Math in Tenali Ramalinga’s puzzle on elephants

          I came to know about this story through my friend. This is about a problem solved by the great Tenali Ramalinga. I always enjoy Ramalinga’s stories and this is one among those tales:

An old man had three sons. During his life time he acquired 17 elephants (Exactly do not remember whether they are elephants or horses. Let us consider elephants for example). He wrote a note which specifies how these elephants shall be distributed among his three sons after his death. The note says:

“Half of the elephants shall be given to the eldest son. Two third of the remaining shall be give to the second son.  Two third of the remaining shall be give to the third son.”  

Finally the day came and the elephants needed to be distributed among the sons according to the note. But how can it be done? How can we divide 17 elephants such that the eldest son gets half of the share?

As usual, Ramalinga has resolved the problem. This is how Ramalinga has solved the puzzle:

To this 17 elephants, Ramalinga added one elephant taken from King’s elephant force. This made the count 18. Then he distributed 9 elephants (which is equivalent to half part) to the eldest son. Then he distributed 6 out of the remaining 9 (which is equivalent to 2/3 part) to the second son. Then he distributed 2 out of the remaining 3 (which is equivalent to 2/3 part) to the third son. This exercise left one elephant and that was given back to the king’s elephant force.

Math in this puzzle:

The fractions mentioned in the note are 1/2, 2/3 and 2/3. So to evenly distribute, we need to have at least 2*3*3=18 elephants (these are the denominators of the fractions).