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

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