Random Puzzles 

Workings

Hint
This is a very common sequence.

Answer
5.

The numbers represent the number of letters of the words ONE, TWO, THREE, etc. Therefore the answer is the number of letters in the word EIGHT.

Workings

Hint
deny + e = needy.

Answers
deny + e = needy mail + c = claim exit + s = exist gosh + t = ghost city + h = itchy newt + i = twine type + m = empty
The letters ECSTHIM are an anagram of CHEMIST.

Workings

Hint
3,876 would cost £1.52.

Answer
House numbers at 38p each.

Workings

Hint
Say each number, one digit at a time.

Answer
11131221141113122112.

Reasoning
Each term describes the previous term.

For example, 42 = one four, one two = 1412.

And, 1412 = one one, one four, one one, one two = 11141112.