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After dinner, three friends at a restaurant paid their bill and noticed a bowl of mints on the front counter. Sean took one-third of the mints but returned four because he had a momentary pang of guilt. Fred then took one-fourth of what was left but returned three for similar reasons. Gene then took half of the remainder but threw two green ones back in the bowl. The bowl had only 17 mints left over when they were done. How many mints were originally in the bowl?
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