Algebra articles, problems, and puzzles.

What Is Arithmetic?
What Is Algebra?
Arithmetic: Articles and Problems

  1. 17 rooks on an 8×8 chessboard
  2. 1962 IMO, Problem 2: an inequality with a twist
  3. 1=2 via Continued Fractions
  4. 3-Colors Tower of Hanoi [Java]
  5. 3 glass puzzle [JavaScript]
  6. 3-Term Arithmetic Progression
  7. A 2-Variable Optimization From a China Competition
  8. A 4-variable Inequality from the RMM
  9. 4x4 coloring problem
  10. 6th European Mathematical Cup (2017), Junior Problem 4
  11. A 49th Degree Challenge
  12. A Case for Determinants
  13. A Case of Divergence
  14. A Clique of Acquaintances
  15. A Curious Property of Numbers 3 and 5
  16. A Cyclic But Not Symmetric Inequality in Four Variables
  17. A Cyclic Inequality by Seyran Ibrahimov
  18. A Cyclic Inequality from Math Phenomenon
  19. A Cyclic Inequality in Three Variables
  20. A Cyclic Inequality in Three Variables II
  21. A Cyclic Inequality in Three Variables III
  22. A Cyclic Inequality in Three Variables IV
  23. A Cyclic Inequality in Three Variables V
  24. A Cyclic Inequality in Three Variables VI
  25. A Cyclic Inequality in Three Variables VII
  26. A Cyclic Inequality in Three Variables VIII
  27. A Cyclic Inequality in Three Variables IX
  28. A Cyclic Inequality in Three Variables X
  29. A Cyclic Inequality in Three Variables XI
  30. A Cyclic Inequality in Three Variables XII
  31. A Cyclic Inequality in Three Variables XIII
  32. A Cyclic Inequality in Three Variables XIV
  33. A Cyclic Inequality in Three Variables XV
  34. A Cyclic Inequality in Three Variables XVI
  35. A Cyclic Inequality in Three Variables XVII
  36. A Cyclic Inequality in Three Variables XVIII
  37. A Cyclic Inequality in Three Variables XIX
  38. An Estimate for the Roots of Quadratic Equation
  39. An Exercise in Complex Numbers: Problem 4217 from Crux
  40. An Inequality with Constraint XX
  41. A Cyclic Inequality in Three Variables XX
  42. A Cyclic Inequality in Three Variables XXI
  43. A Cyclic Inequality in Three Variables XXII
  44. A Cyclic Inequality in Three Variables XXIII
  45. A Cyclic Inequality in Three Variables XXIV
  46. A Cyclic Inequality in Three Variables XXV
  47. A Cyclic Inequality in Three Variables And One More
  48. >A Cyclic Inequality In Three Variables by Sorin Radulescu
  49. A Cyclic Inequality in Three Variables by Uche E. Okeke
  50. A Cyclic Inequality from India In Three Variables And More
  51. A Cyclic Inequality in Three Variables with Constraint
  52. A Cyclic Inequality in Three or More Variables
  53. A Cyclic Inequality of Degree Four
  54. A Cyclic Inequality With Constraint in Two Triples of Variables
  55. A Cycling Inequality with Integrals
  56. A Cycling Inequality with Integrals II
  57. A Cyclic Inequality with Many Sums
  58. A Cyclic Inequality with Powers 2 through 7
  59. A Cyclic Inequality in Three Variables with a Variable Hierarchy
  60. A Cyclic Inequality on [-1,1]
  61. A Diophantine Equation - Problem from 2000 Belarus MO
  62. A Diophantine Equation with Square Roots - Problem from the 2008 British MO
  63. A DIY Proof of the Irrationality of sqrt(2)
  64. A Fancy Sum from the APMO 2000, Problem 1
  65. A Few Variants of a Popular Inequality And a Generalization
  66. A Formula for sin(3x)
  67. A Functional Equation from 1968 IMO
  68. A Functional Equation from the 2012 IMO
  69. A Generalization of an Inequality from a Romanian Olympiad
  70. A Limit of a Sequence
  71. A Limit of Another Sequence
  72. A Limit of a Series of Determinants
  73. A Limit with Fractions, Roots, Powers and Series
  74. A Limit With Sums, Roots, And Binomial Coefficients
  75. A Little of Algebra for an Inequality, A Little of Calculus for a Generalization
  76. A Little More of Algebra for an Inequality, A Little Less of Calculus for a Generalization
  77. A Long Cyclic Inequality of Degree 4
  78. A Low Bound for 1/2 * 3/4 * 5/6 * ... * (2n-1)/2n
  79. A Mathematical Rabbit out of an Algebraic Hat
  80. A Memorable Fact
  81. A Middle School Problem from a Moscow Olympiad
  82. A New Proof That the Rationals Are Countable
  83. A Not Quite Cyclic Inequality
  84. A Not Quite Cyclic Inequality from Tibet
  85. A Not Symmetric Inequality [JavaScript]
  86. A Not So Simple Inequality in Three Variables
  87. A One-Line Proof of the Infinitude of Primes
  88. A Partly Cyclic Inequality in Four Variables
  89. A Problem for the 2015 New Year's Eve
  90. A Problem From a Mongolian Olympiad for Grade 11
  91. A Problem from Croatian TST
  92. A Problem from the Danubius Contest 2016
  93. A Problem from the Danubius-XI Contest
  94. A Problem From the Romanian Mathematical Competitions (2016)
  95. A Problem in Complex Numbers Sets 3 Aside
  96. A Problem in Division of Polynomials
  97. A Problem with a Magical Solution from Secrets in Inequalities
  98. A Proof by Game for a Sum of a Convergent Series
  99. A Property of Number 4
  100. A Property of Product of Special Matrices, Probably Folklore
  101. A Property of the fusc() Function
  102. A Refinement of Turkevich's Inequality
  103. A Representation of Rational Numbers
  104. A Quartic Equation
  105. A Series with k-Permutations
  106. A Simple Inequality with Many Variables
  107. A Simple Cyclic Inequality in Three Variables
  108. A Simple Inequality in Three Variables
  109. A simple integral
  110. A simple integral, III
  111. A Simple Integral of a Peculiar Function
  112. A Simplified Version of Leo Giugiuc's Inequality from the AMM
  113. A Sum by Dorin Marghidanu
  114. A Sum of a Double Series
  115. A System of Equations Begging for Generalization
  116. A System of Equations in Determinants
  117. A System of Two Equations Replete with Squares
  118. A Telescoping Series
  119. A Tricky Integral Inequality
  120. A Trigonometric Inequality from the RMM
  121. >A Trigonometric Observation in Right Triangle
  122. A Triple Integral Inequality
  123. A Warmup Inequality from Vasile Cirtoaje
  124. ab + bc + ca ≤ aa + bb + cc
  125. About numbers
  126. Absolute Value
  127. Absolute Value and 1998 integers
  128. Achieve the Equilibrium [Flash]
  129. Addition
  130. Addition and Subtraction Formulas for Sine and Cosine III
  131. Addition and Subtraction Formulas for Sine and Cosine IV
