Puzzle - A Gold For 7 Days

Puzzle

A loyal worker is working under you for 7(seven) days and you have only one gold bar to pay him. You must pay the worker at the end of each day. Otherwise, he wont come for next day's work. One more constraint is you have to make only two cuts in the gold bar. How can you pay him at the end of each day ?

Hint:   Barter System

Puzzle - Three Ants Problem

Puzzle

Three ants are sitting in the corners of the equilateral triangle. All ants start at same time and move at same speed constantly. The speeds of three ants are equal. Each ant picks up a direction randomly at first and moves in that direction. What is the probability that none of the ants will collide with each other ?

Puzzle - Red and Blue Marble

Puzzle

We have 50 Red , 50 Blue Marbles and 2 jars. One of the jar is chosen at random and then one marble is chosen from that jar at random. How would we maximize the chance of choosing red marble ? What is the probability of choosing red marble ?. All 100 marbles should be placed in the jar.