Friday, November 4, 2011

17 Horses and 3 Brothers

This is a very old story of a super rich man and his three sons.  Of his vast properties and possessions that included seventeen horses.  A story some may have heard or read, but can be re-heard or  re-read one more time.  It is not just a story, but more of a mathematical problem.

Once upon a time, there lived a very rich man.   Who became rich by sheer hard work, and more importantly by honest means.   He had three sons and he loved them very much.  The sons also loved and respected their father equally.   The sons were as honest and hard working as the father.  The family lived happily.

The rich man became very old and realised that his end was near.  He wrote a Will dividing his properties and possessions among the three sons. He called all the three sons together and handed it over to them.  He knew that the sons could be trusted and there was no need for an attorney or witnesses for the Will.  He told the sons to open the Will after his death and distribute the properties and possessions as detailed in the Will.   He told them that there may be some differentiation in dividing the properties among the three brothers.  One may get more land than the others.  Another may get more buildings than the other two.  The third may get more movables assets than immovable properties.  The division was based on economies of scale and preservation of property value as against dividing each item equally among the three brothers and thereby resulting in loss in net value.  Sound Economic principles.   He assured them that the division made in the Will, though may not look equitable on the face of it, was actually fair and all the three brothers would get a third of the overall value of the estate.  The sons believed in the judgement of the father and the father believed in the understanding the sons would show.  And more importantly, in the understanding the three daughters-in-law would show.   Difficult to believe that such an ideal family ever existed, but it is true.  At least in this story.

The super rich man died in the normal course and peacefully.   The customary last rites were performed by the heirs and all the relatives, friends, well wishers and the not-so-well-wishers of the family participated in them.  On the last day, just before dispersing, the elders in the gathering offered their services for supervising and dividing the property among the three brothers.  The brothers politely declined the offer and  told them that they would themselves do it as suggested by their father before his death.  The well wishers were indeed happy and left after remarking that the rich man was really lucky for having such children.  The not-so-well-wishers were disappointed at denial of an opportunity to fish in troubled waters.  Nevertheless, they also repeated that the rich man was really lucky to have such sons and they also left.

All the assets were distributed as directed in the will.  The only item left to be distributed were the horses.  The will stated that they should be divided thus:  Half to the elder son, One Third to the middle son and One Ninth to the Youngest son.  The three sons tried their best to solve the division issue, but failed in their efforts.  For the first time in their lives, fissures appeared and they started discussing the issue agitatedly.

An old friend of the rich old man, himself very old but still alive, was going on his horse when he heard the heated discussion among the brothers.  He came to them and asked what the problem was.  In deference to the old man and a good friend of their father, they explained the problem of division of the horses.  He thought for a moment and told them that he would divide them as per the wishes of their father, if they all agreed to his method.  When they agreed, he added his horse to the pool and told them he would divide the pool of 18 horses.  He gave 9 horses to the elder brother, being half of the 18 horses.  The middle brother was given 6 horses being one third of the 18 horses.  The youngest got 2 horses being one ninth of 18 horses.  That still left one more horse, the one belonging to the wise old man.   He thanked them for their co-operation, mounted on his horse and rode away!

The brothers stood there, amazed at the simple way in which the wise man had solved the tough problem.   They realised that this was not just a division of horses, but the last lesson their father wanted to teach them.  They took the advice of the old wise man whenever the need arose, as long as he was around.

Is not this story a better way of teaching "Fractions" in "Mathematics" to the children?   One could use Apples or Chocolates instead of horses to give a practical touch.  There are many such riddles in ancient Indian books like "Leelavati".  Some are simple, some more complex and some, they say, have not yet been solved.


  1. Uh ! I had to read the last part-- the solution to the problem part- twice :P Terrible at Maths !
    Smart old man and smarter father-- leaving a mathematical quiz for his sons to solve !

  2. And very smart sons, who learnt so quickly the last lesson their wise old father wished to teach them !

  3. Very interesting.Finding an easy solution is the real knowledge of a
    subject,a person can possess.I remember,the method suggested is used
    invariably in solving Factorisation problems in algebra.We should be
    proud that our country has given birth to many such mathematics genius like Leelavathy, Bhaskaracharya,Rmamnujam and many more.

  4. It's a good thing the man didn't have 18 horses or the sons would have been fighting over who got the remaining horse.