Arithmetic articles, problems, and puzzles.

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

Note that in the list below the pages that carry Java applets are designated with (*).

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

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Copyright © 1996-2010 Alexander Bogomolny