An Elderly Rancher Died and Left Her Estate to Her

An elderly rancher died and left her estate to her three children. She bequeathed her 35 prize horses in the following manner: 1/2 to the eldest, 1/3 to the second child, and 1/9 to the youngest.
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The children decided to call in a very wise judge to help in the distribution of the rancher's estate. The judge arrived with a horse of his own. He put his horse in with the 35 belonging to the estate, and then told each child to pick from among the 36 in the proportions stipulated by the will (but be careful, he warned, not to pick his horse). The first child took eighteen horses, the second child took twelve, and the third child, four. The 35 horses were thus divided among the children. The wise judge took his horse from the corral, took a fair sum for his services, and rode off into the sunset.
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The youngest son complained that the oldest son received 18 horses (but was entitled to only 35/2 = 17.5 horses). The judge was asked about this, and he faxed the children the following message: "You all received more than you deserved. The eldest received 1/2 of an 'extra' horse, the middle child received 1/3 more, and the youngest, 1/9 of a horse 'extra.'" Apportion the horses according to Adams', Jefferson's, and Webster's plans. Which plan gives the appropriate distribution of horses?
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__________ (Adams' plan and Jefferson's plan, Webster's plan and Jefferson's plan, Adams' plan and Webster's plan, Adams' plan, None of the plans)