Solution:

1

Explanation.
At every step number of joints goes down by 1.
i.e
8 have 6 joints
9 have 5 joints
5 have 4 joints
3 have 3 joints
7 have 2 joints
1 has 1 joint

You can also watch the video for an explanation

Solution:

The Patient will follow the path from room number-13 to room-no.4 as shown in the picture below.

Solution:

1 7
X 4
---
68
25
---
93

For an explanation, you can watch the video.

Solution:

Add two squares as shown in the picture below.

Solution:

Image
https://gpuzzles.com/new/img/riddles/Presence-Of-Mind-Picture-Riddle.png
can be changed to
https://gpuzzles.com/new/img/riddles/Presence-Of-Mind-Picture-RiddleAns.png
By adding 3 letters "Ans".

Solution:

U472BMT

Explanation:
The code can be decoded to sound as "U four seven two B M T"
U
four (4)
seven (7)
two (2)
B
M
T

Solution:

Mahrez Pick 4 marbles.

Explanation:
How many marbles Vardy picks, Mahrez needs to make sure that only 1 marble is left after his move, So Vardy needs to pick the last marble.

Example:
If Vardy picks 1, Mahrez picks 5
If Vardy picks 2, Mahrez picks 4
....
...
If Vardy picks 5, Mahrez picks 1

Solution:

XI - I = X

Explanation:
Remove I (Roman equivalent of number 1) from the left side, you will the get the number on the right.
29 - 1 = 30
XXIX - I = XXX (Roman equivalent of number 30)

14 - 1 = 15
XIV - I = XV (Roman equivalent of number 15)

9 - 1 =10
IX - I = X (Roman equivalent of number 10)

Similarly,
11 - 1 = 10
XI - I = X (Roman equivalent of number 10)

Solution:

Step5 is Wrong.

Explanation:
We divided the two sides by (A-B).Since A = B which indicates that (A - B) = 0 and we cannot divide by zero.

Solution:

31

Explanation:
Ramanujan lighting the candles in binary.
11110 =30
11111 =31