  132. Advancing a Millenium Problem [JavaScript]
  133. Affirmative Action Problem [Java]
  134. Algebraic-Geometric Inequality
  135. Algebraic Structure of Complex Numbers
  136. All Integers Are Equal to 1
  137. All Integers Are Even
  138. All Powers of 2 Are Equal to 1
  139. All Powers of x are Constant
  140. Almost every integer has the digit 3 in it
  141. Almost Integers - Gaussian Integers
  142. Amazing Mix of Triangular Numbers and Golden Ratio
  143. Ambassadors at a Round Table [Java]
  144. An Acyclic Inequality in Three Variables
  145. An Algebraic Lemma with Geometric Consequences [JavaScript]
  146. An Application of Quadratic Formula
  147. An Arctan Identity and its Consequence [JavaScript, GeoGebra]
  148. An Easy Cyclic Inequality And a Remark
  149. An Easy Inequality with Three Integrals
  150. An Elementary Inequality by Non-elementary Means
  151. An Elementary Proof for Euler's Series
  152. An Equation in Determinants
  153. An Equation in Factorials
  154. An Equation in Matrices
  155. An Equation in Radicals
  156. An Equation in Reciprocals
  157. An Equation in RxR from Romania
  158. An Equation in Squares [JavaScript]
  159. An Equation Involving Four Collinear Points
  160. An Exercise without Calculating Aids
  161. An Identity between the Roots of a Cubic Polynomial - Problem from the 2007 Irish MO
  162. An Identity From the 2010 China Mathematical Competition
  163. An Identity Involving the Integer Part - Problem from the 1981 Canadian MO
  164. An Increasing Sequence from 2014 IMO
  165. An Inequality and Its Modifications
  166. An Inequality between AM, QM and GM
  167. An Inequality by Uncommon Induction
  168. An Inequality for Grade 8
  169. An Inequality from the 1967 IMO Shortlist
  170. An inequality from 1971 Canadian Mathematical Olympiad
  171. An Inequality from Marocco [JavaScript]
  172. An Inequality from Tibet
  173. An inequality in 2+2 variables from SSMA magazine
  174. Inequality in Convex Quadrilateral
  175. An Inequality in Determinants
  176. An Inequality in Four Weighted Variables
  177. An Inequality in Fractions with Absolute Values
  178. An Inequality in Integers [JavaScript]
  179. An Inequality in Integers II
  180. An Inequality in Parallelogram of Unit Area
  181. An Inequality in Reciprocals
  182. An Inequality in Reciprocals II An Inequality in Reciprocals III
  183. An Inequality in Three (Or Is It Two) Variables
  184. An Inequality in Triangle and In General
  185. An Inequality In Triangle and Without
  186. An Inequality In Triangle and Without II
  187. An Inequality in Two Or More Variables
  188. An Inequality in Two Or More Variables II
  189. An Inequality Involving Arithmetic And Geometric Means
  190. An Inequality Solved by Changing Appearances
  191. An Inequality with Angles and Integers
  192. An Inequality with Arbitrary Roots
  193. An Inequality with Areas, Norms, and Complex Numbers An Inequality with Central Binomials
  194. An Inequality with Complex Numbers of Unit Length
  195. An Inequality with Complex Numbers of Unit Length II
  196. An Inequality with Cubic Roots
  197. An Inequality with Cyclic Sums And Products
  198. An Inequality with Cyclic Sums on Both Sides
  199. An Inequality with Cyclic Sums on Both Sides II
  200. An Inequality with Cyclic Sums on Both Sides III
  201. An Inequality with Exponents
  202. An Inequality with Five Variables, Only Three Cyclic
  203. An Inequality with Fractions
  204. An Inequality with Integrals
  205. An Inequality with Integrals and Radicals
  206. An Inequality with Just Two Variable And an Integer
  207. An Inequality with Sines But Not in a Triangle
  208. An Inequality with One Tangent and Six Sines
  209. An Inequality with Powers And Logarithm
  210. An Inequality With Six Variables and Constraints
  211. An Inequality Where One Term Is More Equal Than Others
  212. An Inequality with a Parameter and a Constraint
  213. An Inequality with Absolute Values
  214. An Inequality with an Infinite Series
  215. An Inequality with Constraint
  216. An Inequality with Constraints II
  217. An Inequality with Constraint III
  218. An Inequality with Constraint IV
  219. An Inequality with Constraint V
  220. An Inequality with Constraint VI
  221. An Inequality with Constraint VII
  222. An Inequality with Constraint VIII [JavaScript]
  223. An Inequality with Constraint IX [JavaScript]
  224. An Inequality with Constraint X [JavaScript]
  225. An Inequality with Constraint XI [JavaScript]
  226. An Inequality with Constraint XII
  227. An Inequality with Constraint XIII
  228. An Inequality with Constraint XIV
  229. Inequalities with Constraint XV and XVI
  230. An Inequality with Constraint XVII
  231. An Inequality with Constraint XVIII
  232. An Inequality with Constraint XIX
  233. An Inequality with Constraint in Four Variables
  234. An Inequality with Constraint in Four Variables II
  235. An Inequality with Constraint in Four Variables III
  236. An Inequality with Constraint in Four Variables IV
  237. An Inequality with Constraint in Four Variables V
  238. An Inequality with Constraint in Four Variables VI
  239. An Inequality with Cot, Cos, and Sin
  240. An Inequality with Cycling Sums
  241. An Inequality with Determinants [JavaScript]
  242. An Inequality with Determinants II
  243. An Inequality with Determinants III
  244. An Inequality with Determinants IV
  245. An Inequality with Determinants V
  246. An Inequality with Determinants VI
  247. An Inequality with Determinants VII
  248. An Inequality with Exponents [JavaScript]
  249. An Inequality with a Generic Proof [JavaScript]
  250. An Inequality with Nested Radicals
  251. An Inequality via Young's Theorem
  252. An Inequality with Just Two Variable
  253. An Inequality with Just Two Variable II
  254. An Inequality with Just Two Variable III
  255. An Inequality with Just Two Variables IV
  256. An Inequality with Just Two Variables V
  257. An Inequality with Just Two Variables VI
  258. An Inequality with Just Two Variable VII
  259. An Inequality with Just Two Variable VIII
  260. An Inequality with Permutations, I [JavaScript]
  261. An Inequality with Permutations, II [JavaScript]
  262. An Inequality with Two Cyclic Sums
  263. An Inequality with Two Pairs of Triplets An Inequality with Two Triples of Variables
