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. A Clique of Acquaintances
7. Abacus in Various Number Systems [Java]
8. About numbers
9. Achieve the Equilibrium [Flash]
10. Addition
    • Addition and Subtraction of Functions [Java]
11. Affirmative Action Problem [Java]
12. Algorithm for Computing LCM [Java]
13. The Aliquot Game [Java]
14. Algebraic Structure of Complex Numbers
15. Almost every integer has the digit 3 in it
16. Almost Integers - Gaussian Integers
17. An Application of Mental Arithmetic to Highway Safety
18. An Arithmetic Magic Trick [Java]
19. An Inequality With an Infinite Series
20. An Interesting Number
21. Arithmetic-Geometric Means Inequality
22. Arithmetic magic matrix [Java]
23. Arithmetic Operations in Various Bases [Java]
24. Arithmetic Paradoxes
25. A simple integral
26. Another simple integral
27. Averages, Arithmetic and Harmonic Means [Java]
28. Averages in a sequence
29. Bachet's Magic Trick [Java]
30. Barcode Encoding
31. Barcode Magic [Java]
32. Base Converter [JavaScript]
    • Binary System
    • Conversion of Fractions in Various Bases
33. Basic Rules of Counting
34. Bayes' Theorem
35. Beatty Sequences
36. Bilateral Diagrams [Java]
37. Binary Color Device [Java]
38. Binary Euclid's Algorithm
39. Binomial Distribution [Java]
40. Binomial Theorem
41. Boys and Girls Solving Problems
42. Breaking Chocolate Bars [Java]
43. Broken Calculator [Java]
44. Byzantine Basketball
45. Calculation of the Digits of pi by the Spigot Algorithm [Java]
    • Calculation of the Digits of pi (Faster Version) [Java]
46. Cantor-Bernstein-Schroeder theorem
47. Cardinal Numbers
48. Cartesian Coordinate System [Java]
49. Caterpillar [Flash]
50. Chameleons of Three Colors
51. Chinese Remainder Theorem
52. Collatz Conjecture [Java]
53. Coloring a Graph [Java]
54. Combinatorial Proofs
55. Committee Chairs
56. Comparing complex numbers
57. Completing a Square and Quadratic Formula
58. Complex Numbers: A Dynamic Tool [Java]
59. Complex number to a complex power may be real
60. Computer As a Magician [Java]
61. Constructible Numbers
62. Continued fractions
    Continued Fractions on the Stern-Brocot Tree
63. Countability of Rational Numbers
64. Counting: The Beginning of Mathematics [Java]
    • Let Them Count
65. Counting Chips On a Circle [Java]
66. Counting Triangles [Java]
67. Counting Triangles II [Java]
68. Covering A Chessboard With Domino
    • Dominoes on a Chessboard [Java]
69. Cryptarithms [JavaScript, Frames]
70. Descartes' Rule of Signs
71. Distance Between Strings [Java]
72. Distance From a Point to a Straight Line [Java]
73. Distributive Law [Java]
74. Dividing Loot Fairly
75. Divisibility and Modulo Arithmetic at IMO 2007
76. Divisibility by 7
77. Divisibility by 9 and 11
78. Divisibility by 81
79. Divisibility Criteria
80. Divisibility by 7, 11, and 13
    • A Problem of Divisibility [Java]
81. Dot Patterns and Sierpinski Gasket [Java]
    • Arithmetic in Disguise [Java]
82. Dots and fractions [Java]
83. Ducci Sequences [Java]
84. EAN-13 Encoding [Java]
85. Egyptian Multiplication [Java]
86. Eigenvectors by Inspection
87. Equations of the Staight Line [Java]
88. Equivalence Relations
89. Euclid's Algorithm
90. Euclid's Game [Java]
91. Euler’s formula for e^iθ
92. Euler's Function and Congruence Theorem
93. Evolution of Algebraic Symbolism
94. Every composite number is the product of some factors and also the sum of the same numbers
95. Extension of Euclid's Algorithm
96. Factorials and division
97. Falsity implies anything
98. Farey Series
99. Fast Arithmetic Tips
100. Fermat's Little Theorem
101. First Geometric Interpretation of Complex Numbers [Java]
102. Five Lattice Points [Java]
103. Flipping Items Simultaneously [Java]
104. Flipping Items Simultaneously II [Java]
105. Flipping pancakes [Java]
106. Floor Function
107. Formal Framework, an example
108. Formula for Primes
109. Four 3s
110. Four 4s
111. Four 5s
112. Four Pegs That Form a Square
     • Four Pegs That Form a Square [Java]
113. Fractions on a Binary Tree
114. Fractions on a Binary Tree II
115. Frieze Patterns [Java]
116. Fun with digits
117. Function
118. Fundamental Theorem of Algebra
     • Fundamental Theorem of Algebra - Yet Another Proof
119. Funny Arithmetic [JavaScript]
120. Gasoline Stations on a Circular Trek
121. Generating Functions
     • Generating Functions [Java]
     • Coin Change [Java]
     • Fast Power indices [Java]
     • Weighted Voting and Power Indices [Java]
122. Geometric Construction of Roots of Quadratic Equation [Java]
123. Geometric view of the Sieve of Eratosthenes [Java]
124. Gergonne Magic Trick [Java]
125. Graph and Roots of a Third Degree Polynomial [Java]
126. Graph and Roots of Quadratic Polynomial [Java]
127. Graph of a Polynomial [Java]
128. Graph of a Polynomial Defined by Its Roots [Java]
129. Group multiplication of permutations [Java]
130. Guessing Two Consecutive Integers
131. Harmonic Serires And Its Parts
132. Heads and Tails [Java]
133. Horner's Method [Java]
134. Hour glass timing
135. How to Ask an Embarrassing Question
136. How to define a permutation? [Java]
137. How to efficiently defend a castle
138. Identical Twins Puzzle
139. Identities in the Multiplication Table [Java]
140. Implementation of Base Conversion
141. Impossible Machine
142. Inclusion-Exclusion Principle
143. Inequality 1/2·3/4·5/6· ... ·99/100 < 1/10
144. Inequality (1 + 1^-3)(1 + 2^-3)(1 + 2^-3)...(1 + n^-3) < 3
145. Inequality 1 + 2^-2 + 3^-2 + 4^-2 + ... + n^-2 < 2.
146. 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
147. Infinity As a Limit
148. Inflection Points of Fourth Degree Polynomials [Java]
149. Integer Iterations on a Circle [Java]
     • What Is Your Answer to That Question? [Java]
