• # Can any member come out with a solution?

There was an old man in a village. He had three sons. He had 17 horses. His elder son was innocent and the other two are intelligent. So this old man before his death called and advised them to get the horses distributed in the following proportion. Half of the horses to his elder son. 1/3 portion of his horses to his second son and 1/9 portion of horses to his third son. He died.
All three sons sat together and started discussing how to distribute the horses in the proportions told by their father. They were not able to find a solution. They approached the Village head and explained their problem. The village head told them that the next day morning he would come on his horse and distribute the horses as per the proportions suggested by their father without killing a single horse.
Can any member come out with a solution without killing even a single horse?
• As a child, I learnt the trick to solve this question by borrowing a horse from the neighbour. But later, when I developed a convoluted brain, I understood that the trick solved the question, but the answer was not mathematically accurate.

Let me try to explain. The elder son gets 1/2 of the share, but after the actual division, he gets 9 horses out of 17. Isn't 9 out of 17 more than 1/2?

(a) Those who have forgotten Noakhali, how can they protest Sandeshkhali?
(b) Have no fear of perfection - you'll never reach it. ---------- Salvador Dali

• Yes. You are correct. After distribution, if you see the mathematics, the division is not as per the proportions mentioned by the old man. But everybody got more than what they should get and the borrowed horse has been given back. That is why all the sons are happy.
The elder son got more than 1/2, the second son got more than 1/3 and the third son also got more than 1/9. The village head's horse is back to him. 1/2 + 1/3 + 1/9 is not equal to one. That is the issue in this tricky question.

drrao
always confident

• This is a popular maths trick that we learned during our school days. Whenever some entity is not divisible by some numbers then to solve the problem we add some more to it and then after distribution take that addition back.
In this case also as a horse cannot be distributed in fractions so such tricks are used.

Knowledge is power.

• While solving such questions, we need to apply some tricks to get a practical solution devoid of fractions. The solution might not be correct mathematically but at least we don't get the answer in fraction. Such solutions are acceptable in the sense that horses distributed among the sons were on higher sides to some extent making them pleased with such a distribution.