The Herd of Camels Puzzle - Solution
The Puzzle:
An Arab Sheik, finding himself about to die, called his sons about him and said: "Divide my camels among you in the proportion of one-half of the herd to the eldest son, the second son one-third, and to the youngest son one-ninth."
Thereupon the oldest son cried: "O, my father, one-half, one-third, and one-ninth do not constitute a whole. To whom, therefore, shall the remainder of the herd be given?"
"To any poor man who may be standing by when the division is made," replied the Sheik, who thereupon died.
When the herd was collected a new difficulty arose. The number of the camels could not be divided either by two or three or nine. While the brothers were disputing, a poor but crafty Bedouin, standing by with his camel, exclaimed, "Behold, I will sell you my beast for ten pieces of silver, so that you may then divide the herd."
Seeing that the addition of one camel would solve the difficulty, the brothers jumped at the offer, and proceeded to divide the herd, but when each had received his allotted portion there yet remained one camel.
"I am the poor man standing by." Said the crafty Bedouin, and gaily mounting the camel, he rode away, with the ten pieces of silver in his turban.
Now, how many camels were in the Sheik's herd?
Our Solution:
The camels could be divided exactly according to the Sheik's will only if it were a multiple of 2,3 and 9 i.e. 18,36,54,72,...
But according to the brothers, they needed one more camel to divide it according to the Sheik's will; so the Sheik had 17,35,52,71,... camels.
But "only 18" (18/2=9, 18/3=6, 18/9=2 so that 9+6+2=17) leaves remainder one (18-17=1). So there were 17 camels in the Sheik's herd.
But, the problem is that the number of camels 9,6,2 that the brothers received are not yet in the proportion of one-half, one-third and one-ninth. This is the paradoxical situation. The Camels could be divided exactly according to the Sheik's will only if he had 18+...,36+...,54+...,72+...,...camels.
Probably the Sheik was not good at mathematics.
But according to the brothers, they needed one more camel to divide it according to the Sheik's will; so the Sheik had 17,35,52,71,... camels.
But "only 18" (18/2=9, 18/3=6, 18/9=2 so that 9+6+2=17) leaves remainder one (18-17=1). So there were 17 camels in the Sheik's herd.
But, the problem is that the number of camels 9,6,2 that the brothers received are not yet in the proportion of one-half, one-third and one-ninth. This is the paradoxical situation. The Camels could be divided exactly according to the Sheik's will only if he had 18+...,36+...,54+...,72+...,...camels.
Probably the Sheik was not good at mathematics.