What is both possible and impossible at the same time?

There are four 3-link chains. All you have to do is join them into a big 12-link chain. For joining two closed links, one of the links must be cut and placed onto the other link for closing.

How many minimum links will you have to cut to make the big chain?

Make the seating arrangement of 10 children in such a way that there are 5 rows with 4 children in each row.

All of Jacob's shoes are red except two.
All of Jacob's shoes are green except two.
All of Jacob's shoes are yellow except two.

How many shoes does Jacob have?

Luis Garavito killed Density x Volume.

Who is Luis Garavito ?

A car meter reading shows 72927 miles a palindromic number.
what is the minimum number of miles you would need to travel to see another palindromic number on the car meter reading?

John and Jacob are twin brothers. One of them is a liar whereas the other one is a truth-teller.

I called their home number and one of them picked up.
I asked. 'Does John lie?' The person replied with a yes.

Whom did I talk with, John or Jacob?

By moving exactly three matchsticks can you make the below equation true.It can be solved by 3 ways.

If you had an infinite supply of water and 5-quart and 3-quart pails, how would you measure exactly 4 quarts? What is the least number of steps you need?

In the picture that is attached with this question, you can find a square which comprises of four little squares inside it. Consider this square to be made with matchsticks. You have to remove two matchsticks such that only two squares remain instead of five.How will you do it ?