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 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]
    • Binary System
    • Conversion of Fractions in Various Bases
    • Base (Binary, Decimal, etc.) Converter [Java]
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
    • Chinese Remainder Theorem (Pigeonhole principle)
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]
    • Let Them Count
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
    • Dominoes on a Chessboard [Java]
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
    • A Problem of Divisibility [Java]
72. Doubling Investment for a Fee And Getting Zero [JavaScript]
73. EAN-13 Encoding [Java]
74. Egyptian Multiplication [Java]
76. Elegance in Integers by Dorin Marghidanu
77. Emptying a Big Number of Boxes
78. Euclid's Algorithm
79. Euclid's Algorithm: An Interactive Illustration [Java]
80. Euclid's Game [Java]
    • Extension of Euclid's Game
81. Euclid's Game on a Square Grid [Java]
82. Every composite number is the product of some factors and also the sum of the same numbers
83. Extension of Euclid's Algorithm
84. Factorial Divisibility
85. Factorials and division
86. Factoring with the Factor Tree [Java]
87. Factors And Multiples
88. Falsity implies anything
89. Farey Series
90. Fast Arithmetic Tips
91. Fibonacci Numbers in Equilateral Triangle
92. Finger Counting
93. Formal Framework, an example
94. Formula for Primes
95. Four 3s
96. Four 4s
97. Four 5s
98. Four Pegs That Form a Square
    • Four Pegs That Form a Square [Java]
99. Four Weighings Suffice
100. Fraction Comparison [Java]
101. Fraction Comparison Sped up [Java]
102. Fractions on a Binary Tree
103. Fractions on a Binary Tree II
104. Frieze Patterns [Java]
105. Fun with digits
106. Funny Arithmetic [JavaScript]
107. Gasoline Stations on a Circular Trek
108. GCD and LCM via Factor Tree [Java]
109. GCD and LCM by Plain Factorization [Java]
110. GCD(M, N) × LCM(M, N) = M × N [Java]
111. Geometric view of the Sieve of Eratosthenes [Java]
112. Gergonne Magic Trick [Java]
113. Grandfather's Bill [Javascript]
114. Hardy's Example of Non-Serious Theorems
115. Heads and Tails [Java]
116. Hour glass timing
117. How to efficiently defend a castle
118. Identical Twins Puzzle
119. Identities in the Multiplication Table [Java]
120. Illustrated Sum of Cubes - All in a Plane
121. Impossible Machine
122. Infinitely many proofs that there are infinitely many primes
123. Infinitude of Primes Via Powers of 2
124. Integer Iterations on a Circle [Java]
     • What Is Your Answer to That Question? [Java]
125. Integer Iterations on a Circle III [Java]
126. Is a Sum a Prime Number?
127. ISBN Encoding [Java]
128. Jumping Isn't Everything [Java]
129. Langford and Skolem Sequences [Java]
130. Latin Squares [Java]
     • Infinite Latin Squares
     • A Problem on an Infinite Checkerboard
131. Lattice Multiplication [Java]
132. Leibniz and Pascal Triangles [Java]
133. Less than, Equal to, Greater Than Symbols
134. Listing All the Composite Numbers [Java]
135. Long Multiplication [Java]
136. Long Runs of Composite Numbers
137. Looking for the Prime Decomposition
138. Loop or Halt [Java]
139. Magic in Square [Java]
140. Make An Identity [Java]
141. Make It All Zeros [Java]
142. Many Jugs to One I
143. Many Jugs to One II
144. Market Day
145. Math Card Trick
146. Math Telepathy [Java]
147. Mathematical Proof
148. Mathematicians and Musicians [JavaScript]
149. Mediant Fractions
150. Minimax Principle [Java]
151. Modular Arithmetic [Java]
152. Moving Chips in Pairs Down a Checkerboard [Java]
153. Napier Bones [Java]
154. Negative Coconuts
155. Nine Squares [Java]
156. Number Guessing Game [Java]
157. Number of Factors of an Integer
158. Number sequences and Pigeonhole [Java]
159. Number System With Base 36
160. Numbers That Divide the Others' Sum
161. Odd Scoring [Java]
162. On Gauss' Shoulders
163. One Dimensional Ants
164. Operations on Fractions [Java]
165. Order. Well-ordered sets.
166. Ordinal Numbers
167. 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]
       
