Magic with numbers

1. The Paradox of the digits

It's now official: 1=2

And here is the proof...

(1) Given X = Y
(2) XX = XY Multiply both sides by X
(3) XX - 2Y = XY - 2Y Subtract 2Y from both sides
(4) (X+Y)(X-Y) = Y(X-Y) Factor both sides
(5) (X+Y) = Y Cancel out common factors
(6) Y+Y = Y Substitute in from line (1)
(7) 2Y = Y Collect the Y's
(8) 2 = 1 Divide both sides by Y

Therefore 2 = 1 !!!!

Brain teasers

1. Mjinga wa kwanza kamwambia mjinga wa mwisho "Ukinishinda werevu ujue kwa ujinga
huniwezi" wa mwisho naye kajibu "Huniwezi hata kidogo"!. Swali : Je yupi ndiye
mjinga zaidi?



2. Three boys decided to contribute 10/= each to buy a book worth 30/=. On reaching the
Book store they were told that it now costs 25/=. They decide to take back 1/= each
and save the remaining 2/=.

Observation..
>If each took back 1/=, doesn't it mean that they contributed 9/= each? This implies
that the total contribution is : 9*3 + 2(saved) giving 29.

Question is..
> Where is the remaining 1/= ?????



3. A Lawyer stood up and said "All lawyers are liars". The question is, is the
statement true or false? (Hint: concentrate on the statement).
Observer 1: It is True.
But if it is true then the statement is false since it was made by a
by a lawyer and a lawyer is supposed to be a liar.
Observer 2: It is False.
But if it is false (ie All lawyers are not liars) then the statement
may be true because we assume that a lawyer can tell the truth.

4. A male barber SWEARS and writes outside his shop:
"FROM NOW ON I WILL ONLY SHAVE MEN IN THIS TOWN WHO DO NOT SHAVE THEMSELVES"

Question: Does the barber shave himself?