why number 8549176320 is one of a kind?

Can you fill the blank with the correct number?

6 30 870 756030 _____

There is a square of a particular number which when doubled, becomes 7 more than its quarter.

Can you find the number?

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?

John is selling fruits.
He sells grapes at $30, Dates $25, and a Wolfberry $45.
At what price does he sell fig?

PS: Logical Thinking

The picture shows the dice results in each couple of throws. If they are actually following a pattern, can you find out the missing one?

The Puzzle: A girl, a boy, and a dog start walking down a road.

They start at the same time, from the same point, in the same direction.

The boy walks at 5 km/h, the girl at 6 km/h.

The dog runs from boy to girl and back again with a constant speed of 10 km/h. The dog does not slow down on the turn.
How far does the dog travel in 1 hour?

A boy purchased a book from a bookkeeper and gave him $100.
The cost of the book is $50 but the bookkeeper has no change, so he gets the change from the next shop and returns the boy his $50.

After some time the next shopkeeper came with the $100 note and told the bookkeeper that the note was a fraud, so he took the money back.

How much loss did the bookkeeper face?

While preparing the table for dinner, wife came up with an idea to tease his mathematician husband. She asked her husband to pick nine toothpicks and make ten without breaking any toothpick.

The husband was also smart and did it within seconds. How ?

The warden meets with 23 new prisoners when they arrive. He tells them, "You may meet today and plan a strategy. But after today, you will be in isolated cells and will have no communication with one another.

"In the prison is a switch room, which contains two light switches labeled 1 and 2, each of which can be in either up or the down position. I am not telling you their present positions. The switches are not connected to anything.

"After today, from time to time whenever I feel so inclined, I will select one prisoner at random and escort him to the switch room. This prisoner will select one of the two switches and reverse its position. He must flip one switch when he visits the switch room, and may only flip one of the switches. Then he'll be led back to his cell.

"No one else will be allowed to alter the switches until I lead the next prisoner into the switch room. I'm going to choose prisoners at random. I may choose the same guy three times in a row, or I may jump around and come back. I will not touch the switches, if I wanted you dead you would already be dead.

"Given enough time, everyone will eventually visit the switch room the same number of times as everyone else. At any time, anyone may declare to me, 'We have all visited the switch room.'

"If it is true, then you will all be set free. If it is false, and somebody has not yet visited the switch room, you will all die horribly. You will be carefully monitored, and any attempt to break any of these rules will result in instant death to all of you"

What is the strategy they come up with so that they can be free?