Interactive Mathematic Miscellany and Puzzles

Arithmetic and Algebra

What Is Arithmetic?
What Is Algebra?
Mental Calculations

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

Copyright © 1996-2008 Alexander Bogomolny