  264. An Inequality with Two Triples of Variables II
  265. Inequality with Two Variables? Think Again
  266. An Infinite Product from Recursion
  267. An Integral Estimate
  268. An Integral Identity with Two Functions
  269. An Integral from the RMM
  270. An Integral Inequality from the RMM
  271. An Old Inequality
  272. An Unsolvable Riccati Equation
  273. An Unusual Quadratic Equation
  274. Another Face and Proof of a Trigonometric Identity
  275. Another Inequality with Logarithms, But Not Really
  276. Another Integral Inequality from the RMM
  277. Another Problem from the 2016 Danubius Contest
  278. Another Property of Number 4
  279. Another simple integral
  280. An Unusual Problem by Leo Giugiuc
  281. Any Integer with Three 2s
  282. Application of Cauchy-Schwarz Inequality
  283. Applications of Schweitzer's Inequality
  284. Approximation Of Roots
  285. Area of a Circle by Rabbi Abraham bar Hiyya Hanasi [Java]
  286. Areas on the Graphs of Power Functions
  287. Arithmetic-Geometric Means Inequality
  288. Arithmetic of Pie Sharing
  289. Ascending Bases and Exponents in Pascal's Triangle
  290. Assigning Numbers to Points in the Plane
  291. Associativity from 1977 IMO
  292. Averages, Arithmetic and Harmonic Means [Java]
  293. Averages in a sequence
  294. Ballot Lemma [Java]
  295. Banzhaf Power Index Calculator [Java]
  296. Barcode Encoding
  297. Barcode Magic [Java]
  298. Base Converter [JavaScript]
  299. Bergström's inequality
  300. Birth of an Inequality
  301. Bayes' Theorem
  302. Beatty Sequences
  303. Beauty and the Beast - in Trigonometry
  304. Bertrand's Postulate
  305. Bicubal Domino [JavaScript]
  306. Bilateral Diagrams [Java]
  307. Binet's Formula via Generating Functions
  308. Binet's Formula with Cosines
  309. Binomial Distribution [Java]
  310. Binomial Theorem
  311. Bisector of an imaginary angle may be real
  312. Brahmagupta-Fibonacci Identity [JavaScript]
  313. Byzantine Basketball
  314. Calculation of the Digits of pi by the Spigot Algorithm [Java]
  315. Calculus Proof of the Pythagorean Theorem
  316. Candido's Identity
  317. Cantor-Bernstein-Schroeder theorem
  318. Cantor's First Uncountability Proof
  319. Cardinal Numbers
  320. Cartesian Coordinate System [Java]
  321. Cassini's Identity
  322. Catalan Numbers in Pascal's Triangle
  323. Cavalieri's Principle [Java]
  324. Central and Inscribed Angles in Complex Numbers
  325. Chebyshev Inequality
  326. Chebyshev Holds a Key
  327. Chess tournament with 1.5 Points Winners
  328. Chinese Remainder Theorem
  329. Clifford Algebras
  330. Clubs in a Vector Space
  331. Collatz Conjecture [Java]
  332. Coloring a Graph [Java]
  333. Coloring Squares, Adding up Numbers
  334. Combinatorial Proofs
  335. Combo Playground: Calculating the Number of Paths on a Square Grid
  336. Committee Chairs
  337. Comparing complex numbers
  338. Completing a Square and Quadratic Formula
  339. Completing the Square Where It Matters
  340. Complex Numbers: A Dynamic Tool [Java]
  341. Complex number to a complex power may be real
  342. Complicated Constraint - Simple Inequality
  343. Composition of Functions, an Exercise Constrained Inequality with Reciprocals
  344. Constrained Intermarriages [JavaScript]
  345. Constructible Numbers
  346. Construction of Pascal's Triangle [Java]
  347. Constructive Existence of the de Bruijn Cycles
  348. Continued fractions
  349. cos/sin inequality
  350. cos(π/7)-cos(2π/7)+cos(3π/7) = 1/2
  351. Cospherical Points
  352. Countability of Rational Numbers
  353. Countability Principle
  354. Counting Chips On a Circle [Java]
  355. Counting Fat Sets
  356. Counting Squares in a Square [Java]
  357. Counting Triangles [Java]
  358. Counting Triangles II [Java]
  359. Covering a Chessboard with a Hole with L-Trominoes [Java]
  360. Covering A Chessboard With Domino
  361. Cubes Constrained
  362. Cubes in Pascal's Triangle
  363. Cubic Equation for the Sides of a Triangle
  364. Cubic Formula [JavaScript]
  365. Cubics and Bézout's Theorem
  366. Cubic Optimization with Linear Constraints
  367. Cubic Optimization with Partly Linear Constraints
  368. Curious Identities In Pythagorean Triangles
  369. Curious Identities Involving Integer Products

    Cute Exercise by Dorin Marghidanu

  370. Cyclic Inequality in Four Variables
  371. Cyclic Inequality in Four Variables By D. Sitaru
  372. Cyclic Inequality in Three Variables by Marian Cucoanes
  373. Cyclic Inequality In Three Variables from the 2018 Romanian Olympiad, Grade 9
  374. Cyclic Inequality In Three Variables From Vietnam by Rearrangement
  375. Cyclic Inequality with Arctangents
  376. Cyclic Inequality with Logarithms
  377. Cyclic Inequality with Square Roots
  378. Cyclic Inequality with Square Roots And Absolute Values
  379. Dan Sitaru's Amazing, Never Ending Inequality
  380. Dan Sitaru's Cyclic Inequality in Four Variables
  381. Dan Sitaru's Cyclic Inequality In One Variable
  382. Dan Sitaru's Cyclic Inequality In Many Variables
  383. Dan Sitaru's Cyclic Inequality In Three Variables
  384. Dan Sitaru's Cyclic Inequality in Three Variables II
  385. Dan Sitaru's Cyclic Inequality in Three Variables III
  386. Dan Sitaru's Cyclic Inequality in Three Variables IV
  387. Dan Sitaru's Cyclic Inequality in Three Variables V
  388. Dan Sitaru's Cyclic Inequality in Three Variables VI
  389. Dan Sitaru's Cyclic Inequality in Three Variables VII
  390. Dan Sitaru's Cyclic Inequality in Three Variables VIII
  391. Cyclic Inequality In Three Variables From Kvant
  392. Dan Sitaru's Cyclic Inequality In Three Variables with Constraints
  393. Dan Sitaru's Cyclic Inequality In Three Variables with Constraints IV
  394. Dan Sitaru's Cyclic Inequality In Three Variables with Constraints V
  395. Dan Sitaru's Exercise with Pi and Ln
  396. Dan Sitaru's Inequality: From Three Variables to Many in Two Ways
  397. Dan Sitaru's Cyclic Inequality In Three Variables with Constraints II
  398. Dan Sitaru's Cyclic Inequality In Three Variables with Constraints III
  399. Dan Sitaru's Inequality by Induction
  400. Dan Sitaru's Cyclic Inequality with a Constraint and Cube Roots
  401. Dan Sitaru's Cyclic Inequality with a Constraint and Cube Roots II
  402. Dan Sitaru's Inequality with a Double Integral
