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“Women are now equal to the Men” Really? It is so?
यत्र नार्यस्तु पूज्यंते, रमन्ते तत्र देवता । Means: Where women are honoured, There roams God. The Protection of Women from Domestic Violence Act, (PWDVA) 2005 resulted from years of effort by women’s...
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Solving Ramanujan’s Puzzling Problem
Consider a sequence of functions as follows:- ……and so on to Evaluate this function as n tends to infinity. Or logically: Find . Solution Ramanujan discovered which gives the special cases for and...
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Derivative of x squared is 2x or x ? Where is the fallacy?
As we know that the derivative of , with respect to , is . i.e., However, suppose we write as the sum of ‘s written up times.. i.e., Now let then, This argument appears to show that the derivative of...
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Six Puzzles
Assume that the English letters are digits (from 0 to 9 ) and they satisfy the given relations, then you have to solve each equation for these letters. For Example: can have a solution: Similarly, Try...
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A College Level Problem on Jensen’s Inequality
Problem Given, . Prove that . Solution It is natural to make trigonometric substitution for some , Note that the monotonicity of the cosine function combined with the given inequalities shows that the...
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A Problem on Ordinary Nested Radicals
Problem Prove or disprove that Solution In order to simplify the radicals, the radicands should be forced to equal square numbers (e.g., should be a square of some number). Numbers whose squares have...
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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. Math problems often require established procedures and one must know What & When to apply them. To identify...
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A Problem on Infinite Sum and Recurrence Relations
Problem Consider the infinite sum where the sequence is defined by , and the recurrence relation for all positive integers . If can be expressed in the form where & are relatively prime positive...
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Number Game: The Word Addition
Consider the summation of letters : In the addition shown above, the sum represents a word. We have to find this word — on the conditions given below: Each letter represents a different digit. No...
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Applications of Complex Number Analysis to Divisibility Problems : Two...
Problem Prove that is divisible by if is an odd number not divisible by . Prove that is divisible by if Solution 1.Considering the given expression as a polynomial in , let us put . We see that at the...
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A General Problem on functions
Problem Let denote the set of all integers (as usually it do ). Consider a function with the following properties: for all . Is it possible that all positive divisors of occur as values of ? A happy...
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D’ ALEMBERT’s Test of Convergence of Series
Statement A series of positive terms is convergent if from and after some fixed term , where r is a fixed number. The series is divergent if from and after some fixed term. D’ Alembert’s Test is also...
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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 for , all being positive integers. – This problem is quit easy...
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Bicycle Thieves – A puzzle
One day a man, who looked like a tourist, came to a bicycle shop and bought a bicycle from a shop for $70. The cost price of the bicycle was $60. So the shopkeeper was happy that he had made a profit...
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Fox – Rabbit Chase Problems
Part I: A fox chases a rabbit. Both run at the same speed . At all times, the fox runs directly toward the instantaneous position of the rabbit , and the rabbit runs at an angle relative to the...
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How many apples did each automattician eat?
Image via Wikipedia Four friends Matt, James, Ian and Barry, who all knew each other from being members of the Automattic, called Automatticians, sat around a table that had a dish with 11 apples in...
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Chess Problems
In how many ways can two queens, two rooks, one white bishop, one black bishop, and a knight be placed on a standard chessboard so that every position on the board is under attack by at least one...
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Two Interesting Math Problems
Problem1: Smallest Autobiographical Number: A number with ten digits or less is called autobiographical if its first digit (from the left) indicates the number of zeros it contains,the second digit...
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A Problem On Several Triangles
A triangle is divided into smaller triangles such that any two of the smaller triangles either have no point in common, or have a vertex in common, or actually have an edge in common. Thus no two...
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How Genius You Are?
Let have a Test: You need to make a calculation. Please do neither use a calculator nor a paper. Calculate everything “in your brain”. Take 1000 and add 40. Now, add another 1000. Now add 30. Now, add...
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