Maths puzzles

Maths puzzles:

   1. Prove -*-=+

-1*0=0

-1*(-1+1)=0

(-1*(-1))+(-1*1)=0, since a*(b+c)=a*b+a*c

(-1*(-1))+(-1)=0

(-1*(-1))-1=0

(-1*(-1))=1, hence -*-=+

2. Magic Square( other similar things explained at https://www.quora.com/profile/Choutapally-Prabhakar)

1 2 3                             è              

4 5 6                                                    

7 8 9

Draw lines diagonally, then jump each digit to empty boxes. It will become a magic square. Add any row, column or diagonal it will give same result.

Similarly, 4X4 magic square.

3.    Prove 2=1

Assume, x=1,

Multiply with x on both sides

X2=x

Deduct one on both sides

X2-1=x-1

(x-1)(x+1)=(x-1),

Divide by x-1 on both sides.

x+1=1,

substitute x=1,

2=1

Something is wrong in above proof, find out what?

4. How many squares are there in below diagram? [a 3X3 square]