Interactive Mathematic Miscellany and Puzzles

Arithmetic and Algebra

What Is Arithmetic?
What Is Algebra?

1. 3-Colors Tower of Hanoi [Java]
2. 3 glass puzzle [JavaScript]
   • 3 glasses puzzle, second, more general tool [JavaScript]
   • 3 Glasses Problem in Barycentric Coordinates
   • Three Jugs Problem [Java]
   • Two Pails Puzzle [Java]
3. 3-Term Arithmetic Progression
4. 4x4 coloring problem
5. A 49^th Degree Challenge
6. Abacus in Various Number Systems [Java]
7. About numbers
8. Achieve the Equilibrium [Flash]
9. Addition
   • Addition and Subtraction of Functions [Java]
10. Affirmative Action Problem [Java]
11. The Aliquot Game [Java]
12. Algebraic Structure of Complex Numbers
13. Almost every integer has the digit 3 in it
14. Almost Integers - Gaussian Integers
15. An Application of Mental Arithmetic to Highway Safety
16. An Arithmetic Magic Trick [Java]
17. An Inequality With an Infinite Series
18. An Interesting Number
19. Arithmetic-Geometric Means Inequality
20. Arithmetic magic matrix [Java]
21. Arithmetic Operations in Various Bases [Java]
22. Arithmetic Paradoxes
23. A simple integral
24. Another simple integral
25. Averages, Arithmetic and Harmonic Means [Java]
26. Averages in a sequence
27. Bachet's Magic Trick [Java]
28. Barcode Encoding
29. Barcode Magic [Java]
30. Base Converter [JavaScript]
    • Binary System
    • Conversion of Fractions in Various Bases
31. Basic Rules of Counting
32. Bayes' Theorem
33. Beatty Sequences
34. Bilateral Diagrams [Java]
35. Binary Color Device [Java]
36. Binary Euclid's Algorithm
37. Binomial Theorem
38. Boys and Girls Solving Problems
39. Breaking Chocolate Bars [Java]
40. Broken Calculator [Java]
41. Byzantine Basketball
42. Calculation of the Digits of pi by the Spigot Algorithm [Java]
    • Calculation of the Digits of pi (Faster Version) [Java]
43. Cartesian Coordinate System [Java]
44. Caterpillar [Flash]
45. Chameleons of Three Colors
46. Chinese Remainder Theorem
47. Collatz Conjecture [Java]
48. Coloring a Graph [Java]
49. Combinatorial Proofs
50. Committee Chairs
51. Comparing complex numbers.
52. Complex Numbers: A Dynamic Tool [Java]
53. Complex number to a complex power may be real
54. Computer As a Magician [Java]
55. Constructible Numbers
56. Continued fractions
    Continued Fractions on the Stern-Brocot Tree
57. Countability of Rational Numbers
58. Counting: The Beginning of Mathematics [Java]
    • Let Them Count
59. Counting Chips On a Circle [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. Descartes' Rule of Signs
65. Distance Between Strings [Java]
66. Distance From a Point to a Straight Line [Java]
67. Distributive Law [Java]
68. Dividing Loot Fairly
69. Divisibility by 7
70. Divisibility by 9 and 11
71. Divisibility by 81
72. Divisibility Criteria
73. Divisibility by 7, 11, and 13
    • A Problem of Divisibility [Java]
74. Dot Patterns and Sierpinski Gasket [Java]
    • Arithmetic in Disguise [Java]
75. Dots and fractions [Java]
76. Ducci Sequences [Java]
77. EAN-13 Encoding [Java]
78. Egyptian Multiplication [Java]
79. Eigenvectors by Inspection
80. Equations of the Staight Line [Java]
81. Equivalence Relations
82. Euclid's Algorithm
83. Euclid's Game [Java]
84. Euler’s formula for e^iθ
85. Euler's Function and Congruence Theorem
86. Evolution of Algebraic Symbolism
87. Every composite number is the product of some factors and also the sum of the same numbers
88. Extension of Euclid's Algorithm
89. Factorials and division
90. Falsity implies anything
91. Farey Series
92. Fast Arithmetic Tips
93. Fermat's Little Theorem
94. First Geometric Interpretation of Complex Numbers [Java]
95. Five Lattice Points [Java]
96. Flipping Items Simultaneously [Java]
97. Flipping Items Simultaneously II [Java]
98. Flipping pancakes [Java]
99. Floor Function
