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Interstate 77's original southern end was at I-85 in Charlotte, which seemed quite reasonable; so did its later extension to Columbia, S. C.
But the north end... In Cleveland, I-77 was to overlap with I-90 from west of Cleveland to east of Toledo; then overlap with I-75 north to Detroit; and finally use today's I-94 northeast to end in Port Huron, Mich.
In 1958, Ohio requested that I-77 be truncated to Cleveland and Michigan renumber its portion of I-77 to I-75E. This sparked the Ohio-Michigan hostility that even today manifests itself as bickering in MTR.
I-177 (preliminary numbering) Ohio
Interstate 177 was a proposed number for what is today's I-77 and I-90 between I-490 and the lakefront in Cleveland. Today's I-90 portion would have been an overlap of I-177 and I-71. I-90 would have continued farther west along the shore until roughly exit 167. 
I-177 was proposed sometime in 1958, for in February of that year I-77 did not yet exist there. On Nov. 10, 1958, AASHO approved the deletion of I-177. 
See also: Ohio Interstate Route Numbering (Stephen Summers)
I-277 North Carolina
The northern part of I-277, the Brookshire Freeway, pairs with NC 16. It is accessible from I-77 at exit 11. The southern part, the John Belk Freeway,. also carries US 74. It is accessible from I-77 at exit 9. The two freeways head east to the other side of uptown Charlotte to merge and form the Independence Freeway (US 74). 
See also: I-277 (Matt Steffora, ncroads.com)
In 1957 and 1958, the original proposed number for I-77 was Interstate 79. At the time, however, the proposed number for the Akron loop was not I-279 but I-480; I-80 was to take a southerly route from Norwalk to Youngstown via Akron. Later I-80 was moved, and the Akron loop was attached to I-77 instead. 
I-277 (unknown history) South Carolina
State route 277 leads from I-77 into Columbia, S. C. Reportedly SCDOT had two plans for this highway: 1) connect to another interstate, and 2) get interstate designation.  Neither of these happened, and I have basically no information on SC 277's history.