image source: Mental confusion

Mental Exercises:
12 Best mental exercises
Mindboggling puzzles
Mathematic puzzles
Miscellaneous mindstimulators
Logical paradoxes or fallacies
Synchronic thinking
Multidimensional
Optical Illusion
Main references: Wikipedia's Paradoxes
Fallacy
Deductive fallacy
plato.stanford.edu Paradoxes and Contemporary Logic
Click on individual answers or links to get the answers.
Moderately difficult  Moderately difficult 
Can 2=1 ?If A=BMultiply both sides by A, you get A²=AB. Subtract B² from both sides, you get A²B²=ABB². Factor both sides make it (A+B)(AB)=B(AB). Divide both sides by (AB), you get A+B=B. Because A=B, therefore B+B=B, If 2B=B, then 2=1. Answer Similar puzzle can also be seen at http://www.omardo.com/en/: Math Puzzle (2=1). 
This is the puzzle slightly modified from: www.mindbreakers.com: Dime turns into a dollar If you square $ 0.10 it equals to this $ 0.01. $ (0.10)² = $ 0.01. So you will get a penny However if you square 10 cents you get 100 cents. (10)² cents = 100 cents. So you just earned a full dollar out of a dime If you square $ 1 it equals to this $ 1. $ 1² = $ 1. So you will still get a dollar. However if you square 100 cents you get 10000 cents. (100)² cents = 10000 cents. So you just earned a hundred dollars out of a dollar. Answer Answer 
Can 2=1 ?.  Penny is bettwr than dollar. 
Bird brain  Nobrainer 
Source: larrymwalkerjr.blogspot.com Natural Born Conservative (alt)> Black and White 
Source: instruct.westvalley.edu INTRODUCTION TO LOGIC> I think, Therefore I am. 
Black and White  Dogs = Cats 
Good examples of logical fallacies can seen at these sites: www.infidels.org: Logic & Fallacies. www.nizkor.org: Fallacies. 
Good examples of logical paradoxes can seen at these sites: Wikipedia's List of paradoxes. Socratic paradox: "I know nothing at all." Quine's paradox: "Never say 'never'" Liar paradox : "This sentence is false." Liar paradox: The fictional speaker Epimenides, a Cretan: "All Cretans are liars." 
Logical fallacies.  Logical paradoxes. 
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