ . . 2025 SSMO Accuracy Round Problems/Problem 8 ‎ (→‎Problem)
• 11:26, 9 September 2025 (diff | hist) . . (+575)‎ . . N 2025 SSMO Accuracy Round Problems/Problem 10 ‎ (Created page with "==Problem== Let <math>ABCDE</math> be a convex pentagon with <math>\angle{BAC} = \angle{CAD} = \angle{DAE}</math> and <math>\angle{ABC} = \angle{ACD} = \angle{ADE}</math>. Le...")
• 11:26, 9 September 2025 (diff | hist) . . (+442)‎ . . N 2025 SSMO Accuracy Round Problems/Problem 9 ‎ (Created page with "==Problem== For a positive integer <math>n,</math> let <math>r(n)</math> denote the value of the binary number obtained by reading the binary representation of <math>n</math>...") (current)
• 11:26, 9 September 2025 (diff | hist) . . (+680)‎ . . N 2025 SSMO Accuracy Round Problems/Problem 8 ‎ (Created page with "==Problem== We say that a permutation <math>(a_1, a_2, \dots ,a_{10})</math> of the integers <math>1</math> through <math>10</math> inclusive is \textit{peaked} if there do n...")
• 11:26, 9 September 2025 (diff | hist) . . (+487)‎ . . N 2025 SSMO Accuracy Round Problems/Problem 7 ‎ (Created page with "==Problem== There is a unique ordered triple of positive reals <math>(a,b,c)</math> satisfying the system of equations <cmath>\begin{align*} a^2 + 9 &= (b-8\sqrt{3})^2 + 4 \...")
• 11:26, 9 September 2025 (diff | hist) . . (+613)‎ . . N 2025 SSMO Accuracy Round Problems/Problem 6 ‎ (Created page with "==Problem== Andy the ant starts at the square labeled <math>1</math>. On each move Andy moves to any orthogonal square (a square with which his current square shares a side)....")
• 11:26, 9 September 2025 (diff | hist) . . (+855)‎ . . N 2025 SSMO Accuracy Round Problems/Problem 5 ‎ (Created page with "==Problem== <math>ABC</math> is an isosceles triangle with base <math>BC = 6</math> and <math>AB = AC</math>. Point <math>M</math> is the midpoint of <math>BC</math> such tha...")
• 11:26, 9 September 2025 (diff | hist) . . (+334)‎ . . N 2025 SSMO Accuracy Round Problems/Problem 4 ‎ (Created page with "==Problem== Let <math>a,</math> <math>b,</math> and <math>c</math> be the roots of the polynomial <math>x^3+4x^2-3x-4</math>. Suppose that <cmath>\left|\frac{a}{b+c}+\frac{b...")
• 11:26, 9 September 2025 (diff | hist) . . (+303)‎ . . N 2025 SSMO Accuracy Round Problems/Problem 3 ‎ (Created page with "==Problem== Nonnegative real numbers <math>x,y,</math> and <math>z</math> satisfy <cmath>\frac{\sqrt{x}+13}{y} = \frac{\sqrt{y}+29}{z} = \frac{\sqrt{z} + 46}{x} = 2</cmath> a...")

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