     • Problem #6 from the Italian MO 2000
     • Robbery #1 [Java]
       
     • Robbery #2 [Java]
       
     • Robbery #3 [Java]
       
     • Robbery #4 [Java]
       
     • Samuel G. Walters' Congruence
     • Smallest multiple of 9 with no odd digits [Java]
       
     • The Contest Corner Problem 210 from Crux
     • The Lucky Find [Java]
       
     • Three digit twister [Java]
       
     • Who Has Beard? [Java]
168. Parity counting [Java]
169. Party Acquaintances [Java]
170. Peasant Multiplication [Java]
171. Pennies in Boxes [Java]
172. Permutations
     • Permutations as a Product of Transpositions
173. Pigeonhole Principle
     • Pigeonhole Principle and Extensions
174. Place Value [Java]
     • Letter Count in a Sentence [Java]
175. Powers of 6 and 7771
176. Probability of Divisibility
177. Problem 4132 from Crux Mathematicorum
178. Product of Simple Fractions [Java]
179. Proizvolov's Identity [Java]
180. Proofs Without Words [Java]
181. Properties of GCD and LCM
182. Psychology of 0.99999...
183. Question That Changes with Time
184. Represent 4 with four digits
185. Representation of 3 with Three Equal Digits
186. Represent 6 with three digits
187. Review of Arithmetic for Parents: A Book for Grownups about Children's Mathematics by R. Aharoni
188. Rhind Papyrus
189. Right Replacement [Java]
190. The Rule of Change of Addends [Java]
191. Russell's Paradox
192. Scrub Tile Puzzle [Java]
193. Self-descriptive Strings [Java]
194. Self-reference
195. Seven Integers That Add Up to 100
196. Seven Terms Periodic Sequence
197. Ship-Dock Theorem
     • Ship-Dock Theorem,a formalization
198. Sieve of Eratosthenes [Java]
199. Sieve of Squares [Java]
200. Simple Cellular Automaton [Java]
201. Six Balls, Two Weighings
202. Six Misnamed Coins, Two Weighings
203. Slider Puzzles [Java]
204. Solitaire in Two Colors [Java]
205. Soriteses
206. Soroban in Various Number Systems
207. Splitting piles
208. Squares, Circles, and Triangles [Java]
209. Steinhaus' Problem [Java]
210. Stern-Brocot Tree
211. Straight Tromino on a Chessboard [Java]
212. Suan Pan in Various Number Systems [Java]
213. Subtraction Game [Java]
214. Subtraction in a Rectangular Array [Java]
215. Sums and Products [Java]
216. Sums of powers of digits [Java]
217. Superposition Principle
218. Tables for Multiplication
219. The ass and the mule [Java]
220. Three 3s
221. Three 4s
222. Three 5s
223. Tony Foster's Integer Powers in Pascal's Triangle
224. Tool for Constructing Orthogonal Latin Squares [Java]
225. Treasure Hunt in a Square Grid
226. Treasure Hunt from Outside the Grid
227. Two Colors in Two Rows [Java]
     • Two Colors in Two Rows II [Java]
228. Two Numbers Guessing Game [Java]
229. Uncountability of the Reals - via a Game
230. Uniqueness of Number 5
231. Universal Product Code [Java]
232. Unproperty of the Powers of 2
233. Using Math Rules: An Example
234. Weighing 12 coins
     • Oddball Problem
     • Odd Coin Problems
235. What, how, and the Web [Java]
236. What Is Fraction?
237. When Two Wrongs Make One Right
238. Why 1/3 + 1/4 = 7/12?
239. With One 4
240. With One Weighing
241. Wolf and Rabbit [Flash]
242. Word Problems [Java]
243. Yet Another Puzzle with Hats
244. Zeros and Nines [Java]

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