Surprise your buddies: A wonderful number trick

The trick:

We tell our friend to think of any random number. Then perform some random operations on it and .. Surprise! We tell him the final answer.

Note: Before we start the trick, we must think of two numbers, a and m. a is the number that we want as our answer and m is an arbitrary multiplier. Preferably a and m should be small for our convenience during arithmetic operations. Of course, we never disclose a and m to our friend before or during the trick !!

Let us begin !!

i) Think of a and m.
ii) Multiply a and m. P=a*m.

iii) Tell your friend to think of any number, say x.
iv) Tell him to multiply x with m.
v) Tell him to subtract P from the obtained product of x and m.
vi) Now, tell your buddy to divide the obtained difference by m.
vii) Now, you tell your friend to subtract the obtained quotient from x.

TADA !! Tell your friend - The answer is a.

Let us try the trick (An example) :

i) I think of two numbers:
   a=3. (3 should be my final answer.)
   m=2.
ii) P=6.

iii) You think of a number, say 7.         (x=7)
iv) Multiply 7 with 2. Result is 14.
v) Subtract 6 from 14. Result is 8.       (P=6)
vi) Divide obtained difference by 2, i.e. 8 by 2. Result is 4      (Here our m=2. Therefore, we divide difference by 2).
vii) Subtract obtained result from the number you had thought first, i.e. Subtract 4 from 7.

The answer is 3 !!!



© Rishabh Bidya

Total number of triangles in an inverted triangle system

Question:

To find total number of triangles in an inverted triangular system which has n triangles, each of which is inverted and contained inside its previous triangle.

Example: 

Solution : 

If the total number of triangles is n, 

Except for the innermost triangle, every triangle made results in three smaller triangles, so the number of such smaller triangles is 3*(n-1)

Apart from the smaller formed triangles, there are n triangles that form the figure.

Thus, the total number of such formed triangles will be the sum of both these numbers, i.e. 3*(n-1)+n

Therefore, we obtain the total number of triangles in an inverted triangle system is 4n-3

© Rishabh Bidya