Random Puzzles 

Workings

Hint
We'll assume that we can actually fold it this many times.

Answer
Very thick indeed! The paper doubles in thickness with each fold. If we could fold it 50 times, it would be around 70 million miles thick!

1 fold would be 0.1 + 0.1 = 0.1 x 2 ^ 1 = 0.2 mm
2 folds would be 0.1 + 0.1 + 0.1 + 0.1 = 0.1 x 2 ^ 2 = 0.4 mm
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10 folds would be 0.1 x 2 ^ 10 = 102.4 mm
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50 folds would be 0.1 x 2 ^ 50 = 112,589,990,684,262.4 mm = 112,589,990.7 km (around 70 million miles).

Workings

Hint
The first letters of one half of the words are: A, B, D, C, F, D, H, A, I.

Answer
ABUNDANT   + SCARCE
BRAVERY    + COWARDICE
DANGER     + SAFETY
CONTRACT   + EXPAND
FAMOUS     + UNKNOWN
DISTRIBUTE + GATHER
HORIZONTAL + VERTICAL
ACCIDENTAL + INTENTIONAL
IGNORANCE  + KNOWLEDGE

Workings

Hint
The words are linked by their letters.

Answer
Approved.

The initial letters spell ORANGE and the last letters spell INDIGO.

Workings

Hint
Snakes don't have legs.

Answer
6 snakes, along with 7 people and 14 lizards.

Reasoning
We know that for each person (2 legs) there were 2 lizards (4 legs each).

Which means for every person, we can count a total of 10 legs.

Snakes don't have legs, so the total of 70 legs must have been 7 people (and 14 lizards).

This is a total of 21 heads, so the remaining 6 heads were all snakes.

Double-Checking
7 people gives 7 heads and 14 feet.

14 lizards gives 14 heads and 56 feet.

6 snakes gives 6 heads and 0 feet.

For a total of 6 + 7 + 14 = 27 heads, and 0 + 14 + 56 = 70 feet.