Can you fill the blank with the correct number?

6 30 870 756030 _____

Complete the given grid with valid words. You can only use the letters AAEEIIMMPPTT.

Hint: The grid reads the same across as down.

Can you divide the below-given shape into four equal and identical pieces?

If,

6 / 7 = 2
3 / 9 = 7
8 / 2 = 6

Then

4 / 5 = ?

What is harder to catch the faster you run?

He runs but never walks. Murmurs, but never talks. Has a bed, but never sleeps. And has a mouth, but never eats?

In a secret society, a buried chamber can be accessed only via a secret password. The password is seven characters long and comprises of just letters and numbers.

You find a code that can help you in cracking the password. The code says "You force heaven to be empty".

Can you deduce the password from that?

The answer I give is yes, but what I mean is no. What was the question?

Count the number of times the letter "F" appears in the following paragraph:

FAY FRIED FIFTY POUNDS OF
SALTED FISH AND THREE POUNDS
OF DRY FENNEL FOR DINNER FOR
FORTY MEMBERS OF HER FATHER'S FAMILY.

There are two beautiful yet remote islands in the South Pacific. The Islanders born on one island always tell the truth, and the Islanders from the other island always lie.
You are on one of the islands and meet three Islanders. You ask the first which island they are from in the most appropriate Polynesian tongue, and he indicates that the other two Islanders are from the same island. You ask the second Islander the same question, and he also indicates that the other two Islanders are from the same island.
Can you guess what the third Islander will answer to the same question?