Solution:

If you look into the picture, you can see the cut lines. If the four people cut along with the lines, each one of them will have 1/5th of the cake.

Solution:

We now have a square of 3x3 size, 2 squares of 2x2 size and 5 squares of 1x1 size.

Solution:

2100 miles.

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

Solution:

100

Series of number that do not contain albhabet 'T'

Solution:

Everyone will done one day or other.

Abraham Lincoln era is too old and we expect most of them(if not all) to be dead by now.

Solution:

10

Explanation:
Equation 1 + 9 + 11 = 1 can be derived from
One (o) + nine (n) + eleven (e) = one => 1

Similarly for equation,
12 + 11 + 9
Twelve (t) + eleven (e) + nine (n) => ten (10)

Solution:

To do it, the marbles must be arranged as the vertices of an octahedron. If you are unsure, check the image below.

Solution:

I am word "Introvert"

Solution:

If you ask the guard who always tells the truth, he would tell you the other guard would point you to the door of death. If you ask the guard who always lies, he would tell you the opposite door of the truth-telling guard and point you to the door of death. In either case, both guards will point to the door of death so you should choose the other one.

Solution:

They use the bricks and dirt from the tunnel to stand on it.

Solution:

Solution can be verified from the picture below.