150. Integer roots of integers are irrational
151. Integers and Rectangles [Java]
152. Integers and Rectangles: a Proof by Induction [Java]
153. Integers and Rectangles: Two Simple Proofs [Java]
154. Interest Calculations [Java]
155. ISBN Encoding [Java]
156. Irrational number to an irrational power may be rational
157. Is 0.999... = 1?
158. It's All About Powers of 10
159. Joachimsthal's Notations
160. Jumping Isn't Everything [Java]
161. Kaprekar's Iterations and Numbers [Java]
162. Lagrange interpolation
163. Langford and Skolem Sequences [Java]
164. Latin Squares [Java]
     • Infinite Latin Squares
     • A Problem on an Infinite Checkerboard
165. Lattice Multiplication [Java]
166. Leibniz and Pascal Triangles [Java]
167. Lewis Carroll's Game of Logic [Java]
168. Light Bulbs in a Circle [Java]
169. Lights Out [Java]
170. Linear functions
171. Linear Programming
172. Listing All Combinations [Java]
173. Listing all permutations [Java]
174. Listing All Permutations: Johnson-Trotter Method [Java]
175. Logistic Model applet [Java]
176. Long Multiplication [Java]
177. Long Runs of Composite Numbers
178. Looking your best
179. Loop or Halt [Java]
180. Lucas' Theorem
181. Magic in Square [Java]
182. Make An Identity [Java]
183. Marriage Theorem
184. Marriage Problem, simulation [Java]
185. Math Card Trick
186. Math Lotto
187. Math Telepathy [Java]
188. Mathematical Induction
189. Mathematical Proof
190. Mathematicians Doze Off
191. Maximum Volume of a Cut Off Box [Java]
192. Means [Java]
193. Mediant Fractions
194. Mini Lights Out [Java]
195. Minimax Principle [Java]
196. Minimax Theorem [Java]
197. Modular Arithmetic [Java]
198. Monotone Number Sequences [Java]
199. Multiplication
200. Napier Bones [Java]
201. Nine Squares [Java]
202. Number Guessing Game [Java]
203. Number sequences and Pigeonhole [Java]
204. Number System With Base 36
205. Operations on Fractions [Java]
206. Order. Well-ordered sets.
207. Ordinal Numbers
208. 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]
209. Parity counting [Java]
210. Parrondo Paradox Via Simpson Paradox [Java]
211. Party Acquaintances [Java]
212. Peano axioms
213. Peasant Multiplication [Java]
214. Pennies in Boxes [Java]
215. Permutations
     • Permutations as a Product of Transpositions
216. Pigeonhole Principle
     • Pigeonhole Principle and Extensions
217. Place Value [Java]
     • Letter Count in a Sentence [Java]
218. Problem of Divisibility by 5ⁿ
219. Product of Diagonals in Regular N-gon
220. Product of permutations [Java]
221. Proizvolov's Identity [Java]
222. Proofs Without Words [Java]
223. Property of aⁿ
224. Property of the Powers of 2 [Java]
225. Puzzlist vs. Mathematician: A Practical Arithmetic Problem
226. Pythagorean Triples [Java]
     • Divisibilty in Pythagorean Triples
     • Pythagorean Triples and Perfect Numbers
     • Pythagorean Triples Calculator [Java]
227. Quasigroups and block designs from triangular grid [Java]
228. Ramsey's Theorem
229. Recombining Permutations [Java]
230. Represent 4 with four digits
