Famous puzzles and the Generalized formulas 

100 people in circle with a sword puzzle

100 people standing in a circle in an order 1 to 100. No. 1 has a sword. He kills the next person (i.e. No. 2) and gives the sword to the next (i.e. No. 3). All people do the same until only 1 survives. Which number survives at the last? 

100 Monkeys and 100 doors puzzle

There are 100 doors, all closed. In a nearby cage are 100 monkeys. The first monkey is let out, and runs along the doors opening every one. The second monkey is then let out, and runs along the doors closing the 2nd, 4th, 6th,… — all the even-numbered doors. The third monkey is let out. He attends only to the 3rd, 6th, 9th,… doors (every third door, in other words), closing any that is open and opening any that is closed, and so on. After all 100 monkeys have done their work in this way, what state are the doors in after the last pass? 

100 cows and milk distribution puzzle

A milkman has 100 cows number from 1 to 100. Every cow gives milk according to their numbers i.e i'th cow gives i litre milk. Milkman has 10 sons and he wants to divide his cows among his 10 sons so that every son should get an equal amount of milk, the task is to help him to know about the division of these cows among the sons.