## Hard Algebra Puzzles Solved by Basic Exponent Concepts and Reasoning

Solve for $x$ in $(x^2-5x+5)^{(x^2-11x+30)}=1$. Looks hard? Rest assured, you too can solve it. Just use basic exponent concepts and a bit of mathematical reasoning...

Submitted by Atanu Chaudhuri on Sun, 16/08/2020 - 20:29

Solve for $x$ in $(x^2-5x+5)^{(x^2-11x+30)}=1$. Looks hard? Rest assured, you too can solve it. Just use basic exponent concepts and a bit of mathematical reasoning...

Submitted by Atanu Chaudhuri on Tue, 04/08/2020 - 22:53

You also can solve this hard but finally not so hard problem if you take up analytical reasoning based approach. Surprisingly, knowledge of only elementary geometry is sufficient to solve it...

Submitted by Atanu Chaudhuri on Sun, 26/04/2020 - 21:39

Find the 10 unique digit number having the special property that the number formed by digits from left to right up to the place for each of the 10 places is divisible by the place number—is a beautiful puzzle presented by John Conway. It is a large and complex puzzle but can be solved using only the basic concepts taught in middle schools…

Submitted by Atanu Chaudhuri on Thu, 27/12/2018 - 23:43

An older version of the monkey and the coconuts puzzle was modified by short story writer Ben Williams and published nearly a century ago. From then on the intriguing puzzle attained the status of one of the most attempted and least solved math puzzles of all time. We will present here easily understandable solutions to both using mathematical reasoning and for the modified version using in addition systematic enumeration…

Submitted by Atanu Chaudhuri on Sun, 09/12/2018 - 19:50

We will first present the classic folk puzzle of counting eggs for you to solve. Proceeding further, two ways to the solution will be presented and then the binding characteristics for this type of puzzles will be brought out in the form of framework for creation and systematic solution of similar types of puzzles...

Submitted by Atanu Chaudhuri on Wed, 28/11/2018 - 17:59

In this first part of NCERT solutions for class 10 maths on Real Numbers, we will introduce briefly the basic concepts on real numbers, the long division method formalized by Euclid in his division lemma and will treat in some details the solutions of a rich classic puzzle highlighting the application of division lemma as well as the power of mathematical reasoning based on the concept rather than formula...

Submitted by Atanu Chaudhuri on Sun, 26/06/2016 - 23:05

The mechanical approach to math problem solving relies heavily on manipulation of terms using low level mathematical constructs without using the problem solving abilities of the student. In this problem we have highlighted the possibility to solve a problem in many ways and also the application of less facts and more procedures approach, both working towards improving the general problem solving skills of the student...

Submitted by Atanu Chaudhuri on Fri, 12/02/2016 - 15:14

All things change. This is nothing new. But the change itself may be considered an important entity to be used as resource for efficient problem solving in various areas of activity and thought. In particular, Change analysis technique may aid you to solve your problem faster at less cost...

Submitted by Atanu Chaudhuri on Sun, 07/02/2016 - 11:18

In a set of components each having multiple entities, identify the base to be equalized; identify the target value to be equalized to and equalize the bases of each component in the set to establish direct relationship between the other entities...

Submitted by Atanu Chaudhuri on Sat, 30/01/2016 - 20:47

Base equalization technique produces quick solutions in indices problems. But that is not the only area of application of this more general concept. For solving problems on fractions also, the base equalization technique is indispensable...