231. Represent 6 with three digits
232. Rectangle on a Chessboard [Java]
233. Review of Arithmetic for Parents: A Book for Grownups about Children's Mathematics by R. Aharoni
234. Rhind Papyrus
235. Riemann Sums - Function Integration [Java]
236. Right Replacement [Java]
237. Rolle's and Mean Value Theorems [Java]
238. Round Robin Tournament
239. Russell's Paradox
240. Scrub Tile Puzzle [Java]
241. Self-descriptive Strings [Java]
242. Self-reference
243. Seven Terms Periodic Sequence
244. Shapley-Shubik Power Index [Java]
245. Ship-Dock Theorem
     • Ship-Dock Theorem,a formalization
246. Sierpinski Gasket and Tower of Hanoi
247. Sierpinski's Gasket and Dihedral Symmetry [Java]
248. Sieve of Eratosthenes [Java]
249. Sieve of Squares [Java]
250. Σ2^-n = Σn·2^-n
251. Signs and Sums in a Sequence [Java]
252. Signs in a Matrix [Java]
253. Simple Cellular Automaton [Java]
254. Simpson Paradox [Java]
255. Single formula to express any integer with digits 0-9 each used just once
256. Six Balls, Two Weighings
257. Slider Puzzles [Java]
258. Solitaire in Two Colors [Java]
259. Solve x^x3 = 3
260. Soriteses
261. Soroban in Various Number Systems
262. Sorting Algorithms
263. Sperner's Theorem
264. Splitting piles
265. Square root of 2 is irrational
266. Squares, Circles, and Triangles [Java]
267. Steinhaus' Problem [Java]
268. Step into the Elliptic Realm
269. Stern-Brocot Tree
270. Straight Tromino on a Chessboard [Java]
271. Suan Pan in Various Number Systems [Java]
272. Subtraction Game [Java]
273. Sums and Products [Java]
274. Sums of powers of digits [Java]
275. Superposition Principle
276. Surreal Numbers
277. Taking Games Seriously [Java]
278. The ass and the mule [Java]
279. Three 3s
280. Three 4s
281. Three 5s
282. Tool for Constructing Orthogonal Latin Squares [Java]
283. Tower of Hanoi, the Hard Way [Java]
284. Transpositions
285. Triangular numbers that are also square
286. Trilateral Diagrams [Java]
287. Trinary Tree(s) underlying Primitive Pythagorean Triples
288. Twenty five boys and twenty five girls around a table.
289. Two Circles and a Limit [Java]
290. Two Colors in Two Rows [Java]
     • Two Colors in Two Rows II [Java]
291. Two Men of Tibet [Java]
292. Two Numbers Guessing Game [Java]
293. Universal Coloring [Java]
294. Universal Product Code [Java]
295. Venn Diagrams
     • Venn Diagrams I [Java]
     • Venn Diagrams II [Java]
296. Ways To Count
297. Weierstrass Product Inequality
298. Weighing 12 coins
     • Oddball Problem
     • Odd Coin Problems
299. What, how, and the Web [Java]
300. What Is Algorithm?
301. What Is Infinity?
302. What Is Limit?
303. What is so natural about “natural logarithms”?
304. WHEN THE COUNTING GETS TOUGH, THE TOUGH COUNT ON MATHEMATICS
     • Matrices Help Relationships
     • An Airline Problem
305. Where To Start? [Java]
306. Why 1/3 + 1/4 = 7/12?
307. Why 17?
308. Wilson's Theorem
     • Geometric Proof of Wilson's Theorem
309. With One 4
310. Wolf and Rabbit [Flash]
311. Word Problems [Java]
312. Zeros and Nines [Java]

Copyright © 1996-2008 Alexander Bogomolny