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Puzzle Details

A Proof That 2 = 1:

1.           X = Y              let x=y
2.         X*X = XY             multiply by x on both sides
3.   X*X - Y*Y = XY - Y*Y       subtract y*y from both sides
4.  (X+Y)(X-Y) = Y(X-Y)         factorise
5.       (X+Y) = Y              divide by (x-y) on both sides
6.         Y+Y = Y              replace x with y
7.          2Y = Y              factorise
8.           2 = 1              divide by y on both sides

Where lies the flaw in the logic?

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Answer: On line 4 we are dividing both sides by (X-Y), now, since X=Y, this is 0. We are not allowed to divide by zero. This leads to a meaningless conclusion.

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