Arithmetic articles, problems, and puzzles

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

  1. 100 Grasshoppers on a Triangular Board
  2. 1089 and a Property of 3-digit Numbers [Java]
  3. 12 Coins in Verse
  4. 24 with One Digit
  5. 3 glass puzzle [JavaScript]
  6. A Farewell Problem for the Year 2017
  7. A Welcome Problem for the Year 2018
  8. A Line in a Square Grid [Java]
  9. A Missing Digit
  10. A Number Theoretic Problem With the Floor Function [JavaScript]
  11. A Problem from the 1967 IMO Shortlist
  12. A Problem of Divisibility by 17 from the 1894 Eötvös Competition
  13. A Problem That Fermat Might Have Liked
  14. A Property of Unimodal Integers as a Whole [JavaScript]
  15. A Quadratic Equation in Three Variables
  16. A Remote Decimal Digit
  17. A Short Equation in Reciprocals
  18. Abacus in Various Number Systems [Java]
  19. About numbers
  20. Absolute Value
  21. Achieve the Equilibrium [Flash]
  22. Adding a Long List of Numbers
  23. Addition and Subtraction of Integers
  24. Algorithm for Computing LCM [Java]
  25. Aliquot Game [Java]
  26. An Application of Mental Arithmetic to Highway Safety
  27. An Arithmetic Magic Trick [Java]
  28. An Equation in Factorials
  29. An Equation Involving the Total Number of Digits
  30. An Inequality for Grade 8
  31. An Interesting Number
  32. An Age Conundrum with Men of the Cloth
  33. An Equation in Integers and Rational Numbers [JavaScript]
  34. An Olympiad Problem With the Floor Function [JavaSCript]
  35. Arithmetic magic matrix [Java]
  36. Arithmetic Operations in Various Bases [Java]
  37. Arithmetic Paradoxes
  38. Bachet's Magic Trick [Java]
  39. Barcode Encoding
  40. Barcode Magic [Java]
  41. Base Converter [JavaScript]
  42. Basic Rules of Counting
  43. Billiard Handicap
  44. Binary Color Device [Java]
  45. Binary Euclid's Algorithm
  46. Breaking Chocolate Bars [Java]
  47. Broken Calculator [Java]
  48. Caterpillar [Flash]
  49. Chameleons of Three Colors
  50. Chinese Remainder Theorem
  51. Collatz Conjecture [Java]
  52. Common Multiples and the Least Common Multiple [Java]
  53. Compare Fractions: Interactive Practice [Java]
  54. Computer As a Magician [Java]
  55. Counting and Equivalent Fractions
  56. Counting: The Beginning of Mathematics [Java]
  57. Counting Chips On a Circle [Java]
  58. Counting Coins and Their Values
  59. Counting Squares in a Square [Java]
  60. Counting Triangles [Java]
  61. Counting Triangles II [Java]
  62. Covering A Chessboard With Domino
  63. Cryptarithms [JavaScript, Frames]
  64. Curious Identities Involving Integer Squares
  65. Distributive Law [Java]
  66. Dividing Loot Fairly
  67. Divisibility by 7
  68. Divisibility by 9 and 11
  69. Divisibility by 81
  70. Divisibility Criteria
  71. Divisibility by 7, 11, and 13
  72. Doubling Investment for a Fee And Getting Zero [JavaScript]
  73. EAN-13 Encoding [Java]
  74. Egyptian Multiplication [Java]
  75. Elegance in Integers by Dorin Marghidanu
  76. Emptying a Big Number of Boxes
  77. Euclid's Algorithm
  78. Euclid's Algorithm: An Interactive Illustration [Java]
  79. Euclid's Game [Java]
  80. Euclid's Game on a Square Grid [Java]
  81. Every composite number is the product of some factors and also the sum of the same numbers
  82. Extension of Euclid's Algorithm
  83. Factorial Divisibility
  84. Factorials and division
  85. Factoring with the Factor Tree [Java]
  86. Factors And Multiples
  87. Falsity implies anything
  88. Farey Series
  89. Fast Arithmetic Tips
  90. Fibonacci Numbers in Equilateral Triangle
  91. Finger Counting
  92. Formal Framework, an example
  93. Formula for Primes
  94. Four 3s
  95. Four 4s
  96. Four 5s
  97. Four Pegs That Form a Square
  98. Four Weighings Suffice
  99. Fraction Comparison [Java]
  100. Fraction Comparison Sped up [Java]
  101. Fractions on a Binary Tree
  102. Fractions on a Binary Tree II
  103. Frieze Patterns [Java]
  104. Fun with digits
  105. Funny Arithmetic [JavaScript]
  106. Gasoline Stations on a Circular Trek
  107. GCD and LCM via Factor Tree [Java]
  108. GCD and LCM by Plain Factorization [Java]
  109. GCD(M, N) × LCM(M, N) = M × N [Java]
  110. Geometric view of the Sieve of Eratosthenes [Java]
  111. Gergonne Magic Trick [Java]
  112. Grandfather's Bill [Javascript]
  113. Hardy's Example of Non-Serious Theorems
  114. Heads and Tails [Java]
  115. Hour glass timing
  116. How to efficiently defend a castle
  117. Identical Twins Puzzle
