Solution:

No Excuse

Explanation:
Since there is no X listed =>No Excuse

Solution:

Put one black rock in one sack and put all the rest in the other one. In such manner you will get about 3/4 probability of surviving.

Solution:

If two widows, each having a son married the son of the other widow, and then by the consummation of marriage, both the couples had a daughter, all the aforementioned relationships will turn to be true.

Solution:

2 cakes

At each toll bridge you are required to give half of your cakes, and you receive one back. Which leaves you with 2 cakes after every bridge.

Solution:

16

Explanation:
9 [1x1] squares
5 [2x2] squares
1 [4x4] square
1 [4x4] square

9 + 5 + 1 + 1 = 16 squares.

Solution:

Move the coins as given in the figure and you will get the required result.

Solution:

-3 -1 1

Explanation:
-3 * 1 * -1 = 3(prime)
-1 - (-3) = 1 -(-1) = 2

Solution:

Put one red marble in one box and all other marbles in the 2nd box.

Probability :
50 + 24/49

Solution:

You can ask this question to any one person, "if I ask the man who is next you: which is the correct way and the road to the village, what would the person next to you answer?"
If you happened to ask this question to the liar, he will show you the wrong way.
And if you happened to ask this question to the one who says truth, he will also show you the wrong way.
Once you are done with this, take the other way. This will lead you to the village

Solution:

13 + 11 + 6 = 30

Explanation
The trick is that you just need to rotate '9' to form '6'.

Solution:

There are 3 fruits (1 grapes, 1 apples, and 1 oranges).