21
Dec
09

Solutions to WU’s puzzles and riddles : 2 = 1(medium)


2=1I am trying to find all the solutions and put them together at a single place, So feel free to add comments and if you have a solution please do post. Cheers …🙂

Here is the puzzles link : http://www.wuriddles.com/

Question :

“Proof” that 2 = 1:

a = b
a2 = ab
a2 – b2 = ab-b2
(a-b)(a+b) = b(a-b)
a+b = b
b+b = b
2b = b
2 = 1

Does this argument make sense?

My Solution : This is a wonderful question which tests our basics of Mathematics. In the school we might have studied that we can’t divide a number with zero. Though the concept is very clear, people often tend to forget that basic principle. Here if we carefully observe its given that :

a = b                            =>              a – b = 0

In the 4th step it is given that (a+b)(a-b) = b (a – b)

and we tend to write this step  —— >  b = (a+b) (a – b)/(a – b)

and cancel out (a – b), but (a -b) = 0. So we cant divide the product with (a – b) or cancel out (a – b).

Hence that is the erroneous statement…….🙂


2 Responses to “Solutions to WU’s puzzles and riddles : 2 = 1(medium)”


  1. December 23, 2009 at 8:59 am

    How about this solution??

    0 * 1 = 0
    0 * 2 = 0

    => 0 * 1 = 0 * 2
    => 1 = 2

    hehe…😛

  2. 2 kilua
    December 26, 2009 at 4:54 am

    lol ……… he he …..😛


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