Can you find a pattern and the missing number in the series given below?

100, 155, 258,? , 584, 819.

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.

Our product and our sum always give the same answer. Who are we?

what does the below math rebus puzzle mean?

The person who makes it has no need for it. He who purchases it does not use it. The person who does use it does not know they are. What is it?

You are given four results as below:
1111 = F
2222 = E
3333 = T
Then, can you find out how to code 4444?

Many have heard it, but nobody has ever seen it, and it will not speak back until spoken to. What is it?

Can you solve below mathematical equation?

2^1234 - 2^1233

Which English verb becomes past tense just by rearranging the letters?

I was speeding and ran through a stop sign, yet two traffic officers who were there do nothing about it.

why?