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. A Line in a Square Grid [Java]
8. Abacus in Various Number Systems [Java]
9. About numbers
10. Achieve the Equilibrium [Flash]
11. Addition
    • Addition and Subtraction of Functions [Java]
12. Affirmative Action Problem [Java]
13. Algorithm for Computing LCM [Java]
14. The Aliquot Game [Java]
15. Algebraic Structure of Complex Numbers
16. Almost every integer has the digit 3 in it
17. Almost Integers - Gaussian Integers
18. An Application of Mental Arithmetic to Highway Safety
19. An Arithmetic Magic Trick [Java]
20. An Inequality for Grade 8
21. An Inequality With an Infinite Series
22. An Interesting Number
23. Arithmetic-Geometric Means Inequality
24. Arithmetic magic matrix [Java]
25. Arithmetic Operations in Various Bases [Java]
26. Arithmetic Paradoxes
27. A simple integral
28. Another simple integral
29. Averages, Arithmetic and Harmonic Means [Java]
30. Averages in a sequence
31. Bachet's Magic Trick [Java]
32. Barcode Encoding
33. Barcode Magic [Java]
34. Base Converter [JavaScript]
    • Binary System
    • Conversion of Fractions in Various Bases
35. Basic Rules of Counting
36. Bayes' Theorem
37. Beatty Sequences
38. Bilateral Diagrams [Java]
39. Binary Color Device [Java]
40. Binary Euclid's Algorithm
41. Binomial Distribution [Java]
42. Binomial Theorem\
43. Bisector of an imaginary angle may be real
44. Boys and Girls Solving Problems
45. Breaking Chocolate Bars [Java]
46. Broken Calculator [Java]
47. Byzantine Basketball
48. Calculation of the Digits of pi by the Spigot Algorithm [Java]
    • Calculation of the Digits of pi (Faster Version) [Java]
49. Cantor-Bernstein-Schroeder theorem
50. Cardinal Numbers
51. Cartesian Coordinate System [Java]
52. Caterpillar [Flash]
53. Chameleons of Three Colors
54. Chinese Remainder Theorem
55. Clifford Algebras
56. Collatz Conjecture [Java]
57. Coloring a Graph [Java]
58. Combinatorial Proofs
59. Committee Chairs
60. Comparing complex numbers
61. Completing a Square and Quadratic Formula
62. Complex Numbers: A Dynamic Tool [Java]
63. Complex number to a complex power may be real
64. Computer As a Magician [Java]
65. Constructible Numbers
66. Continued fractions
    Continued Fractions on the Stern-Brocot Tree
67. Countability of Rational Numbers
68. Counting: The Beginning of Mathematics [Java]
    • Let Them Count
69. Counting Chips On a Circle [Java]
70. Counting Squares in a Square [Java]
71. Counting Triangles [Java]
72. Counting Triangles II [Java]
73. Covering A Chessboard With Domino
    • Dominoes on a Chessboard [Java]
74. Cryptarithms [JavaScript, Frames]
75. Cubic Formula [JavaScript]
76. Cubics and Bézout's Theorem
77. Derivatives without Limits
78. Descartes' Rule of Signs
79. Distance Between Strings [Java]
80. Distance From a Point to a Straight Line [Java]
81. Distributive Law [Java]
82. Dividing Loot Fairly
83. Divisibility and Modulo Arithmetic at IMO 2007
84. Divisibility by 7
85. Divisibility by 9 and 11
86. Divisibility by 81
87. Divisibility Criteria
88. Divisibility by 7, 11, and 13
    • A Problem of Divisibility [Java]
89. Dollars in Pockets
90. Dot Patterns and Sierpinski Gasket [Java]
    • Arithmetic in Disguise [Java]
91. Dots and fractions [Java]
92. Ducci Sequences [Java]
93. EAN-13 Encoding [Java]
94. Egyptian Multiplication [Java]
95. Eigenvectors by Inspection
96. Equations of the Staight Line [Java]
97. Equivalence Relations
98. Euclid's Algorithm
99. Euclid's Game [Java]
100. Euler’s formula for e^iθ
101. Euler's Function and Congruence Theorem
102. Evolution of Algebraic Symbolism
103. Every composite number is the product of some factors and also the sum of the same numbers
104. Extension of Euclid's Algorithm
105. Factorials and division
106. Falsity implies anything
107. Farey Series
108. Fast Arithmetic Tips
109. Fermat's Little Theorem
110. Fibonacci's Quickies
111. First Geometric Interpretation of Complex Numbers [Java]
112. Five Lattice Points [Java]
113. Flipping Items Simultaneously [Java]
114. Flipping Items Simultaneously II [Java]
115. Flipping pancakes [Java]
116. Floor Function
117. Formal Framework, an example
118. Formal Systems - an Example
119. Formula for Primes
120. Four 3s
121. Four 4s
122. Four 5s
123. Four Hinged Squares: using complex numbers
124. Four Pegs That Form a Square
     • Four Pegs That Form a Square [Java]
125. Fraction Comparison [Java]
126. Fractions on a Binary Tree
127. Fractions on a Binary Tree II
128. Frieze Patterns [Java]
129. Fun with digits
130. Function
131. Fundamental Theorem of Algebra
     • Fundamental Theorem of Algebra - Yet Another Proof
132. Funny Arithmetic [JavaScript]
133. Gasoline Stations on a Circular Trek
134. GCD(M, N) × LCM(M, N) = M × N [Java]
135. Generalization That Solves the Problem
136. Generating Functions
     • Generating Functions [Java]
     • Coin Change [Java]
     • Fast Power indices [Java]
     • Weighted Voting and Power Indices [Java]
137. Geometric Construction of Roots of Quadratic Equation [Java]
138. Geometric view of the Sieve of Eratosthenes [Java]
139. Gergonne Magic Trick [Java]
140. Gödel's Incompleteness Theorem
141. Graph and Roots of a Third Degree Polynomial [Java]
142. Graph and Roots of Quadratic Polynomial [Java]
143. Graph of a Polynomial [Java]
144. Graph of a Polynomial Defined by Its Roots [Java]
145. Group multiplication of permutations [Java]
146. Guessing Two Consecutive Integers
147. Harmonic Serires And Its Parts
148. Heads and Tails [Java]
149. Horner's Method [Java]
150. Hour glass timing
151. How to Ask an Embarrassing Question
152. How to define a permutation? [Java]
153. How to efficiently defend a castle
154. Hyperintegers and Hyperreal Numbers
155. Identical Twins Puzzle
156. Identities in the Multiplication Table [Java]
157. Implementation of Base Conversion
158. Impossible Machine
159. Inclusion-Exclusion Principle
160. Inequality 1/2·3/4·5/6· ... ·99/100 < 1/10
161. Inequality (1 + 1^-3)(1 + 2^-3)(1 + 2^-3)...(1 + n^-3) < 3
162. Inequality 1 + 2^-2 + 3^-2 + 4^-2 + ... + n^-2 < 2.
163. Infinite Discent for x⁴ + y⁴ = z⁴
164. Infinitesimals. Non-standard Analysis
165. Infinitude of Primes
     • Infinitude of Primes - A Topological Proof
     • Infinitude of Primes - A Topological Proof without Topology
     • Infinitude of Primes Via *-Sets
     • Infinitude of Primes Via Coprime Pairs
     • Infinitude of Primes Via Fermat Numbers
     • Infinitude of Primes Via Harmonic Series
166. Infinity As a Limit
167. Inflection Points of Fourth Degree Polynomials [Java]
168. Integer Iterations on a Circle [Java]
     • What Is Your Answer to That Question? [Java]