  403. Dan Sitaru's Inequality with Roots and Powers
  404. Dan Sitaru's Inequality with Tangents
  405. Dan Sitaru's Inequality with Three Related Integrals and Derivatives
  406. Dan Sitaru's Integral Inequality with Powers of a Function
  407. Dan Sitaru's Sum of a Series
  408. Daniel Dan's Optimization in Three Variables
  409. Darij Grinberg's Inequality In Three Variables
  410. Deceptive Appearances
  411. Decimal Sums of Successive Integers
  412. Derivatives without Limits
  413. Descartes' Rule of Signs
  414. Determinant and Divisibility
  415. Determinant on a Circle
  416. Determinants in Pascal's Triangle
  417. Diagonal Argument
  418. Diophantine Equations
  419. Distance between the Orthocenter and Circumcenter
  420. Distance Between Strings [Java]
  421. Distance From a Point to a Straight Line [Java]
  422. Distance Inequality
  423. Distances to Three Points on a Circle
  424. Distinct Multisets with the Same Pairwise Sum
  425. Divergence of {cos(n)} [JavaScript]
  426. Divergence of the Harmonic Series (Details)
  427. Divide And Conquer in Cyclic Sums
  428. Dividing Loot Fairly
  429. Divisibility and Modulo Arithmetic at IMO 2007
  430. Divisibility by Powers of 2
  431. Dollars in Pockets
  432. Doodling on April 1st
  433. Dorin Marghidanu's Believe It Or Not
  434. Dorin Marghidanu's Calculus Lemma
  435. Dorin Marghidanu's Cyclic Inequality in Three Variables
  436. Dorin Marghidanu's Cyclic Inequality in Three Variables II
  437. Dorin Marghidanu's Cyclic Inequality in Three Variables III
  438. Dorin Marghidanu's Cyclic Inequality with Constraint
  439. Dorin Marghidanu's Inequality in Complex Plane
  440. Dorin Marghidanu's Inequality in Integer Variables
  441. Dorin Marghidanu's Inequality in Many Variables
  442. Dorin Marghidanu's Inequality in Many Variables Plus Two More
  443. Dorin Marghidanu's Inequality with Constraint
  444. Dorin Marghidanu's Inequality with Generalization
  445. Dorin Marghidanu's Inequality with Radicals
  446. Dorin Marghidanu's Light Elegance in Four Variables
  447. Dorin Marghidanu's Permuted Inequality
  448. Dorin Marghidanu's Spanish Problem Dorin Marghidanu's Sums and Products
  449. Dorin Marghidanu's Tribute to Descartes
  450. Dorin Marghidanu's Two-Sided Inequality
  451. Dot Patterns and Sierpinski Gasket [Java]
  452. Dots and fractions [Java]
  453. Double and Half Angle Formulas
  454. Double Sums by Dorin Marghidanu
  455. Ducci Sequences [Java]
  456. e in the Pascal Triangle
  457. EAN-13 Encoding [Java]
  458. Eigenvectors by Inspection
  459. Elves and Gnomes [JavaScript]
  460. Entry 1.414... in Ramanujan's Notebooks
  461. Equation in Permutations
  462. Equation in Radicals as a System of Equations
  463. Equations of the Staight Line [Java]
  464. Equivalence Relations
  465. Escape of the Clones
  466. Euclid's Algorithm
  467. Euclid's Algorithm: An Interactive Illustration [Java]
  468. Euler Cycles in Digraph
  469. Euler's formula for e
  470. Euler's Function and Congruence Theorem
  471. Evolution of Algebraic Symbolism
  472. Exercise with Square Spiral [GeoGebra]
  473. Existence of the de Bruijn Cycles via Graphs
  474. Exponential Inequalities for Means
  475. Extension of Euclid's Algorithm
  476. Extrema of x^3+y^3+z^3-xyz on the unit sphere
  477. Factorial Products
  478. Factorials and division
  479. Fair Division: Method of Sealed Bids II [Java]
  480. Falsity implies anything
  481. Farey Series
  482. Fermat's Like Equation
  483. Fermat's Little Theorem
  484. Fermat's Only Published Proof
  485. Fibonacci Idendtities with Matrices
  486. Fibonacci's Quickies
  487. Fibonacci Tilings
  488. Filling a Grid with Good Neighbors [Java]
  489. Filling an Array with 0s and 1s - and Counting [Java]
  490. Filling Pool with Fluids
  491. Find Minimum without Calculus
  492. Finding Hamilton Paths and Circuits [Java]
  493. Finite Sums of Terms 2^(n-i) i²
  494. First 1008 Digits
  495. First Geometric Interpretation of Complex Numbers [Java]
  496. Five Methods of Apportionment [Java]
  497. Five Lattice Points [Java]
  498. Five Squares in Complex Numbers [GeoGebra]
  499. Fleury's Algorithm and Euler's Paths and Cycles [Java]
  500. Flipping Items Simultaneously [Java]
  501. Flipping Items Simultaneously II [Java]
  502. Flipping Items Simultaneously III [Java]
  503. Flipping pancakes [Java]
  504. Floor Function
  505. Formal Systems - an Example
  506. Formula for Primes
  507. Four Hinged Squares: using complex numbers
  508. Four Integrals in One Inequality
  509. Four Numbers, Six Differences, GCD of the Products
  510. Four Pegs That Form a Square
  511. Four Voting Methods [Java]
  512. From The Sum of Angles To The Sum of Sines
  513. Function
  514. Function in the Plane That Vanishes
  515. Functional Inequality from Vietnam
  516. Fundamental Theorem of Algebra
  517. Futurama Theorem and Puzzle [Java]
  518. Gasoline Stations on a Circular Trek
  519. Gauss and Euler Integrals
  520. Gauss' Lemma
  521. Gauss' theorem on constructibility of regular polygons
  522. GCD of Fibonacci Numbers
  523. GCD(M, N) × LCM(M, N) = M × N [Java]
  524. Generalization That Solves the Problem
  525. Generating Functions
  526. Geometric Construction of Roots of Quadratic Equation [Java]
  527. Getting a Scout out of Desert [Java]
  528. Getting Your Rightful Share Back [JavaScript]
  529. Gheorghe Stoica's Problem from Gazeta Matematica Gireaux's Theorem
  530. Gödel's Incompleteness Theorem
  531. Golden Ratio is Irrational
  532. Graph and Roots of a Third Degree Polynomial [Java]
  533. Graph and Roots of Quadratic Polynomial [Java]
  534. Graph of a Polynomial [Java]
  535. Graph of a Polynomial Defined by Its Roots [Java]
  536. Graph with Nodes of Even Degree
  537. Graph without 3-Cycles
  538. Graphing Equations Is Useful
  539. Graphing Equations Is Useful, II [Java]
  540. Graphing Equations Is Useful, III
  541. Graphing Equations Is Useful, IV
  542. Graphing Equations Is Useful, V
  543. Greatest Difference in Arithmetic Progression
  544. Group multiplication of permutations [Java]
  545. 1/2 = 1
  546. Hadamard's Determinant Inequalities and Applications I
  547. Hadamard's Determinant Inequalities and Applications II
  548. Harmonic Serires And Its Parts
  549. 2006 Hellenic Mathematical Olympiad, Problem 4 [JavaScript]
