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]
   • Four Digits Magic Prediction [Java]
   • Five Digits Magic Prediction [Java]
3. 12 Coins in Verse
4. 24 with One Digit
5. 3 glass puzzle [JavaScript]
   • 3 glasses puzzle, second, more general tool [JavaScript]
   • 3 Glasses Problem in Barycentric Coordinates
   • Three Jugs Problem [Java]
   • Three Jugs - Equal Amounts
   • Two Jugs - One's Volume Unknown
   • Two Pails Puzzle [Java]
6. A Line in a Square Grid [Java]
7. A Number Theoretic Problem With the Floor Function [JavaScript]
8. A Property of Unimodal Integers as a Whole [JavaScript]
9. A Quadratic Equation in Three Variables
10. A Short Equation in Reciprocals
11. Abacus in Various Number Systems [Java]
12. About numbers
13. Absolute Value
14. Achieve the Equilibrium [Flash]
15. Adding a Long List of Numbers
16. Addition and Subtraction of Integers
17. Algorithm for Computing LCM [Java]
18. Aliquot Game [Java]
19. An Application of Mental Arithmetic to Highway Safety
20. An Arithmetic Magic Trick [Java]
21. An Equation Involving the Total Number of Digits
22. An Inequality for Grade 8
23. An Interesting Number
24. An Age Conundrum with Men of the Cloth
25. An Equation in Integers and Rational Numbers [JavaScript]
26. An Olympiad Problem With the Floor Function [JavaSCript]
27. Arithmetic magic matrix [Java]
28. Arithmetic Operations in Various Bases [Java]
29. Arithmetic Paradoxes
30. Bachet's Magic Trick [Java]
31. Barcode Encoding
32. Barcode Magic [Java]
33. Base Converter [JavaScript]
    • Binary System
    • Conversion of Fractions in Various Bases
    • Base (Binary, Decimal, etc.) Converter [Java]
34. Basic Rules of Counting
35. Billiard Handicap
36. Binary Color Device [Java]
37. Binary Euclid's Algorithm
38. Breaking Chocolate Bars [Java]
39. Broken Calculator [Java]
40. Caterpillar [Flash]
41. Chameleons of Three Colors
42. Chinese Remainder Theorem
    • Chinese Remainder Theorem (Pigeonhole principle)
43. Collatz Conjecture [Java]
44. Common Multiples and the Least Common Multiple [Java]
45. Compare Fractions: Interactive Practice [Java]
46. Computer As a Magician [Java]
47. Counting and Equivalent Fractions
48. Counting: The Beginning of Mathematics [Java]
    • Let Them Count
49. Counting Chips On a Circle [Java]
50. Counting Squares in a Square [Java]
51. Counting Triangles [Java]
52. Counting Triangles II [Java]
53. Covering A Chessboard With Domino
    • Dominoes on a Chessboard [Java]
54. Cryptarithms [JavaScript, Frames]
55. Curious Identities Involving Integer Squares
56. Distributive Law [Java]
57. Dividing Loot Fairly
58. Divisibility by 7
59. Divisibility by 9 and 11
60. Divisibility by 81
61. Divisibility Criteria
62. Divisibility by 7, 11, and 13
    • A Problem of Divisibility [Java]
63. EAN-13 Encoding [Java]
64. Egyptian Multiplication [Java]
65. Euclid's Algorithm
66. Euclid's Algorithm: An Interactive Illustration [Java]
67. Euclid's Game [Java]
    • Extension of Euclid's Game
68. Euclid's Game on a Square Grid [Java]
69. Every composite number is the product of some factors and also the sum of the same numbers
70. Extension of Euclid's Algorithm
71. Factorials and division
72. Factoring with the Factor Tree [Java]
73. Factors And Multiples
74. Falsity implies anything
75. Farey Series
76. Fast Arithmetic Tips
77. Fibonacci Numbers in Equilateral Triangle
78. Finger Counting
79. Formal Framework, an example
80. Formula for Primes
81. Four 3s
82. Four 4s
83. Four 5s
84. Four Pegs That Form a Square
    • Four Pegs That Form a Square [Java]
85. Four Weighings Suffice
86. Fraction Comparison [Java]
87. Fraction Comparison Sped up [Java]
88. Fractions on a Binary Tree
89. Fractions on a Binary Tree II
90. Frieze Patterns [Java]
91. Fun with digits
92. Funny Arithmetic [JavaScript]
93. Gasoline Stations on a Circular Trek
94. GCD and LCM via Factor Tree [Java]
95. GCD and LCM by Plain Factorization [Java]
96. GCD(M, N) × LCM(M, N) = M × N [Java]
97. Geometric view of the Sieve of Eratosthenes [Java]
98. Gergonne Magic Trick [Java]
99. Grandfather's Bill [Javascript]
100. Hardy's Example of Non-Serious Theorems
101. Heads and Tails [Java]
102. Hour glass timing
103. How to efficiently defend a castle
104. Identical Twins Puzzle
105. Identities in the Multiplication Table [Java]
106. Impossible Machine
107. Infinitely many proofs that there are infinitely many primes
108. Infinitude of Primes Via Powers of 2
109. Integer Iterations on a Circle [Java]
     • What Is Your Answer to That Question? [Java]