169. Integer roots of integers are irrational
170. Integers and Rectangles [Java]
171. Integers and Rectangles: a Proof by Induction [Java]
172. Integers and Rectangles: Two Simple Proofs [Java]
173. Interest Calculations [Java]
174. ISBN Encoding [Java]
175. Irrational number to an irrational power may be rational
176. Is 0.999... = 1?
177. It's All About Powers of 10
178. Joachimsthal's Notations
179. Jumping Isn't Everything [Java]
180. Kaprekar's Iterations and Numbers [Java]
181. Lagrange interpolation
182. Langford and Skolem Sequences [Java]
183. Latin Squares [Java]
     • Infinite Latin Squares
     • A Problem on an Infinite Checkerboard
184. Lattice Multiplication [Java]
185. Leibniz and Pascal Triangles [Java]
186. Lewis Carroll's Game of Logic [Java]
187. Light Bulbs in a Circle [Java]
188. Lights Out [Java]
189. Linear functions
190. Linear Programming
191. Listing All Combinations [Java]
192. Listing all permutations [Java]
193. Listing All Permutations: Johnson-Trotter Method [Java]
194. Logistic Model applet [Java]
195. Long Multiplication [Java]
196. Long Runs of Composite Numbers
197. Looking your best
198. Loop or Halt [Java]
199. Lucas' Theorem
200. Magic in Square [Java]
201. Make An Identity [Java]
202. Market Day
203. Marriage Theorem
204. Marriage Problem, simulation [Java]
205. Math Card Trick
206. Math Lotto
207. Math Telepathy [Java]
208. Mathematical Induction
209. Mathematical Proof
210. Mathematicians Doze Off
211. Matrix Groups
212. Maximum Volume of a Cut Off Box [Java]
213. Means [Java]
214. Mediant Fractions
215. Minesweeper Theorem
216. Mini Lights Out [Java]
217. Minimax Principle [Java]
218. Minimax Theorem [Java]
219. Modular Arithmetic [Java]
220. Monotone Convergence Theorem
221. Monotone Number Sequences [Java]
222. Multiplication
223. Napier Bones [Java]
224. Nested Radicals
225. Newton's Method [Java]
226. Nine Squares [Java]
227. Number 8 Is Interesting
228. Number Guessing Game [Java]
229. Number sequences and Pigeonhole [Java]
230. Number System With Base 36
231. On the Games of Hex and Y
232. One Dimensional Ants
233. One Trigonometric Formula and Its Consequences
234. Operations on Fractions [Java]
235. Order. Well-ordered sets.
236. Ordinal Numbers
237. 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]
238. Parity counting [Java]
239. Parrondo Paradox Via Simpson Paradox [Java]
240. Party Acquaintances [Java]
241. Peano axioms
242. Peasant Multiplication [Java]
243. Pennies in Boxes [Java]
244. Percent
245. Permutations
     • Permutations as a Product of Transpositions
246. Pigeonhole Principle
     • Pigeonhole Principle and Extensions
247. Place Value [Java]
     • Letter Count in a Sentence [Java]
248. Probability of Divisibility
249. Problem of Divisibility by 5ⁿ
250. Product of Diagonals in Regular N-gon
251. Product Of Four Consecutive Integers
252. Product of Simple Fractions [Java]
253. Product of permutations [Java]
254. Proizvolov's Identity [Java]
255. Proofs Without Words [Java]
256. Property of aⁿ
257. Property of the Powers of 2 [Java]
258. Puzzlist vs. Mathematician: A Practical Arithmetic Problem
259. Pythagorean Triples [Java]
     • Divisibilty in Pythagorean Triples
     • Pythagorean Triples and Perfect Numbers
     • Pythagorean Triples Calculator [Java]
