Solution:

512

Explanation:
The cube that remains will be 8 x 8 x 8. This will make a total of 512. This is because, when a layer is taken, it will be taken from all sides of the cube which will reduce the dimension be two and not one.

Solution:

The first figure tells you where you have to make the cut in the paper. Now you have two pieces of paper. If you rotate the right piece to 180 degrees, you will get what is shown in the figure two. Now the hole is in the center of the paper.

Solution:

QHJRPBWF

CYLINDER = UHGQGJWA
Reverse the letters of CYLINDER
REDNILYC
Position increase in first four letters by 3.
REDN becomes UHGQ

Position decrease in last four letters by 2.
ILYC becomes GJWA.

Thus in the same manner
HYDROGEN = QHJRPBWF

Solution:

10992

Explanation:
Each girl has seven bags with seven adult cats each.
Also, each adult cat has seven little cats.
Thus each girl has 49 adult cats and 343 little cats.

Hence, seven girls will have
343 adult cats and 2410 little cats.

If we calculate the number of legs now.
Girls = 7 * 2 = 14
Cats + Little cats = 2744 * 4 = 10976

Total legs = 10976 + 14 = 10990

Since I also walked in the room, there will be two more legs.
Now total legs = 10990 + 2 = 10992.

Solution:

The Pink servant is the truthful one.

In order to prove the same, let us take all of them one by one assuming that the selected one is telling the truth. This is because all of them are disagreeing with each other which means that three servants are lying while one is telling the truth.

Assume that the Orange servant is the truthful one. Under this condition, the orange one is having either 6 or 8 legs. And each of the other octopus is lying will then have 7 legs. Under this condition, the total number of legs will be 6 + 7 + 7 + 7 = 27 legs or 8 + 7 + 7 + 7 = 29 legs. But the Orange servant said that they have 28 legs all together. Thus he is lying.

Now if we simply follow the same logic with all other servants as well, we will come up to the conclusion that only the Pink servant is truthful.

Solution:

Time

Solution:

If we take the worst case, she will have to take out 12 + 1 = 13 candies.

Solution:

The wife booked a two way ticket for herself and booked a one way ticket for her husband.

Solution:

THINK

Change N to C
THICK

Change H to R
TRICK

Change I to A
TRACK

Change K to T
TRACT

Change C to I
TRAIT

Change T to N
TRAIN

Change T to B
BRAIN

Solution:

29 rungs.
Since he is standing on the middle rung in the beginning,
Let the middle rung be x
He climbs 6 rungs first and then climbs down rungs and again climbs 18 rungs to reach the top.
Thus the position is now,
X+6-10+18 = x + 14.
This position is on the top rung.
Thus the ladder has 14 rungs above the middle rung and also it must be having 14 rungs down the middle point as well.
14+14+1 = 29.
Thus there are total 29 rungs in the ladder.