You can look at this as a morality tale too. Instead of respecting their father and caring that he is getting older, all the brothers can think about is being king. If one of the brothers was kinder than the other, the one with the slowest horse metaphorically, he would be chosen king.
The classic answer to this depends on the king's exact words. He says that the one who owns the slowest horse wins. So if the brothers switch horses, they can have a regular race because whoever goes faster actually wins because that means the horse that he owns is actually slower.
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