260. Quasigroups and block designs from triangular grid [Java]
261. Ramsey's Theorem
262. Recombining Permutations [Java]
263. Represent 4 with four digits
264. Represent 6 with three digits
265. Rectangle on a Chessboard [Java]
266. Review of Arithmetic for Parents: A Book for Grownups about Children's Mathematics by R. Aharoni
267. Rhind Papyrus
268. Riemann Sphere and Möbius Transformation
269. Riemann Sums - Function Integration [Java]
270. Right Replacement [Java]
271. Rolle's and Mean Value Theorems [Java]
272. Round Robin Tournament
273. Russell's Paradox
274. Scrub Tile Puzzle [Java]
275. Self-descriptive Strings [Java]
276. Self-reference
277. Seven Terms Periodic Sequence
278. Shapley-Shubik Power Index [Java]
279. Ship-Dock Theorem
     • Ship-Dock Theorem,a formalization
280. Sierpinski Gasket and Tower of Hanoi
281. Sierpinski's Gasket and Dihedral Symmetry [Java]
282. Sieve of Eratosthenes [Java]
283. Sieve of Squares [Java]
284. Σ2^-n = Σn·2^-n
285. Signs and Sums in a Sequence [Java]
286. Signs in a Matrix [Java]
287. Simple Cellular Automaton [Java]
288. Simpson Paradox [Java]
289. Single formula to express any integer with digits 0-9 each used just once
290. Six Balls, Two Weighings
291. Slider Puzzles [Java]
292. Solitaire in Two Colors [Java]
293. Solve x^x3 = 3
294. Soriteses
295. Soroban in Various Number Systems
296. Sorting Algorithms
297. Sperner's Theorem
298. Splitting piles
299. Square root of 2 is irrational
300. Squares, Circles, and Triangles [Java]
301. Steinhaus' Problem [Java]
302. Step into the Elliptic Realm
303. Stern-Brocot Tree
304. Straight Tromino on a Chessboard [Java]
305. Structure of Hyperreal Numbers
306. Suan Pan in Various Number Systems [Java]
307. Subtraction Game [Java]
308. Sum without Adding
309. Sums and Products [Java]
310. Sums of powers of digits [Java]
311. Superposition Principle
312. Surreal Numbers
313. Taking Games Seriously [Java]
314. The ass and the mule [Java]
315. Three 3s
316. Three 4s
317. Three 5s
318. Tool for Constructing Orthogonal Latin Squares [Java]
319. Tower of Hanoi, the Hard Way [Java]
320. Transpositions
321. Triangular numbers that are also square
322. Trilateral Diagrams [Java]
323. Trinary Tree(s) underlying Primitive Pythagorean Triples
324. Twenty five boys and twenty five girls around a table.
325. Two Circles and a Limit [Java]
326. Two Colors in Two Rows [Java]
     • Two Colors in Two Rows II [Java]
327. Two Men of Tibet [Java]
328. Two Numbers Guessing Game [Java]
329. Universal Coloring [Java]
330. Universal Product Code [Java]
331. Venn Diagrams
     • Venn Diagrams I [Java]
     • Venn Diagrams II [Java]
332. Ways To Count
333. Weierstrass Product Inequality
334. Weighing 12 coins
     • Oddball Problem
     • Odd Coin Problems
335. What, how, and the Web [Java]
336. What Is Algorithm?
337. What Is Fraction?
338. What Is Infinity?
339. What Is Limit?
340. What is so natural about “natural logarithms”?
341. WHEN THE COUNTING GETS TOUGH, THE TOUGH COUNT ON MATHEMATICS
     • Matrices Help Relationships
     • An Airline Problem
342. Where To Start? [Java]
343. Why 1/3 + 1/4 = 7/12?
344. Why 17?
345. Wilson's Theorem
     • Geometric Proof of Wilson's Theorem
346. With One 4
347. Wolf and Rabbit [Flash]
348. Word Problems [Java]
349. Zeros and Nines [Java]

Copyright © 1996-2009 Alexander Bogomolny