Question

this is only for intelligent person

Answer 1

a) Let's assume following is the number line

  |-----------------|------|
-11                  0      +6

Clearly, the total distance is 17.

We can also represent the same thing as follows:

 |-----------------|------|
0                  +11      +17


Let's assume that there are m number of Heads and n number of Tails so that Pi reaches his destination. So Pi took total 2m steps towards destination and 4n steps away from destination.

So 2*m - 4*n = 17 
=> 4n = 2m - 17
if we put x and y by trial and error we see a following trend:

m             n
---------------------
0            -17/4
1            -15/4
2            -13/4
.             .
.             .
.             .
9             1/4      
10           3/4
11            5/4

So we see that for successive values of m, n is in form of an (odd number)/4, which will never be an integer because odd numbers are not divisible by 4.

Since we have assumed that m and n are the numbers of tosses, they must be integers. So we get a contradiction and hence no moves are possible such that Pi reaches to a position of +6 from an initial position of -11.

b) Assuming that moving left will be negative and moving right will be positive, the sequence will be as following:
-20 - 1 + 2 - 3 + 4 -5 + 6 - ... -99 + 100
= -20 + (2 + 4 + 6 + ... + 100) - ( 1 + 3 + 5 + ... + 99 )
= -20 + (50 * (2+100))/2 - (50 * (1 + 99))/2
 [Since sum of AP = n * (first term + last term) / 2, where n is the total number of terms in AP. Here n = 50]
= -20 + 2550 - 2500
=30
So his final position will be X=+30

Answer 2

Answer is given below:-----

A) Let's assume following is the number line

  |-----------------|------|
-11                  0      +6

Clearly, the total distance is 17.

We can also represent the same thing as follows:

 |-----------------|------|
0                  +11      +17


Let's assume that there are m number of Heads and n number of Tails so that Pi reaches his destination. So Pi took total 2m steps towards destination and 4n steps away from destination.

So 2*m - 4*n = 17 
=> 4n = 2m - 17
if we put x and y by trial and error we see a following trend:

m             n
---------------------
0            -17/4
1            -15/4
2            -13/4
.             .
.             .
.             .
9             1/4      
10           3/4
11            5/4

So we see that for successive values of m, n is in form of an (odd number)/4, which will never be an integer because odd numbers are not divisible by 4.

Since we have assumed that m and n are the numbers of tosses, they must be integers. So we get a contradiction and hence no moves are possible such that Pi reaches to a position of +6 from an initial position of -11.

b) Assuming that moving left will be negative and moving right will be positive, the sequence will be as following:
-20 - 1 + 2 - 3 + 4 -5 + 6 - ... -99 + 100
= -20 + (2 + 4 + 6 + ... + 100) - ( 1 + 3 + 5 + ... + 99 )
= -20 + (50 * (2+100))/2 - (50 * (1 + 99))/2
 [Since sum of AP = n * (first term + last term) / 2, where n is the total number of terms in AP. Here n = 50]
= -20 + 2550 - 2500
=30
So his final position will be X=+30
0.0

It is answered by me only.
My answer and pmadukar's answer may look same....but this is how the answer of this question will be.