100. Formal Framework, an example
101. Formula for Primes
102. Four 3s
103. Four 4s
104. Four 5s
105. Four Pegs That Form a Square
     • Four Pegs That Form a Square [Java]
106. Fractions on a Binary Tree
107. Fractions on a Binary Tree II
108. Frieze Patterns [Java]
109. Fun with digits
110. Function
111. Fundamental Theorem of Algebra
     • Fundamental Theorem of Algebra - Yet Another Proof
112. Funny Arithmetic [JavaScript]
113. Gasoline Stations on a Circular Trek
114. Generating Functions
     • Generating Functions [Java]
     • Coin Change [Java]
     • Fast Power indices [Java]
     • Weighted Voting and Power Indices [Java]
115. Geometric view of the Sieve of Eratosthenes [Java]
116. Gergonne Magic Trick [Java]
117. Graph of a Polynomial [Java]
118. Graph of a Polynomial Defined by Its Roots [Java]
119. Group multiplication of permutations [Java]
120. Guessing Two Consecutive Integers
121. Harmonic Serires And Its Parts
122. Heads and Tails [Java]
123. Horner's Method [Java]
124. Hour glass timing
125. How to define a permutation? [Java]
126. How to efficiently defend a castle
127. Identical Twins Puzzle
128. Identities in the Multiplication Table [Java]
129. Implementation of Base Conversion
130. Impossible Machine
131. Inclusion-Exclusion Principle
132. Inequality 1/2·3/4·5/6· ... ·99/100 < 1/10
133. Inequality (1 + 1^-3)(1 + 2^-3)(1 + 2^-3)...(1 + n^-3) < 3
134. Inequality 1 + 2^-2 + 3^-2 + 4^-2 + ... + n^-2 < 2.
135. Infinitude of Primes
     • Infinitude of Primes - A Topological Proof
     • Infinitude of Primes Via *-Sets
     • Infinitude of Primes Via Coprime Pairs
     • Infinitude of Primes Via Fermat Numbers
     • Infinitude of Primes Via Harmonic Series
136. Inflection Points of Fourth Degree Polynomials [Java]
137. Integer Iterations on a Circle [Java]
     • What Is Your Answer to That Question? [Java]
138. Integer roots of integers are irrational
139. Integers and Rectangles [Java]
140. Integers and Rectangles: a Proof by Induction [Java]
141. Integers and Rectangles: Two Simple Proofs [Java]
142. Interest Calculations [Java]
143. ISBN Encoding [Java]
144. Irrational number to an irrational power may be rational
145. Is 0.999... = 1?
146. It's All About Powers of 10
147. Joachimsthal's Notations
148. Jumping Isn't Everything [Java]
149. Kaprekar's Iterations and Numbers [Java]
150. Lagrange interpolation
151. Langford and Skolem Sequences [Java]
152. Latin Squares [Java]
     • Infinite Latin Squares
     • A Problem on an Infinite Checkerboard
153. Lattice Multiplication [Java]
154. Leibniz and Pascal Triangles [Java]
155. Lewis Carroll's Game of Logic [Java]
156. Light Bulbs in a Circle [Java]
157. Lights Out [Java]
158. Linear functions
159. Linear Programming
160. Listing All Combinations [Java]
161. Listing all permutations [Java]
162. Listing All Permutations: Johnson-Trotter Method [Java]
163. Logistic Model applet [Java]
164. Long Multiplication [Java]
165. Long Runs of Composite Numbers
166. Looking your best
167. Loop or Halt [Java]
168. Lucas' Theorem
169. Magic in Square [Java]
170. Make An Identity [Java]
171. Marriage Theorem
172. Marriage Problem, simulation [Java]
173. Math Card Trick
174. Math Lotto
175. Math Telepathy [Java]
176. Mathematical Induction
177. Mathematical Proof
178. Mathematicians Doze Off
179. Maximum Volume of a Cut Off Box [Java]
180. Means [Java]
181. Mediant Fractions
182. Mini Lights Out [Java]
183. Minimax Principle [Java]
184. Minimax Theorem [Java]
185. Modular Arithmetic [Java]
186. Monotone Number Sequences [Java]
187. Multiplication
188. Napier Bones [Java]
189. Nine Squares [Java]
190. Number Guessing Game [Java]
191. Number sequences and Pigeonhole [Java]
192. Number System With Base 36
193. Operations on Fractions [Java]
194. 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]