  550. Hlawka's Inequality
  551. Horner's Method [Java]
  552. How Jost Burgi Computed the Sines of All Integer Angles in 1586
  553. How to Ask an Embarrassing Question
  554. How to define a permutation? [Java]
  555. How to write an equation of the union of two sets
  556. However You Solve It ... A Wonderful Equation
  557. Hung Viet's Inequality
  558. Hung Viet's Inequality II
  559. Hung Viet's Inequality III
  560. Hung Viet's Inequality IV
  561. Hyperintegers and Hyperreal Numbers
  562. Identities with Triangular Numbers
  563. Imad Zak's Cyclic Inequality in Three Variables
  564. Imad Zak's Cyclic Inequality in Three Variables II
  565. Implementation of Base Conversion
  566. Importance of the Absolute Value
  567. Improving an Inequality [JavaScript]
  568. Improving on an Escalator [JavaScript]
  569. In Calculus too 1 = 0
  570. Inclusion-Exclusion Principle
  571. Inclusion-Exclusion Principle: an Example
  572. Inequalities and Quadratic Forms
  573. An Inequality for Mixed Means
  574. An Inequality from RMM with a Generic 5
  575. An Inequality from RMM with Powers of 2
  576. Inequality 101 from the Cyclic Inequalities Marathon
  577. Inequality 1/2·3/4·5/6· ... ·99/100 < 1/10
  578. Inequality (1 + 1-3)(1 + 2-3)(1 + 2-3)...(1 + n-3) < 3
  579. Inequality 1 + 2-2 + 3-2 + 4-2 + ... + n-2 < 2.
  580. Inequality by Calculus
  581. Inequality for Integer Sequences
  582. Inequality for Integer Sequences II
  583. Inequality for Mixed Means
  584. An Inequality from Gazeta Matematica, March 2016
  585. An Inequality from Gazeta Matematica, March 2016 II
  586. An Inequality from Gazeta Matematica, March 2016 III
  587. An Inequality from Gazeta Matematica, March 2016 IV
  588. Inequalities with Double And Triple Integrals
  589. Inequality from Math Magazine 2009
  590. Inequality from Math Phenomenon
  591. Inequality in Acute Triangle
  592. Inequality of a Series of Square Roots
  593. Inequality with Constraint from Dan Sitaru's Math Phenomenon
  594. Inequality with Csc And Sin
  595. An Inequality with Exponents [JavaScript]
  596. An Inequality with Finite Sums
  597. An Inequality with Integrals and Rearrangement
  598. Inequality with Logarithms
  599. Inequality with Powers And Radicals
  600. Inequality with Three Linear Constraints
  601. Inequality with Three Numbers, Not All Zero
  602. Inequality with Two Minima
  603. Infinite Discent for x4 + y4 = z4
  604. Infinitesimals. Non-standard Analysis
  605. Infinitude of Primes
  606. Infinity As a Limit
  607. Inflection Points of Fourth Degree Polynomials [Java]
  608. Inheriting Inequality
  609. An innovative recurrence
  610. Integer Iterations on a Circle [Java]
  611. Candy Game (Change Discharged) [Java]
  612. Integer Iterations on a Circle III [Java]
  613. Integer roots of integers are irrational
  614. Integer Triangle That Sums to Cube
  615. Integers and Rectangles [Java]
  616. Integers and Rectangles: a Proof by Induction [Java]
  617. Integers and Rectangles: Two Simple Proofs [Java]
  618. Integers With Digits 1 and 2 and Residues Modulo Powers of 2
  619. Integral in Normal Distribution
  620. Integral Is Area
  621. Integrals of a Function And Its Inverse
  622. Interest Calculations [Java]
  623. Integral of a Piece-wise Function
  624. Irrationality of k-th roots
  625. Irrationality of sqrt(2) via a Difference Equation
  626. Is GLOBALHELLFRY a Prime? [JavaScript]
  627. Is the Triangle Inequality Necessary?
  628. Is There a Limit?
  629. ISBN Encoding [Java]
  630. Irrational number to an irrational power may be rational
  631. Is 0.999... = 1?
  632. It's All About Powers of 10
  633. Iterations on Monotone Functions
  634. Jensen's Inequality [JavaScript]
  635. Ji Chen's Inequality
  636. Joachimsthal's Notations
  637. Jumping Isn't Everything [Java]
  638. Kaprekar's Iterations and Numbers [Java]
  639. Kulikowski's Theorem
  640. Kunihiko Chikaya's Inequality
  641. Kunihiko Chikaya's Inequality with a Constraint
  642. Kunihiko Chikaya's Inequality with Parameter
  643. Lagrange's identity, Proof
  644. Lagrange interpolation
  645. Lamé's Theorem - First Application of Fibonacci Numbers
  646. Langford and Skolem Sequences [Java]
  647. Latin Squares [Java]
  648. Le Khanh Sy's Problem
  649. Leech Trees and Taylor's Criterion
  650. Legendre's Formula
  651. Legendre's Theorem - The Prime Factorization of Factorials
  652. Leibniz and Pascal Triangles [Java]
  653. Leo Giugiuc's Cyclic Inequality in Three Variables
  654. Leo Giugiuc's Cyclic Quickie in Four Variables
  655. Leo Giugiuc's Exercise
  656. Leo Giugiuc's Inequality with Constraint
  657. Leo Giugiuc's Optimization with Constraint
  658. Leo Giugiuc's Trigonometric Lemma
  659. Less than, Equal to, Greater Than Symbols
  660. Lewis Carroll's Game of Logic [Java]
  661. Light Bulbs in a Circle [Java]
  662. Lights Out [Java]
  663. Limit of a Recursive Sequence
  664. Linear Algebra Tools for Proving Inequalities
  665. Linear Algebra Tools for Proving Inequalities: Cauchy-Binet Formula
