A pie eating contest seems a more likely option than olympic games. Any sort of contest you'd find at a county fair, (cooking, livestock, vegetable contests), all are closer to a hobbit's taste than games of strength and will. They were simple folk and simple contests would have fit them well.
Olympic type games would have been better suited in the world of men. Archery, riding, etc. were already being taught to young men so contests like that make more sense in the world of Big People.
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"Let us live so that when we come to die even the undertaker will be sorry." - Mark Twain
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