110. Integer Iterations on a Circle III [Java]
111. ISBN Encoding [Java]
112. Jumping Isn't Everything [Java]
113. Langford and Skolem Sequences [Java]
114. Latin Squares [Java]
     • Infinite Latin Squares
     • A Problem on an Infinite Checkerboard
115. Lattice Multiplication [Java]
116. Leibniz and Pascal Triangles [Java]
117. Less than, Equal to, Greater Than Symbols
118. Listing All the Composite Numbers [Java]
119. Long Multiplication [Java]
120. Long Runs of Composite Numbers
121. Loop or Halt [Java]
122. Magic in Square [Java]
123. Make An Identity [Java]
124. Make It All Zeros [Java]
125. Many Jugs to One I
126. Many Jugs to One II
127. Market Day
128. Math Card Trick
129. Math Telepathy [Java]
130. Mathematical Proof
131. Mathematicians and Musicians [JavaScript]
132. Mediant Fractions
133. Minimax Principle [Java]
134. Modular Arithmetic [Java]
135. Moving Chips in Pairs Down a Checkerboard [Java]
136. Napier Bones [Java]
137. Negative Coconuts
138. Nine Squares [Java]
139. Number Guessing Game [Java]
140. Number of Factors of an Integer
141. Number sequences and Pigeonhole [Java]
142. Number System With Base 36
143. Numbers That Divide the Others' Sum
144. Odd Scoring [Java]
145. One Dimensional Ants
146. Operations on Fractions [Java]
147. Order. Well-ordered sets.
148. Ordinal Numbers
149. Outline Mathematics
     Billy is twice as old as Sally [Java]
     Coin Counting Word Problem [Java]
     Crab's Weight [Java]
     "Math trick" with two dice [Java]
     
     • Practical Relativity [JavaScript] Primes as differences of squares [Java]
       Problem #24 from the Rhind Papyrus [Java]
       Robbery #1 [Java]
       Robbery #2 [Java]
       Robbery #3 [Java]
       Robbery #4 [Java]
       Smallest multiple of 9 with no odd digits [Java]
       The Lucky Find [Java]
       Three digit twister [Java]
       Who Has Beard? [Java]
150. Parity counting [Java]
151. Party Acquaintances [Java]
152. Peasant Multiplication [Java]
153. Pennies in Boxes [Java]
154. Permutations
     • Permutations as a Product of Transpositions
155. Pigeonhole Principle
     • Pigeonhole Principle and Extensions
156. Place Value [Java]
     • Letter Count in a Sentence [Java]
157. Powers of 6 and 7771
158. Probability of Divisibility
159. Product of Simple Fractions [Java]
160. Proizvolov's Identity [Java]
161. Proofs Without Words [Java]
162. Properties of GCD and LCM
163. Psychology of 0.99999...
164. Represent 4 with four digits
165. Representation of 3 with Three Equal Digits
166. Represent 6 with three digits
167. Review of Arithmetic for Parents: A Book for Grownups about Children's Mathematics by R. Aharoni
168. Rhind Papyrus
169. Right Replacement [Java]
170. The Rule of Change of Addends [Java]
171. Russell's Paradox
172. Scrub Tile Puzzle [Java]
173. Self-descriptive Strings [Java]
174. Self-reference
175. Seven Terms Periodic Sequence
176. Ship-Dock Theorem
     • Ship-Dock Theorem,a formalization
177. Sieve of Eratosthenes [Java]
178. Sieve of Squares [Java]
179. Simple Cellular Automaton [Java]
180. Six Balls, Two Weighings
181. Six Misnamed Coins, Two Weighings
182. Slider Puzzles [Java]
183. Solitaire in Two Colors [Java]
184. Soriteses
185. Soroban in Various Number Systems
186. Splitting piles
187. Squares, Circles, and Triangles [Java]
188. Steinhaus' Problem [Java]
189. Stern-Brocot Tree
190. Straight Tromino on a Chessboard [Java]
191. Suan Pan in Various Number Systems [Java]
192. Subtraction Game [Java]
193. Subtraction in a Rectangular Array [Java]
194. Sums and Products [Java]
195. Sums of powers of digits [Java]
196. Superposition Principle
197. Tables for Multiplication
198. The ass and the mule [Java]
199. Three 3s
200. Three 4s
201. Three 5s
202. Tool for Constructing Orthogonal Latin Squares [Java]
203. Treasure Hunt in a Square Grid
204. Treasure Hunt from Outside the Grid
205. Two Colors in Two Rows [Java]
     • Two Colors in Two Rows II [Java]
206. Two Numbers Guessing Game [Java]
207. Uncountability of the Reals - via a Game
208. Universal Product Code [Java]
209. Unproperty of the Powers of 2
210. Using Math Rules: An Example
211. Weighing 12 coins
     • Oddball Problem
     • Odd Coin Problems
212. What, how, and the Web [Java]
213. What Is Fraction?
214. When Two Wrongs Make One Right
215. Why 1/3 + 1/4 = 7/12?
216. With One 4
217. With One Weighing
218. Wolf and Rabbit [Flash]
219. Word Problems [Java]
220. Yet Another Puzzle with Hats
221. Zeros and Nines [Java]

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