  118. Identities in the Multiplication Table [Java]
  119. Illustrated Sum of Cubes - All in a Plane
  120. Impossible Machine
  121. Infinitely many proofs that there are infinitely many primes
  122. Infinitude of Primes Via Powers of 2
  123. Integer Iterations on a Circle [Java]
  124. Integer Iterations on a Circle III [Java]
  125. Is a Sum a Prime Number?
  126. ISBN Encoding [Java]
  127. Jumping Isn't Everything [Java]
  128. Langford and Skolem Sequences [Java]
  129. Latin Squares [Java]
  130. Lattice Multiplication [Java]
  131. Leibniz and Pascal Triangles [Java]
  132. Less than, Equal to, Greater Than Symbols
  133. Listing All the Composite Numbers [Java]
  134. Long Multiplication [Java]
  135. Long Runs of Composite Numbers
  136. Looking for the Prime Decomposition
  137. Loop or Halt [Java]
  138. Magic in Square [Java]
  139. Make An Identity [Java]
  140. Make It All Zeros [Java]
  141. Many Jugs to One I
  142. Many Jugs to One II
  143. Market Day
  144. Math Card Trick
  145. Math Telepathy [Java]
  146. Mathematical Proof
  147. Mathematicians and Musicians [JavaScript]
  148. Mediant Fractions
  149. Minimax Principle [Java]
  150. Modular Arithmetic [Java]
  151. Moving Chips in Pairs Down a Checkerboard [Java]
  152. Napier Bones [Java]
  153. Negative Coconuts
  154. Nine Squares [Java]
  155. Number Guessing Game [Java]
  156. Number of Factors of an Integer
  157. Number sequences and Pigeonhole [Java]
  158. Number System With Base 36
  159. Numbers That Divide the Others' Sum
  160. Odd Scoring [Java]
  161. On Gauss' Shoulders
  162. One Dimensional Ants
  163. Operations on Fractions [Java]
  164. Order. Well-ordered sets.
  165. Ordinal Numbers
  166. Outline Mathematics
  167. Parity counting [Java]
  168. Party Acquaintances [Java]
  169. Peasant Multiplication [Java]
  170. Pennies in Boxes [Java]
  171. Permutations
  172. Pigeonhole Principle
  173. Place Value [Java]
  174. Powers of 6 and 7771
  175. Probability of Divisibility
  176. Problem 4132 from Crux Mathematicorum
  177. Product of Simple Fractions [Java]
  178. Proizvolov's Identity [Java]
  179. Proofs Without Words [Java]
  180. Properties of GCD and LCM
  181. Psychology of 0.99999...
  182. Question That Changes with Time
  183. Represent 4 with four digits
  184. Representation of 3 with Three Equal Digits
  185. Represent 6 with three digits
  186. Review of Arithmetic for Parents: A Book for Grownups about Children's Mathematics by R. Aharoni
  187. Rhind Papyrus
  188. Right Replacement [Java]
  189. The Rule of Change of Addends [Java]
  190. Russell's Paradox
  191. Scrub Tile Puzzle [Java]
  192. Self-descriptive Strings [Java]
  193. Self-reference
  194. Seven Integers That Add Up to 100
  195. Seven Terms Periodic Sequence
  196. Ship-Dock Theorem
  197. Sieve of Eratosthenes [Java]
  198. Sieve of Squares [Java]
  199. Simple Cellular Automaton [Java]
  200. Six Balls, Two Weighings
  201. Six Misnamed Coins, Two Weighings
  202. Slider Puzzles [Java]
  203. Solitaire in Two Colors [Java]
  204. Soriteses
  205. Soroban in Various Number Systems
  206. Splitting piles
  207. Squares, Circles, and Triangles [Java]
  208. Steinhaus' Problem [Java]
  209. Stern-Brocot Tree
  210. Straight Tromino on a Chessboard [Java]
  211. Suan Pan in Various Number Systems [Java]
  212. Subtraction Game [Java]
  213. Subtraction in a Rectangular Array [Java]
  214. Sums and Products [Java]
  215. Sums of powers of digits [Java]
  216. Superposition Principle
  217. Tables for Multiplication
  218. The ass and the mule [Java]
  219. Three 3s
  220. Three 4s
  221. Three 5s
  222. Tony Foster's Integer Powers in Pascal's Triangle
  223. Tool for Constructing Orthogonal Latin Squares [Java]
  224. Treasure Hunt in a Square Grid
  225. Treasure Hunt from Outside the Grid
  226. Two Colors in Two Rows [Java]
  227. Two Numbers Guessing Game [Java]
  228. Uncountability of the Reals - via a Game
  229. Uniqueness of Number 5
  230. Universal Product Code [Java]
  231. Unproperty of the Powers of 2
  232. Using Math Rules: An Example
  233. Weighing 12 coins
  234. What, how, and the Web [Java]
  235. What Is Fraction?
  236. When Two Wrongs Make One Right
  237. Why 1/3 + 1/4 = 7/12?
  238. With One 4
  239. With One Weighing
  240. Wolf and Rabbit [Flash]
  241. Word Problems [Java]
  242. Yet Another Puzzle with Hats
  243. Zeros and Nines [Java]

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