Solution:

Sam : 2
Dean : 5
Castiel : 7

Age diff
7 - 2 = '5' is prime
7 - 5 = '2' is prime
5 - 2 = '3' is prime

Solution:

As shown in the picture below, you should tilt the barrel so the liquid will touch the upper end of the barrel. So if the bottom part of the barrel is visible then it's not half full.

Solution:

111111111

Explanation:
It's a maths magical square root series as :
Square root of number 121 is 11
Square root of number 12321 is 111
Square root of number 1234321 is 1111
Square root of number 123454321 is 11111
Square root of number 12345654321 is 111111
Square root of number 1234567654321 is 1111111
Square root of number 123456787654321 is 11111111
Square root of number 12345678987654321 is 111111111 (answer)

Solution:

They were the same person "Grover Cleveland".

Solution:

Both 3 and 4th

Explanation:
- The water in tank1 will get filled up to the connectivity of tank1 and the tank2 and then it will start flowing to tank2.
- The water in tank2 will get filled up to the connectivity of tank2 and the -tank3 and then it will start flowing to tank3.
- The water in tank3 will get filled up to the connectivity of tank2 and the tank3 and then it will start flowing to tank3.
- As the outlet of tank3 and inlet of tank4 are not at the same level, water will continue to fill tank3 till the inlet of tank4.
- Now both the tank3 and tank4 fill simultaneously until both fill together.

Solution:

The five cards must contain at least one card of the same suit.
Let's assume Rhodes placed one of the two cards of the same suit at the end and the second card was given to Daniel.
In that case, Daniel will know the suit of the card.

Now the real question is how Rhodes made sure that Daniel also knows the number of the card.

Daniel got four cards and one of them will determine the suit, so we are left with 3 cards.
3 cards can be arranged in 3! ways i.e. 6 ways but our card numbers can vary from 1 to 13.
Since we have two cards of the same suit we will make sure that we don't pick the King (13). This leaves us with 12 numbers.

We can also distinguish card from upside down position, therefore, we now have 6 * 2 ways to arrange these card.
"TADA.... We cracked the magic trick".

Let us assume that the smallest card is C1U (upwards position) and C1D (downwards position). Similarly, we have C2U, C2D, C3U and C3D

According to that, the 12 possible arrangements are:
C1U C2U C3U => NUMBER 1
C1U C3U C2U => NUMBER 2
C2U C1U C3U => NUMBER 3
C2U C3U C1U => NUMBER 4
C3U C1U C2U => NUMBER 5
C3U C2U C1U => NUMBER 6
C1D C2D C3D => NDMBER 7
C1D C3D C2D => NDMBER 8
C2D C1D C3D => NDMBER 9
C2D C3D C1D => NDMBER 10
C3D C1D C2D => NDMBER 11
C3D C2D C1D => NDMBER 12

Please note that king (number 13) is not possible as discussed already.

Solution:

8! minutes

Explanation:
28 days x 24 hours x 60 minutes = 40,320 = 8! minutes.

Solution:

It can be done as shown in the picture below.

Solution:

No

Explanation:
Assume that the rope can be stretched forever. Assume the rope is evenly stretched. The moving speed of the end point of the rope (relative to the starting point) is 1000 cm/second.

Each second the ant moves 1cm, at the same time that 1cm rope stretches to be 1000+1000t1000+1000(t−1)= t+1tcm where t is the number of seconds after the ant is on the rope. Therefore, the ant has a moving speed of t+1t cm/second.

Therefore, the moving speed of the ant is far less than the moving speed of the end point of the rope.

Filk will never reach the end of the 1000 cm long rope.

Solution:

Adam betrayed Eve.

Explanation:
Eve may not jump because of the survival instinct or can be related to some emotions and can, therefore, be given a benefit of the doubt, whereas Adam having the parachute seem a calculated plan implies that he definitely betrayed Eve.