  666. Linear Function with Coefficients in Arithmetic Progression [GeoGebra]
  667. Linear functions
  668. Linear Programming
  669. Linear System with Parameter
  670. Listing All Combinations [Java]
  671. Listing all permutations [Java]
  672. Listing All Permutations: Johnson-Trotter Method [Java]
  673. Logistic Model applet [Java]
  674. Long Huynh Huu's Inequality and Solution
  675. Long Runs of Composite Numbers
  676. Long Up Short Down
  677. Looking your best
  678. Loop or Halt [Java]
  679. Lucas' Theorem
  680. Lucas' Theorem II
  681. Lucky Numbers [Java]
  682. Marian Dinca's Refinement of Nesbitt's Inequality
  683. Marriage Theorem
  684. Marriage Problem, simulation [Java]
  685. Math Lotto
  686. Mathematical Induction
  687. Mathematical Proof
  688. Mathematicians Doze Off
  689. Matrices and Determinants as Optimization Tools: an Example
  690. Matrix Groups
  691. Maximum Volume of a Cut Off Box [Java]
  692. Means [Java]
  693. Mediant Fractions
  694. Method of Markers II [Java]
  695. Michael Rozenberg's Inequality in Three Variables with Constraints
  696. Michael Rozenberg's Inequality in Two Variables
  697. Minesweeper Theorem
  698. Mini Lights Out [Java]
  699. Minimax Principle [Java]
  700. Minimax Theorem [Java]
  701. Minimum of a Cyclic Sum with Logarithms
  702. Minumum Spanning Trees and Kruskal's Algorithm [Java]
  703. Minimum under Two Constraints
  704. Minus One But What a Difference
  705. Modular Arithmetic [Java]
  706. Monotone Convergence Theorem
  707. Monotone Number Sequences [Java]
  708. Monthly Problem 11199
  709. Much from Little
  710. Muirhead's Inequality
  711. Multiplication
  712. Multiplication of Points on a Circle [JavaScript, GeoGebra]
  713. Multiplication of Points on an Ellipse [JavaScript, GeoGebra]
  714. Napoleon's Relatives [Java]
  715. Negative on the left, positive on the right: how come?
  716. Nested Radicals
  717. Nested Subsets
  718. New Proof of Euclid's Theorem
  719. Newton's Method [Java]
  720. Newton's and Maclaurin's Inequalities [JavaScript]
  721. Hung Nguyen Viet's Inequality with a Constraint
  722. Nine Squares [Java]
  723. No Flipping without End [Java]
  724. NonSquare Matrix as a Tool for Proving an Inequality
  725. Number 8 Is Interesting
  726. Number Comparison - from the 1969 Canadian MO
  727. Number sequences and Pigeonhole [Java]
  728. Number System With Base 36
  729. Modern Vietnamese Classic
  730. On Dedekind Cuts
  731. On the Games of Hex and Y
  732. On the Intersection of kx and |sin(x)| [JavaScript]
  733. On the Intersection of 1+x and e^x and Trigonometric Consequences [JavaScript]
  734. One Dimensional Ants
  735. One Inequality - Two Domains
  736. One Trigonometric Formula and Its Consequences
  737. Optimization in Four Variables with Two Constraints
  738. Optimization with Many Variables
  739. Order. Well-ordered sets.
  740. Order and Chaos in Multiple Pendulums
  741. Ordinal Numbers
  742. Orthocenter in Complex Plane
  743. Outline Mathematics
  744. Problem 1 From the 2016 Pan-African Math Olympiad
  745. Problem 11867 from the American Mathematical Monthly
  746. Problem 2, the 36th IMO (1995)
  747. Problem 2 from the 2017 IMO
  748. Problem 3824 from Crux Mathematicorum
  749. Problem 3980 from Crux Mathematicorum
  750. Problem 4002 from Crux Mathematicorum
  751. Problem 4010 from Crux Mathematicorum
  752. Problem 4020 from Crux Mathematicorum
  753. Problem 4033 from Crux Mathematicorum
  754. Problem 4117 from Crux Mathematicorum
  755. Problem 4142 From Crux Mathematicorum
  756. Problem 4165 from Crux Mathematicorum
  757. Problem 4186 from Crux Mathematicorum
  758. Problem 6 from Dan Sitaru's Algebraic Phenomenon
  759. Problem 790 from Pentagon: an Inequality in Two Variables
  760. Problem From the 2016 IMO Shortlist
  761. Problem M317 from Crux Mathematicorum
  762. Proofs of Schweitzer's inequality
  763. Prove 2[sqrt(n) - sqrt(n-1)] > 1/sqrt(n)
  764. Sam Walters' Four Questions
  765. Same Integral, Three Intervals
  766. Samuel G. Walters' Congruence
  767. Simple Nameless Inequality
  768. Small Change Makes Big Difference
  769. Smallest multiple of 9 with no odd digits [Java]
  770. Snake Permutations And Their Number
  771. Solving a Peculiar Third Degree Equation
  772. The Basics of Infinite Descent
  773. The Joy of Homogeneity
  774. The Lucky Find [Java]
  775. The Mean Property of the Mean
  776. The Number of Judges and the Number of Votes [JavaScript]
  777. The power of substitution: solving an equation in a right triangle
  778. The power of substitution II: proving an inequality with three variables
  779. The power of substitution III: proving an inequality with two variables
  780. The Very First Functional Equation at IMO
  781. The Very Last, for 2014, proof of the Irrationality of sqrt(2)
  782. Three Colors on a Chessboard
  783. Three digit twister [Java]
  784. Who Has Beard? [Java]
  785. Outline Mathematics: Diophantine Equation I [JavaScript]
