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Just another way to Multiply
Multiplication is probably the most important elementary operation in mathematics; even more important than usual addition. Every math-guy has its own style of multiplying numbers. But have you ever...
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Do you multiply this way!
Before my college days I used to multiply orthodoxly by this way. But as time passed, I learned new things. I remember, In a Hindi magazine named “Bhaskar Lakshya”, I read an article in which a...
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Four Math Problems
Solve the equation The function has derivatives. Show that if and then we can find such that . Let . For , let where the sum ranges over all pairs of positive integer satisfying the indicated...
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Three Children, Two Friends and One Mathematical Puzzle
Two close friends, Robert and Thomas, met again after a gap of several years. Robert Said: I am now married and have three children. Thomas Said: That’s great! How old they are? Robert: Thomas! Guess...
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The problem of the Hundred Fowls
This is a popular Chinese problem, on Linear Diophantine equations, which in wording seems as a puzzle or riddle. However, when used algebraic notations, it looks obvious. The problems states : If a...
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A Yes No Puzzle
This is not just math, but a very good test for linguistic reasoning. If you are serious about this test and think that you’ve a sharp [at least average] brain then read the statement (only) below...
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The Cattle Problem
This is a famous problem of intermediate analysis, also known as ‘Archimedes’ Cattle Problem Puzzle’, sent by Archimedes to Eratosthenes as a challenge to Alexandrian scholars. In it one is required...
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How Many Fishes in One Year? [A Puzzle in Making]
This is a puzzle which I told to my classmates during a talk, a few days before. I did not represent it as a puzzle, instead of a talk suggesting the importance of Math in general life. This is...
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On Ramanujan’s Nested Radicals
Ramanujan (1887-1920) discovered some formulas on algebraic nested radicals. This article is based on one of those formulas. The main aim of this article is to discuss and derive them intuitively....
View ArticleInteresting Egyptian Fraction Problem
Here is an interesting mathematical puzzle alike problem involving the use of Egyptian fractions, whose solution sufficiently uses the basic algebra.ProblemLet a, b, c, d and e be five non-zero complex...
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0.999…=1?
There is a clinical fallacy which proves 0.999… =1.First we assume the repeating decimaln=0.9999… …(i) Then, 10n= 9.9999… …(ii)Subtracting equation (i) from...
View ArticleSmart Fallacies: i squared equals to 1, 1 equals to 2 and 3
This mathematical fallacy is due to a simple simple assumption, that $ -1=\dfrac{-1}{1}=\dfrac{1}{-1}$ .Proceeding with $ \dfrac{-1}{1}=\dfrac{1}{-1}$ and taking square-roots of both sides, we get:$...
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What’s the question, if the answer is ‘No!’
Infinitely many answers questions are possible to the answer, “No”. So, our real task should be to find one of THOSE many, which seems to be a perfect one.A simple and the first ever logical approach...
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An Elementary Problem on Egyptian Fractions
Few math problems, specially, problems on Numbers are very interesting. In this “Note”, I’ve added a classical problem, as follow: Solve $ \dfrac{1}{w} + \dfrac{1}{x}+ \dfrac{1}{y} + \dfrac{1}{z}=1$...
View ArticleA Possible Proof of Collatz Conjecture
Our reader Eswar Chellappa has sent his work on the solution of ’3X+1′ problem, also called Collatz Conjecture. He had been working on the proof of Collatz Conjecture off and on for almost ten years....
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Essential Steps of Problem Solving in Mathematical Sciences
Learning how to solve problems in mathematics is simply to know what to look for. Mathematics problems often require established procedures. To become a problem solver, one must know What, When and...
View ArticleApplications of Complex Number Analysis to Divisibility Problems
Prove that $ {(x+y)}^n-x^n-y^n$ is divisible by $ xy(x+y) \times (x^2+xy+y^2)$ if $ n$ is an odd number not divisible by $ 3$ . Prove that $ {(x+y)}^n-x^n-y^n$ is divisible by $ xy(x+y) \times...
View ArticleD’ ALEMBERT’s Test of Convergence of Series
Statement A series $ \sum {u_n}$ of positive terms is convergent if from and after some fixed term $ \dfrac {u_{n+1}} {u_n} < r < {1} $ , where r is a fixed number. The series is divergent if $...
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