Can you fill the blank with the correct number?

6 30 870 756030 _____

Mr. Buttons was all set to go to the village of Buttonland to meet his friend. So, he packed his bags and left for the village at 5 in the morning. Upon travelling on a road for miles, he came across a point where the road diverged into two. He was confused on which road to take. He gazed around and he saw two owls sitting on a branch. He thought he could ask for directions for the village from the two owls. So he went to the tree. There he saw a sign which read, "One owl always lies, and one is always truthful. They both fly away if you ask them more than 1 question."
Mr. Buttons was caught in the dilemma of what to ask? And from which owl to ask, since he only had one question. What should Mr. Buttons ask?

There are people and strange monkeys on this island, and you can not tell who is who (Edit: until you understand what they said - see below). They speak either only the truth or only lies.
Who are the following two guys?
A: B is a lying monkey. I am human.
B: A is telling the truth.

The current time can be represented by below textual rebus.

0
=========
B.Sc
LLB

Can you tell us the current time?

If I put in one bird per cage, I have one bird too many. If I put in two bird per cage, I have one cage too many. How many cages and birds do I have?

There is an exact a week gap between Christmas and New Year. Hence, It is obvious that the new year that comes right after Christmas comes on the same day of the week.

A Strange thing happened in the Year 1777. Christmas occurs on Wednesday and New Year on Monday. How is that possible?

I am Huge on Sunday and Saturday.
I am small from Tuesday to Thursday.
I do not exist on Monday and Friday.
Who am I?

How many words can a quill made with the feather of a pigeon write with a 100ml bottle of black ink?

What part of the chicken has the most feathers?

What is the relationship between these matchstick pictures below?