## 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...

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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 Wed, 22/04/2020 - 23:14

This is the 6th puzzle session at fourth level of hardness of very hard category. This is a very hard puzzle with multiple bottlenecks to overcome right from the start. Valid DS evaluation for empty cells needs to be done early but in selected cells and limited to 3 digit long DSs. Cross-scan of row, column and 9 cell square, Digit subset analysis, Single digit lockdown and advanced use of Cycles provide the main breakthroughs. Solution of each step with strategies and techniques adopted are explained fully ...

Submitted by Atanu Chaudhuri on Tue, 21/04/2020 - 17:39

This is the 5th puzzle session at fourth level of hardness of very hard category. This is a very hard puzzle with multiple bottlenecks to overcome right from the start. Valid DS evaluation for empty cells needs to be done early but in selected cells and limited to 3 digit long DSs. Cross-scan of row, column and 9 cell square, Digit subset analysis and advanced use of Cycles provide the main breakthroughs. Solution of each step with strategies and techniques adopted are explained fully ...

Submitted by Atanu Chaudhuri on Mon, 20/04/2020 - 16:15

This is the 4th puzzle session at fourth level of hardness of very hard category. This is found to be really a very hard puzzle with multiple bottlenecks to overcome right from the start. Valid Digit subset evaluation to a large extent needed to be done very early that indicates the hardness of the puzzle. Digit subset analysis, Cycles and digit lockdown techniques are the primary techniques and resources used for overcoming the bottlenecks. A new structure of multiple parallel scans is discovered and converted to a new technique for the first time. Solution of each step with strategies and techniques adopted explained fully ...

Submitted by Atanu Chaudhuri on Sun, 19/04/2020 - 00:20

This is the 3rd puzzle session at fourth level of hardness that is placed in very hard category. This is found to be really a very hard puzzle with multiple bottlenecks to overcome right from the start. Valid Digit subset evaluation to a large extent needed to be done very early that indicates the hardness of the puzzle. Digit subset analysis, Cycles and digit lockdown techniques are the primary techniques and resources used for overcoming the bottlenecks. A new structure of chained single digit locks is discovered and converted to a new technique first time. Solution of each step with strategies and techniques adopted explained fully ...

Submitted by Atanu Chaudhuri on Sat, 18/04/2020 - 03:56

This is the 2nd puzzle session at fourth level of hardness that is placed in very hard category. As expected, this is found to be a difficult puzzle with multiple bottlenecks to overcome even at late stages. Digit subset analysis, Cycles and digit lockdown techniques are the primary techniques and resources used for overcoming the bottlenecks. Solution of each step is explained fully with strategies and techniques adopted...

Submitted by Atanu Chaudhuri on Thu, 16/04/2020 - 01:07

This is the 1st puzzle session at fourth level of hardness that is supposed to be very hard. As expected, this is found to be a difficult puzzle with multiple bottlenecks to overcome even at late stages. Digit subset analysis, Cycles and digit lockdown techniques are the primary techniques and resources used for overcoming the bottlenecks. Solution of each step is explained fully...

Submitted by Atanu Chaudhuri on Tue, 14/04/2020 - 00:33

This is the 13th puzzle session at third level of hardness. This is a difficult puzzle with multiple bottlenecks needed to be overcome and broken through. Digit subset analysis, 2, 3 and 4 cell Cycles and digit lockdown techniques are the primary techniques and resources used for overcoming the bottlenecks. Solution of each step is explained fully...