Kentucky
Only a sliver of Kentucky makes it into the path of totality. One of the few cities in the path is Paducah, where totality runs from 2 p.m. CDT to 2:02 p.m. CDT. Totality is so short here because it's on the edge of the path — the closer you are to the center of the path, the longer totality will last.
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Indiana
About half of Indiana will enter totality, beginning south near Evansville, then running up through Vincennes, Bloomington, Indianapolis, and Muncie. In Evansville, totality begins at 2:02 p.m. CDT and ends at 2:05 p.m. CDT. In Muncie, the time zone changes; totality begins at 3:07 p.m. EDT and ends at 3:11 p.m. EDT.