Solution:

Logic Matchsticks Problem can be solved as shown in image below

Solution:

3/7

Explanation:
If a 31day month starts on a Friday, Saturday or Sunday it will have five Sunday, if not it will have 4 Sunday.

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:

Hhe hung herself using big Ice slabs , which are now now melted and hence puddle of water.

Solution:

I + IX = X

The equation read from the other side becomes X = XI + I which is false.

Solution:

Isaac Newton picks up a piece of wood and lights it from the fire on the west end of the island.

He then quickly carries it near the east end of he island and starts a new fire. The wind will cause that fire to burn out the eastern end and he can then shelter in the burnt area.

(Funny Part : Isaac Newton survives the fire, but dies of starvation, with all the food in the forest burnt )

Solution:

2100 miles.

Each vowel equivalent to 500 and each consonant equivalent to -200

Solution:

The stranger said that he thought the room was his. If so, he must have had the keys to the room and thus he must not have knocked.

Solution:

Step one: First you will have to make 3 trips of 1,000 apples 333 miles. Then you will be left with 2,001 apples and 667 miles to go.

Step two: Next you will have to take 2 trips of 1,000 apples 500 miles. In this manner you will be left with 1,000 apples and 167 miles to go (you have to leave an apple behind).

Step three: At last, you will have to travel the last 167 miles with one load of 1,000 apples and you will be left with 833 apples when you reach the town

Solution:

If you see the picture, they formed a pentagonal shape and achieved the required.

Solution:

Six.

There are only five colors, so six socks guarantee that two will be the same color.