## 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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These form resources related to problem solving, critical thinking, creativity and so on.

* Brain teaser: *Puzzles and brain teasers followed by detailed solutions, and not just answers.

* Sudoku:* Detailed explanatory Sudoku game plays at hardness level Easy, Medium, Hard and Very hard. The series is ideal for learning hands-on how to play Sudoku with growing skill even by an absolute beginner.

* Reflections:* Thoughtful articles on varied topics.

* Innovative creations:* Showcasing creativity in ideas or things.

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 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 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...

Submitted by Atanu Chaudhuri on Sun, 12/04/2020 - 18:41

This is the 12th puzzle session at third level of hardness.The hardness of this puzzle arose primarily from the need to use Digit subset analysis and Cycle technique frequently for valid digit identification for a cell. Though the problem didn't pose a real hard bottleneck that needed special efforts to break though, for a large portion of solving process careful analysis was needed. Solution of each step explained fully...

Submitted by Atanu Chaudhuri on Thu, 09/04/2020 - 20:17

This is the 11th game play session at Sudoku third level of hardness.The specialty of this game has been use of large number of cycles that helped at the start. Interesting has been the four cell single digit rectangular lockdown cycle, a special structure that provided the much needed breakthrough in this specially difficult Sudoku game. Solution of each step explained fully...

Submitted by Atanu Chaudhuri on Wed, 08/04/2020 - 20:40

You are given 8 identical looking balls with one of the balls is fake and heavier or lighter than the other 7. You have to identify the fake ball in 3 weighing attempts. Given is a two-pan balance with no weights. In how many ways can you solve the puzzle?

Submitted by Atanu Chaudhuri on Mon, 06/04/2020 - 20:24

You are given 8 identical looking balls with one of the balls slightly heavier than the other 7. You have to identify the heavier ball in 2 weighing attempts. Given is a two-pan balance with no weights. In how many ways can you solve the puzzle is the second harder part of the puzzle...

Submitted by Atanu Chaudhuri on Sun, 05/04/2020 - 00:28

Three couples—king and queen, and minister and washerman with their wives have to cross a river in a boat that can carry at most 2 passengers at a time. The husbands are jealous and without her husband, no lady can be left on any side of the river with other male(s). To make matters worse, the washerman or washerwoman can travel together but not with anyone of the other two couples. Each of the six can row the boat...