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?

I know there are two methods by using three time the same number with a plus(+) operator , you can make sum as 60.

One of them is 20+20+20.

whats the other way ?

A landlord calls both of his sons and tells them that their horses will now decide who will transfer the inheritance. He tells them to race along the land till the end and the one whose horse will be slower will win and be the heir to all the property.

Both of them keep wandering for days but to no result. Then they ask a wise man regarding it. The man advises them on the matter after which they jump on the horses and race as fast as they can till the end. Why did they do it?

What did the wise man say?

The captain of a ship was telling this interesting story: "We travelled the sea far and wide. At one time, two of my sailors were standing on opposite sides of the ship. One was looking west and the other one east. And at the same time, they could see each other clearly." How can that be possible?

You have a square. What you have to do is cut and reassemble the square such that you create a Red Cross sign that has the same volume as that of the square.

4 fathers, 2 grand-fathers and 4 sons went to watch the movie.What is the minimum number of tickets they need to buy ?

Can you calculate the probability of getting a sum of six when a dice is thrown twice?

How many people must be gathered together in a room, before you can be certain that there is a greater than 50/50 chance that at least two of them have the same birthday?

You have two buckets - one holds exactly 5 gallons and the other 3 gallons. How can you measure 4 gallons of water into the 5 gallon bucket?

(Assume you have an unlimited supply of water and that there are no measurement markings of any kind on the buckets.)

Three people enter a room and have a green or blue hat placed on their heads. They cannot see their own hat but can see the other hats.
The colour of each hat is purely random. They could all be green, blue, or any combination of green and blue.
They need to guess their own hat colour by writing it on a piece of paper, or they can write 'pass'.
They cannot communicate with each other in any way once the game starts. But they can have a strategy meeting before the game.
If at least one of them guesses correctly they win $10,000 each, but if anyone guesses incorrectly they all get nothing.
What is the best strategy?