195. Parity counting [Java]
196. Parrondo Paradox Via Simpson Paradox [Java]
197. Party Acquaintances [Java]
198. Peano axioms
199. Peasant Multiplication [Java]
200. Pennies in Boxes [Java]
201. Permutations
     • Permutations as a Product of Transpositions
202. Pigeonhole Principle
     • Pigeonhole Principle and Extensions
203. Place Value [Java]
     • Letter Count in a Sentence [Java]
204. Problem of Divisibility by 5ⁿ
205. Product of Diagonals in Regular N-gon
206. Product of permutations [Java]
207. Proizvolov's Identity [Java]
208. Proofs Without Words [Java]
209. Property of aⁿ
210. Property of the Powers of 2 [Java]
211. Puzzlist vs. Mathematician: A Practical Arithmetic Problem
212. Pythagorean Triples [Java]
     • Divisibilty in Pythagorean Triples
     • Pythagorean Triples and Perfect Numbers
     • Pythagorean Triples Calculator [Java]
213. Quasigroups and block designs from triangular grid [Java]
214. Ramsey's Theorem
215. Recombining Permutations [Java]
216. Represent 4 with four digits
217. Represent 6 with three digits
218. Rectangle on a Chessboard [Java]
219. Rhind Papyrus
220. Riemann Sums - Function Integration [Java]
221. Rolle's and Mean Value Theorems [Java]
222. Russell's Paradox
223. Scrub Tile Puzzle [Java]
224. Self-descriptive Strings [Java]
225. Self-reference
226. Seven Terms Periodic Sequence
227. Shapley-Shubik Power Index [Java]
228. Ship-Dock Theorem
     • Ship-Dock Theorem,a formalization
229. Sierpinski Gasket and Tower of Hanoi
230. Sierpinski's Gasket and Dihedral Symmetry [Java]
231. Sieve of Eratosthenes [Java]
232. Sieve of Squares [Java]
233. Σ2^-n = Σn·2^-n
234. Signs and Sums in a Sequence [Java]
235. Signs in a Matrix [Java]
236. Simple Cellular Automaton [Java]
237. Simpson Paradox [Java]
238. Single formula to express any integer with digits 0-9 each used just once
239. Six Balls, Two Weighings
240. Slider Puzzles [Java]
241. Solitaire in Two Colors [Java]
242. Solve x^x3 = 3
243. Soriteses
244. Soroban in Various Number Systems
245. Sorting Algorithms
246. Sperner's Theorem
247. Splitting piles
248. Square root of 2 is irrational
249. Squares, Circles, and Triangles [Java]
250. Steinhaus' Problem [Java]
251. Step into the Elliptic Realm
252. Stern-Brocot Tree
253. Straight Tromino on a Chessboard [Java]
254. Suan Pan in Various Number Systems [Java]
255. Subtraction Game [Java]
256. Sums and Products [Java]
257. Sums of powers of digits [Java]
258. Superposition Principle
259. Taking Games Seriously [Java]
260. The ass and the mule [Java]
261. Three 3s
262. Three 4s
263. Three 5s
264. Tool for Constructing Orthogonal Latin Squares [Java]
265. Tower of Hanoi, the Hard Way [Java]
266. Transpositions
267. Triangular numbers that are also square
268. Trilateral Diagrams [Java]
269. Trinary Tree(s) underlying Primitive Pythagorean Triples
270. Twenty five boys and twenty five girls around a table.
271. Two Circles and a Limit [Java]
272. Two Colors in Two Rows [Java]
     • Two Colors in Two Rows II [Java]
273. Two Men of Tibet [Java]
274. Two Numbers Guessing Game [Java]
275. Universal Coloring [Java]
276. Universal Product Code [Java]
277. Venn Diagrams
     • Venn Diagrams I [Java]
     • Venn Diagrams II [Java]
278. Ways To Count
279. Weierstrass Product Inequality
280. Weighing 12 coins
     • Oddball Problem
     • Odd Coin Problems
281. What, how, and the Web [Java]
282. What is so natural about “natural logarithms”?
283. WHEN THE COUNTING GETS TOUGH, THE TOUGH COUNT ON MATHEMATICS
     • Matrices Help Relationships
     • An Airline Problem
284. Where To Start? [Java]
285. Why 1/3 + 1/4 = 7/12?
286. Why 17?
287. Wilson's Theorem
288. With One 4
289. Wolf and Rabbit [Flash]
290. Word Problems [Java]
291. Zeros and Nines [Java]

Copyright © 1996-2008 Alexander Bogomolny