What is more useful when it is broken?

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

Can you find the number?

What is the fewest number of coins that would be required in order to make sure each and every coin touches exactly three other coins?

What is harder to catch the faster you run?

Place the numbers from 1 to 9 in the circles in a manner that each side of the triangle sums up to 17.

A man was telling some of his war stories to his grandchildren.
"When the World War I was on the verge of end, I was awarded for my bravery for I had saved a group of my men." He coughed and then added, "When we were fighting in northern France, an enemy soldier threw a grenade at us. Before it could explode, I picked it up and threw it away. For my act of bravery, right before the war ended, A General gave me a sword engraved with the words "Awarded for Display of Bravery and Heroism in World War 1"."

Hearing this, one of the grandson spoke up. "Grandpa, this is not a true story. It can"t be true!"

The truth is that it was not. How did the grand children know it?

A man in a car saw a Golden Door, Silver Door and a Bronze Door. What door did he open first?

A mad serial killer kidnaps people and forces them to play the game of 2 pills with them, In this game, there are pills in the table and one of them is normal pill while the other one is deadly poisonous.
The victim will choose one pill and the killer will pick the other pill and both simultaneously will swallow the pill with water.
victim dies every time.

One day the serial killer kidnaps the Joseph and forces him to play the same game with him.

Joseph solves the mystery of the two pills and remains alive.

Explain?

Pronounced as 1 letter, And written with 3, 2 letters there are, and 2 only in me. I’m double, I’m single, I’m black blue and grey, I’m read from both ends, and the same either way. What am I?

A number can be multiplied by multiple of nine
i.e 9 18 27 36 45 ...

and the resulting number consist of only one digit.

Can you identify the number ?