  786. p-adic Expansions
  787. p-adic Numbers
  788. Pairing Monotone and Convex Functions
  789. Parabola and Abutting Equilateral Triangles
  790. Parabolic Sieve of Prime Numbers
  791. Parity counting [Java]
  792. Parrondo Paradox Via Simpson Paradox [Java]
  793. Partial But General Case Of Fermat's Last Theorem
  794. Party Acquaintances [Java]
  795. Patterns in Pascal's Triangle
  796. Peano axioms
  797. Pennies in Boxes [Java]
  798. Percent
  799. Permutations
  800. Perrin Sequence
  801. Pi in Pascal's Triangle
  802. Pi in Pascal's Triangle via Triangular Numbers
  803. pi^e vs e^pi [JavaScript]
  804. Pigeonhole Principle
  805. Pinocchio as Epimenides
  806. Place Value [Java]
  807. Powers and Fractions Inequality
  808. Presence of the Antipodes on a Circle
  809. Prime Sums in Pairs
  810. Probability of Divisibility
  811. Problem 1 from the IMO 2009
  812. Problem 11804 from the AMM
  813. Problem A1, 69th Putnam Competition
  814. Problem A2, 69th Putnam Competition
  815. Problem of Divisibility by 5n
  816. Product of Diagonals in Regular N-gon
  817. Product Of Four Consecutive Integers
  818. Product of Simple Fractions [Java]
  819. Product of permutations [Java]
  820. Proizvolov's Identity [Java]
  821. Proofs Without Words [Java]
  822. Property of an
  823. Property of Quadratic Polynomials
  824. Property of the Powers of 2 [Java]
  825. Puzzlist vs. Mathematician: A Practical Arithmetic Problem
  826. Pythagorean Triples [Java]
  827. Quadratic Function for Solving Inequalities
  828. Quadratic Inequalities on [-1,1]
  829. An Inequality Where One Term Is More Equal Than Others
  830. Quasigroups and block designs from triangular grid [Java]
  831. Rabbits Reproduce; Integers Don't
  832. Radicals, Radicals, And More Radicals in an Inequality
  833. Radon's Inequality and Applications
  834. Ramsey's Number R(3, 3, 3)
  835. Ramsey Number R(4, 3)
  836. Ramsey Number R(5, 3)
  837. Ramsey Number R(4, 4)
  838. Ramsey's Theorem
  839. Random Walks [Java]
  840. Rascal Triangle
  841. Rational Solutions to xy = yx
  842. Rearrangement Inequality [JavaScript]
  843. Recombining Permutations [Java]
  844. Rectangle on a Chessboard [Java]
  845. Rectilinear Paradox
  846. Reflection Lemma [Java]
  847. Riemann Rearrangement Theorem
  848. Riemann Sphere and Möbius Transformation
  849. Riemann Sums - Function Integration [Java]
  850. Right Replacement [Java]
  851. Rolle's and Mean Value Theorems [Java]
  852. Rolle's Theorem in Action
  853. RomanoNorwegian Inequality
  854. Rooks on a Chessboard
  855. Roots and Tangents [GeoGebra]
  856. Round Robin Tournament
  857. Russell's Paradox
  858. Solve A Fourth Degree Equation
  859. Sophie Germain's Identity
  860. Square Root of 2 is Irrational, Proof 29
  861. Square Roots and Triangle Inequality
  862. Squares in Pascal's Triangle
  863. Squeeze Theorem
  864. Sum of Absolute Values [JavaScript]
  865. Sum of All Natural Numbers
  866. Sums of Binomial Reciprocals in Pascal's Triangle
  867. Squeeze (Sandwich, Pinching ...) Theorem (Lemma): an Example
  868. Scalar Product Optimization [JavaScript]
  869. Scheduling and Critical Path Algorithm [Java]
  870. Schur's Inequality
  871. Scrub Tile Puzzle [Java]
  872. Second Pair of Twin Inequalities: Twin 1
  873. Second Pair of Twin Inequalities: Twin 2
  874. Self-descriptive Strings [Java]
  875. Self-documenting Iterations [JavaScript]
  876. Self-reference
  877. Seven integers under 127 and their Ratios
  878. Seven Terms Periodic Sequence
  879. Shapley-Shubik Power Index [Java]
  880. Shapley-Shubik Power Index Calculator [Java]
  881. Shifting Digits and a Point of View
  882. Ship-Dock Theorem
  883. Shuttle Puzzle Practice II [Java]
  884. Sicherman Dice
  885. Sierpinski Gasket and Tower of Hanoi
  886. Sierpinski's Gasket and Dihedral Symmetry [Java]
  887. Sieve of Squares [Java]
  888. Σ2-n = Σn·2-n
  889. Signs and Sums in a Sequence [Java]
  890. Signs in a Matrix [Java]
  891. Simple But Uncommon Equation from 1968 IMO
  892. Simple Cellular Automaton [Java]
  893. Simple Graph Practice [Java]
  894. Simple Inequality with a Variety of Solutions
  895. Simple Inequality with Many Faces And Variables
  896. Simple Somos Sequence - a Russian Olympiad problem
  897. Simple Somos Sequence Calculator [Java]
  898. Simple Yet Uncommon Inequalities with Absolute Value
  899. Simpson Paradox [Java]
  900. $\sin 1^{\circ}+\sin {2^\circ}+\sin 3^{\circ}+\cdots+\sin 180^{\circ}=\tan 89.5^{\circ}$
  901. Sine And Cosine Are Continuous Functions
  902. Sine of a Sum Formula, Proof Without Words
  903. Single formula to express any integer with digits 0-9 each used just once
  904. Sitaru-Schweitzer Inequality
  905. Six Balls, Two Weighings
  906. Size of a Class: Two Viewpoints
  907. Sladjan Stankovik's Inequality In Four Variables
  908. Sladjan Stankovik's Inequality With Constraint
  909. Sladjan Stankovik's Inequality With Constraint II
  910. Slider Puzzles [Java]
  911. Solitaire in Two Colors [Java]
