# Arithmetic articles, problems, and puzzles

### What Is Arithmetic?

What Is Algebra?

Mental Calculations

Algebra: Articles and Problems

- 100 Grasshoppers on a Triangular Board
- 1089 and a Property of 3-digit Numbers [Java]
- Four Digits Magic Prediction [Java]
- Five Digits Magic Prediction [Java]

- 12 Coins in Verse
- 24 with One Digit
- 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]

- A Farewell Problem for the Year 2017
- A Welcome Problem for the Year 2018
- A Line in a Square Grid [Java]
- A Missing Digit
- A Number Theoretic Problem With the Floor Function [JavaScript]
- A Problem from the 1967 IMO Shortlist
- A Problem of Divisibility by 17 from the 1894 Eötvös Competition
- A Problem That Fermat Might Have Liked
- A Property of Unimodal Integers as a Whole [JavaScript]
- A Quadratic Equation in Three Variables
- A Remote Decimal Digit
- A Short Equation in Reciprocals
- Abacus in Various Number Systems [Java]
- About numbers
- Absolute Value
- Achieve the Equilibrium [Flash]
- Adding a Long List of Numbers
- Addition and Subtraction of Integers
- Algorithm for Computing LCM [Java]
- Aliquot Game [Java]
- An Application of Mental Arithmetic to Highway Safety
- An Arithmetic Magic Trick [Java]
- An Equation in Factorials
- An Equation Involving the Total Number of Digits
- An Inequality for Grade 8
- An Interesting Number
- An Age Conundrum with Men of the Cloth
- An Equation in Integers and Rational Numbers [JavaScript]
- An Olympiad Problem With the Floor Function [JavaSCript]
- Arithmetic magic matrix [Java]
- Arithmetic Operations in Various Bases [Java]
- Arithmetic Paradoxes
- Bachet's Magic Trick [Java]
- Barcode Encoding
- Barcode Magic [Java]
- Base Converter [JavaScript]
- Basic Rules of Counting
- Billiard Handicap
- Binary Color Device [Java]
- Binary Euclid's Algorithm
- Breaking Chocolate Bars [Java]
- Broken Calculator [Java]
- Caterpillar [Flash]
- Chameleons of Three Colors
- Chinese Remainder Theorem
- Collatz Conjecture [Java]
- Common Multiples and the Least Common Multiple [Java]
- Compare Fractions: Interactive Practice [Java]
- Computer As a Magician [Java]
- Counting and Equivalent Fractions
- Counting: The Beginning of Mathematics [Java]
- Counting Chips On a Circle [Java]
- Counting Coins and Their Values
- Counting Squares in a Square [Java]
- Counting Triangles [Java]
- Counting Triangles II [Java]
- Covering A Chessboard With Domino
- Dominoes on a Chessboard [Java]

- Cryptarithms [JavaScript, Frames]
- Curious Identities Involving Integer Squares
- Distributive Law [Java]
- Dividing Loot Fairly
- Divisibility by 7
- Divisibility by 9 and 11
- Divisibility by 81
- Divisibility Criteria
- Divisibility by 7, 11, and 13
- A Problem of Divisibility [Java]

- Doubling Investment for a Fee And Getting Zero [JavaScript]
- EAN-13 Encoding [Java]
- Egyptian Multiplication [Java]
- Elegance in Integers by Dorin Marghidanu
- Emptying a Big Number of Boxes
- Euclid's Algorithm
- Euclid's Algorithm: An Interactive Illustration [Java]
- Euclid's Game [Java]
- Euclid's Game on a Square Grid [Java]
- Every composite number is the product of some factors and also the sum of the same numbers
- Extension of Euclid's Algorithm
- Factorial Divisibility
- Factorials and division
- Factoring with the Factor Tree [Java]
- Factors And Multiples
- Falsity implies anything
- Farey Series
- Fast Arithmetic Tips
- Fibonacci Numbers in Equilateral Triangle
- Finger Counting
- Formal Framework, an example
- Formula for Primes
- Four 3s
- Four 4s
- Four 5s
- Four Pegs That Form a Square
- Four Pegs That Form a Square [Java]

