# Category Archives: Problems

## A Problem On Several Triangles

A triangle $T$ 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 […]

## 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 the number of ones, third digit number of twos and […]

## 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 $8 \times 8$ chessboard so that every position on the board is under attack by at […]

## How many apples did each automattician eat?

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 it. The chat was intense, and they ended […]

## Applications 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 $xy(x+y) \times {(x^2+xy+y^2)}^2$ if $n \equiv \pmod{6}1$ […]

## 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 How to apply them. To identify procedures, […]

## The Mystery of the Missing Money - One Rupee

Puzzle Two women were selling marbles in the market place — one at three for a Rupee and other at two for a Rupee. One day both of then were obliged to return home when each had thirty marbles unsold. […]

## Derivative of x squared is 2x or x ? Where is the fallacy?

As we know that the derivative of $x^2$ , with respect to $x$ , is $2x$. i.e., $\dfrac{d}{dx} x^2 = 2x$ However, suppose we write $x^2$ as the sum of $x$ ‘s written up […]

Consider a sequence of functions as follows:- $f_1 (x) = \sqrt {1+\sqrt {x} }$ $f_2 (x) = \sqrt{1+ \sqrt {1+2 \sqrt {x} } }$ \$ f_3 (x) = \sqrt {1+ \sqrt {1+2 \sqrt {1+3 \sqrt {x} […]