Can you find a number that lies one third of the distance between 1/3 and 2/3?

If you drop me I’m sure to crack, but give me a smile and I’ll always smile back. What am I?

My friends called me Iron59 because my parents are a chemist and a mathematician. What is my real name?

I have a five and a three-gallon jar. Assuming there is an infinite supply of water, how can I measure one-gallon water?

What has no start, end, or centre?

John was working on a Chemical Mixture whose weight comprise 90% liquid and 10% solid. The total weight of the mixture is 20 pounds. After a while, John noticed that some of the liquid evaporated and now the liquid comprises just 50% of the weight.

What is the weight of the chemical mixture now?

When you stop to look, you can always see me. But if you try to touch me, you can never feel me. Although you walk towards me, I remain the same distance from you. What am I?

Detective Rockford was jogging near the beach at 4:30 am.
He hears a sound near the shack "No Michael, Please Do not shoot me".
Next instance he heard the sound of gunfire. Rockford rushes to the shack where he finds women lying dead and a gun in close proximity of three "Doctore Lawyer and a Teacher".

Rockford immediately knew that the Lawyer has committed the crime. How?

Three ants are sitting at the three corners of an equilateral triangle. Each ant starts randomly picks a direction and starts to move along the edge of the triangle. What is the probability that none of the ants collide?

A thief is convicted in Mexico. He gets the death penalty. The judge allows him to say the last sentence to determine how the penalty will be carried out. If the thief lies, he will be hanged, if he speaks the truth he will be beheaded. The thief tells the last sentence and to everybody's surprise some minutes later he is set free because the judge cannot determine his penalty. What did the thief say?