## 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

Restriction of using only elementary geometry makes this math puzzle hard. Analyze and discover key patterns making the triangle more symmetric with respect to the obliquely placed target angle.

Submitted by Atanu Chaudhuri on Tue, 28/04/2020 - 22:05

Remove 2 matchsticks from the stick puzzle figure of 8 triangles to leave 6 triangles. Now the second part of the puzzle, "How many solutions can you find?" Total Recommended time is 30 minutes. Go through the systematic solution only after you try. It'll be fun if you try first..

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, 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...

Submitted by Atanu Chaudhuri on Sat, 04/04/2020 - 14:59

This time Three humans, one big monkey and two small monkeys are to cross a river in a boat that can carry at most two, only the humans and the big monkey can row the boat and most alarmingly—at all times number of monkeys must not become more than the number of humans on any bank of the river, Or else the humans will be eaten by the monkeys!....

Submitted by Atanu Chaudhuri on Thu, 02/04/2020 - 21:21

Two pigs and two hens must cross the river in a boat that starts for the opposite bank automatically when one of the four comes aboard. Constraint is—two pigs cannot cross the river in the boat together—it will sink....

Submitted by Atanu Chaudhuri on Wed, 01/04/2020 - 02:44

A farmer must cross a river with his pet fox, goose and bag of corn using a boat that is so small that he can take only one the three with him in a boat trip. Though he is ready to make as many trips as needed, he knows that the fox cannot be left alone with the goose, and the goose cannot be left alone with the corn....