Even odd magic trick

Even Odd Magic Trick

Step 1. Ask to someone to choose a number and then triple that number.

Step 2. Product  may be even or odd .

    1. if product  is odd :

      Request him to add unity to it & take half of it.

b)   if product is even :

      Request him to take half of it.

Step 3.  Tell  him to multiply the result of the second step  by 3.

Step 4. Ask how many integral times 9 divides into the latter product third step : suppose the answer to be n.

Step 5.  Then the number thought of  was 2n or 2n + 1 , depends on the first step was even or odd.

Explanation :

It is obvious , because even number is of the form 2n . And applies these successive operation step-by-step—

Step 1.   2n x 3 = 6n ( even)

Step 2.   6n / 2 = 3n

Step 3.   3n x 3 = 9n

Step 4.   9n / 9 = n

Step 5.    2n

Every odd number is of the form 2n + 1 . And applies these successive operation step-by-step—

Step 1.   (2n + 1 ) x 3 = 6n + 3        ( odd)

Step 2.(6n+3+1) / 2 = 3n + 2

Step 3.   (3n + 2) x 3 = 9n + 6

Step 4.   (9n + 6) / 9 = n + a ( remainder )

Step 5.    2n + 1.

These results are formulated from above method.

Example :

In this puzzle or math magic at least two parties are involved like A and B.

“A” is a performer in this puzzle.

“B” is a listener in this puzzle.

A asked to B :

choose any number and triple it.

B :  OK done ! (  calculation in mind  , let choose a number 5 , then 5 x3 = 15 )

A : This product may be even or odd .

a)   if product  is odd :

      Request him to add unity to it & take half of it.

b)   if product is even :

      Request him to take half of it.

B : it is odd ( calculation in mind ;  15+1= 16   and 16/2 = 8).

A :  Now multiply by 3 .

B : OK done ! ( calculation in mind 8×3 = 24 )

A : Now divide by 9.

B: OK done ! ( calculation in mind 24 / 9 = 2(quotient) + 6(remainder)

A : Tell me quotient.

B : 2

A : 5 will be the number originally thought.( 2n + 1 )

B : surprised.

Readers can also surprised your friends , using this math magic trick & try it.