- Four Weighings Suffice
- Fraction Comparison [Java]
- Fraction Comparison Sped up [Java]
- Fractions on a Binary Tree
- Fractions on a Binary Tree II
- Frieze Patterns [Java]
- Fun with digits
- Funny Arithmetic [JavaScript]
- Gasoline Stations on a Circular Trek
- GCD and LCM via Factor Tree [Java]
- GCD and LCM by Plain Factorization [Java]
GCD(M, N) × LCM(M, N) = M × N [Java]- Geometric view of the Sieve of Eratosthenes [Java]
- Gergonne Magic Trick [Java]
- Grandfather's Bill [Javascript]
- Hardy's Example of Non-Serious Theorems
- Heads and Tails [Java]
- Hour glass timing
- How to efficiently defend a castle
- Identical Twins Puzzle
- Identities in the Multiplication Table [Java]
- Illustrated Sum of Cubes - All in a Plane
- Impossible Machine
- Infinitely many proofs that there are infinitely many primes
- Infinitude of Primes Via Powers of 2
- Integer Iterations on a Circle [Java]
- Integer Iterations on a Circle III [Java]
- Is a Sum a Prime Number?
- ISBN Encoding [Java]
- Jumping Isn't Everything [Java]
- Langford and Skolem Sequences [Java]
- Latin Squares [Java]
- Lattice Multiplication [Java]
- Leibniz and Pascal Triangles [Java]
- Less than, Equal to, Greater Than Symbols
- Listing All the Composite Numbers [Java]
- Long Multiplication [Java]
- Long Runs of Composite Numbers
- Looking for the Prime Decomposition
- Loop or Halt [Java]
- Magic in Square [Java]
- Make An Identity [Java]
- Make It All Zeros [Java]
- Many Jugs to One I
- Many Jugs to One II
*Market Day*- Math Card Trick
- Math Telepathy [Java]
- Mathematical Proof
- Mathematicians and Musicians [JavaScript]
- Mediant Fractions
- Minimax Principle [Java]
- Modular Arithmetic [Java]
- Moving Chips in Pairs Down a Checkerboard [Java]
- Napier Bones [Java]
- Negative Coconuts
- Nine Squares [Java]
- Number Guessing Game [Java]
- Number of Factors of an Integer
- Number sequences and Pigeonhole [Java]
- Number System With Base 36
- Numbers That Divide the Others' Sum
- Odd Scoring [Java]
- On Gauss' Shoulders
- One Dimensional Ants
- Operations on Fractions [Java]
- Order. Well-ordered sets.
- Ordinal Numbers
- 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]

- Billy is twice as old as Sally [Java]
- Parity counting [Java]
- Party Acquaintances [Java]
- Peasant Multiplication [Java]
- Pennies in Boxes [Java]
- Permutations
- Pigeonhole Principle
- Place Value [Java]
- Letter Count in a Sentence [Java]

- Powers of 6 and 7771
- Probability of Divisibility
- Problem 4132 from Crux Mathematicorum
- Product of Simple Fractions [Java]
- Proizvolov's Identity [Java]
- Proofs Without Words [Java]
- Properties of GCD and LCM
- Psychology of 0.99999...
- Question That Changes with Time
- Represent 4 with four digits
- Representation of 3 with Three Equal Digits
- Represent 6 with three digits
- Review of
*Arithmetic for Parents: A Book for Grownups about Children's Mathematics*by R. Aharoni - Rhind Papyrus
- Right Replacement [Java]
- The Rule of Change of Addends [Java]
- Russell's Paradox
- Scrub Tile Puzzle [Java]
- Self-descriptive Strings [Java]
- Self-reference
- Seven Integers That Add Up to 100
- Seven Terms Periodic Sequence
- Ship-Dock Theorem
- Sieve of Eratosthenes [Java]
- Sieve of Squares [Java]
- Simple Cellular Automaton [Java]
- Six Balls, Two Weighings
- Six Misnamed Coins, Two Weighings
- Slider Puzzles [Java]
- Solitaire in Two Colors [Java]
- Soriteses
- Soroban in Various Number Systems
- Splitting piles
- Squares, Circles, and Triangles [Java]
- Steinhaus' Problem [Java]
- Stern-Brocot Tree
- Straight Tromino on a Chessboard [Java]
- Suan Pan in Various Number Systems [Java]
- Subtraction Game [Java]
- Subtraction in a Rectangular Array [Java]
- Sums and Products [Java]
- Sums of powers of digits [Java]
- Superposition Principle
- Tables for Multiplication
- The ass and the mule [Java]
- Three 3s
- Three 4s
- Three 5s
- Tony Foster's Integer Powers in Pascal's Triangle
- Tool for Constructing Orthogonal Latin Squares [Java]
- Treasure Hunt in a Square Grid
- Treasure Hunt from Outside the Grid
- Two Colors in Two Rows [Java]
- Two Colors in Two Rows II [Java]

- Two Numbers Guessing Game [Java]
- Uncountability of the Reals - via a Game
- Uniqueness of Number 5
- Universal Product Code [Java]
- Unproperty of the Powers of 2
- Using Math Rules: An Example
- Weighing 12 coins
- What, how, and the Web [Java]
- What Is Fraction?
- When Two Wrongs Make One Right
- Why 1/3 + 1/4 = 7/12?
- With One 4
- With One Weighing
- Wolf and Rabbit [Flash]
- Word Problems [Java]
- Yet Another Puzzle with Hats
- Zeros and Nines [Java]

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