  912. Solutions of F(x)=x and F(F(x))=x [JavaScript]
  913. Solve - an Olympiad Problem - in Your Mind
  914. Solve xx3 = 3
  915. Solve cos²x + cos²2x + cos²3x = 1
  916. Solving an Equation with Inverse Functions
  917. Soriteses
  918. Sorting Algorithms
  919. Sperner's Theorem
  920. Splitting piles
  921. Square Root of 2 as a Continued Fraction
  922. Square root of 2 is irrational
  923. Star of David Theorems in Pascal Triangle
  924. Stars in Array
  925. Steinhaus' Problem [Java]
  926. Step into the Elliptic Realm
  927. Stern-Brocot Tree
  928. Straight Tromino on a Chessboard [Java]
  929. Structure of Hyperreal Numbers
  930. Subsets and Intersections
  931. Subtraction Game [Java]
  932. Sums of the Elements of Three Element Subsets [JavaScript]
  933. Sum of Three Squares [JavaScript]
  934. Sums and Products, a Generalization
  935. Sums, Products, and 1-1 Functions
  936. Sums of Geometric Series - Proofs Without Words [Java]
  937. Sums of Power Series
  938. Sums Of Successive Squares
  939. Sum without Adding
  940. Sums and Products [Java]
  941. Sums of powers of digits [Java]
  942. Superposition Principle
  943. Surreal Numbers
  944. Swapping Rows and Columns [Java]
  945. Sylvester's Problem
  946. Taking Games Seriously [Java]
  947. Tangential Chaos
  948. Telescoping Cubes
  949. Telescoping Squares
  950. Telescoping Sums and Series [JavaScript]
  951. Telescoping Tangents
  952. The ass and the mule [Java]
  953. The Averages of Sides and Angles in a Triangle
  954. The Basic Rules of Counting
  955. The Local-Global Principle
  956. The Regula Falsi - Iterated
  957. The Roads We Take
  958. The Size is in the Eyes of the Beholder
  959. Three Complex Numbers Satisfy Fermat's Identity For Prime Powers
  960. Three Dimensional Cross
  961. Three Junior Problems from Vietnam
  962. Three Variables, Three Constraints, Two Inequalities (Only One to Prove) - by Leo Giugiuc
  963. Tool for Constructing Orthogonal Latin Squares [Java]
  964. Tower of Hanoi, the Hard Way [Java]
  965. Train on Bridge [JavaScript]
  966. Tran Hoang Nam's Cyclic Inequality in Three Variables
  967. Transpositions
  968. Traveling Salesman Problem [Java]
  969. Treatise on Arithmetical Triangle
  970. Triangular numbers that are also square
  971. Trigonometric Identity for the Pi Day
  972. Trigonometric Inequality with Integrals
  973. A Trigonometric Inequality with Ordered Triple of Variables
  974. Trilateral Diagrams [Java]
  975. Trinary Tree(s) underlying Primitive Pythagorean Triples
  976. Tromino Puzzle: Deficient Squares [Java]
  977. Twenty five boys and twenty five girls around a table.
  978. Twin Inequalities in Four Variables: Twin 1
  979. Twin Inequalities in Four Variables: Twin 2
  980. Two Circles and a Limit [Java]
  981. Two Colors in Two Rows [Java]
  982. Two Cyclic Inequalities [JavaScript]
  983. Two Equations in Three Variables [JavaScript]
  984. Two Men of Tibet [Java]
  985. Two-Parameter Solutions to Three Almost Fermat Equations
  986. Two-Sided Inequality by Dorin Marghidanu
  987. Two Problems by Kunihiko Chikaya
  988. Two Problems from a Serbian 7 Grade Math Competition
  989. Two Products: Constraint and Inequality
  990. Two Sequences Defined by Recurrence
  991. Two-Sided Inequality - One Provenance
  992. Two Solutions: One Correct, One Illuminating. An Example
  993. Uncountability of the Reals - via a Game
  994. Undefined vs Indeterminate in Mathematics
  995. (Un)fair Division by Consensus
  996. Universal Coloring [Java]
  997. Universal Product Code [Java]
  998. Unproperty of the Powers of 2
  999. Unsolved Problem from Crux Solved
  1000. USA 1975 Problem 3
  1001. Vandermonde's Convolution Formula
  1002. Vandermonde Determinant
  1003. Venn Diagrams
  1004. Viète's Formulas
  1005. Voronoi Diagram [JavaSCript]
  1006. Ways To Count
  1007. Weierstrass Product Inequality
  1008. Weierstrass Substitution
  1009. What, how, and the Web [Java]
  1010. What 1, 6, and 14 Have to Do with 5?
  1011. What Is Algorithm?
  1012. What Is Determinant?
  1013. What Is Finite?
  1014. What Is Infinite Descent?
  1015. What Is Infinity?
  1016. What Is Limit?
  1017. What is so natural about "natural logarithms"?
  1018. What Is Space Completion?
  1019. WHEN THE COUNTING GETS TOUGH, THE TOUGH COUNT ON MATHEMATICS
  1020. When Two Segments Intersect? [JavaScript]
  1021. Where To Start? [Java]
  1022. White and Black Balls in Urn. 1 in, 2 out. What Color Remains?
  1023. Why 17?
  1024. Why Can't They Be All Different?
  1025. Why sin(x)/x tends to 1
  1026. Why The Number of Primes Could Not Be Finite?
  1027. Wilson's Theorem
  1028. Without Definitions: Why $\displaystyle\frac{1}{3}+\frac{2}{5}=\frac{11}{15}?$
  1029. Wonderful Inequality on Unit Circle
  1030. Word Problems [Java]
  1031. Wu's Inequality
  1032. $x_n=\sin 1+\sin 3+\sin 5+\cdots+\sin (2n-1)$
  1033. Yet Another Puzzle with Hats
  1034. Yet Another Simple Integral
  1035. Zeros and Nines [Java]

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