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In his will , a farmer left 17 horses to his 3 sons with the following instructions.

1) The eldest son is to get half of the total horses.

2) The middle son is to get one third of the total horses.

3) The yongest son is to get one ninth of the total horses.

After considerable deliberations the three brothers confused about how to alocate the horses fairly between them sought the counsel of a wise uncle. The uncle said , 'fear not , I know how to solve your problem.'

How did the wise uncle solve the problem?

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The uncle lends them a horse... An oldie. Not sure if on-topic here. – Jyrki Lahtonen Mar 6 '14 at 10:40
up vote 4 down vote accepted

The uncle puts in another horse for the share, and now they have a total of 18 horses. So, by the will of the farmer:

1) The eldest son gets 9 horses.

2) The middle son gets 6 horses.

3) The youngest son gets 2 horses.

They have shared 17 horses, and now the uncle can take back his reaming horse out of the share. Note that this only works because a half, plus a third, plus a ninth doesn't total up one unit.

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Not only the farmer was so unwise to leave a prime number of horses to divide, but his arithmetic was quite poor as $$ \frac12+\frac13+\frac19=\frac{17}{18} $$ so there's always some leftover.

But if you had an 18th horse ..

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$$\frac{1}{2} + \frac{1}{3} + \frac{1}{9} = 17$$

Find common denominator = 18

$$\frac{9}{18} + \frac{6}{18} + \frac{2}{18} = \frac{17}{18}$$ or

$$\frac{1}{2X} + \frac{1}{3X} + \frac{1}{9X} = 17$$

$.500X + .333X + .111X = 17$

$.944X = 17$ X=18

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I guess you have an idea about the solution to this riddle, but you've essentially created a new puzzle for Readers to decipher your meaning. Writing out your solution in declarative sentences would improve the Answer. – hardmath Aug 7 '15 at 2:02

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