A Problem with Horses

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Abdul Hadi Badi-al-Zamar, a Sufi and mathematician, heard a ruckus ahead. Men were shouting at each other. “What ails thee?” he asked of one of the men, who was rending his clothing.
“Our father has just died,” said the man, “and left us with an insoluble problem.”
“What is the problem,” asked the Sufi, for he liked problems. They kept his mind nimble.
“Our father’s dying wish was as follows,” said the man, tears streaming down his face. “We were to divide our father’s horses as follows. I am the youngest, and I am to be given a ninth of the horses. My brother, Karim, is in the middle, and he is due one third of the horses. Our oldest brother, Malik is to receive one half.”

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“How many horses do you have?" said the old Sufi, getting down of his own fiery steed.
Thirty-five,” said Nadir, the youngest of the brothers.
Malik, the oldest walked over and demanded, “Can you help us? If not, be on your way, and leave us to our misery, for we can see no solution, without butchering one or more of the beautiful stallions.”
“I think I can help you,” said the Sufi, “but first I must do something.”
He handed over the bridle of his horse to horse to Malik, who held it, frowning.
“Now let me see,” said the old man, while the three wives and numerous children gathered around. He picked up a stick and sketched some figures in the sand.
[If you wish to think about his solution, now is the time to do so … if not, then click on the link below to see Abdul Hadi Badi-al-Zamar’s elegant solution.]

Abdul Hadi turned to the youngest. 

“You are due a ninth of the horses. Let Malik add my horse, as a gift, to your inheritance. So that makes thirty six horses altogether. A ninth part of 36 gives you four horses. Are you happy with that?” 
“Yes,” said Nadir, who had thought three horses was the maximum he could gain. 

"And to you, Karim, you are due a third of the horses, and that is now twelve thoroughbreds, Are you happy with that?” Karim nodded, wiping the tears from his eyes,

The Sufi sipped a sherbet brought to him by a slave girl. “So,” he continued, turning to the eldest, “if we take half of the 36 horses, then you are due 18. Are you content with that, Malik?”
Malik scowled, counted on his fingers, and then grinned. “Yes,” he said, “for it is one more than the 17 I expected.”

“Good,” said the Sufi, smiling. "So now you each have your due, and the 4 plus the 12 plus the 18 comes to 34 fine horses. You all have more than you expected, and the Prophet, may peace be upon him, has left me with my own horse and one for my troubles.”
The Sufi smiled to himself as he continued his journey, with a beautiful bay following his own white horse He smiled as he heard the sounds of children laughing and playing, as the brothers talked quietly together with peace restored. 

This maths problem I believe is 'traditional' as I have come across it in more than one place, but for this and similar brainteasers, see "The Man Who Counted" by Malba Tahan