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

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