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1. Who was the only major-party presidential nominee whose last name rhymed with the name of his home state?

James G. Blaine, who ran against Grover Cleveland.

2. In what order are the following presidents listed?

Wilson
Reagan
George W. Bush
Grant
Truman
Ford
John Quincy Adams
Nixon
Polk
Clinton
Taft
George H.W. Bush
William Henry Harrison
Cleveland
Harding
Kennedy
Carter
Franklin Roosevelt
Eisenhower
Hoover
Coolidge
Hayes
Lyndon Johnson
Arthur
Garfield

Middle Names in reverse alphabetical order.

3. Twelve presidents have served exactly one full term in office. One of them served a different number of days than the other 11. Who and why?

Rutherford B. Hayes. Took an oath early because Inauguration Day fell on a Sunday.

It's worth mentioning Zachary Taylor refused to be inaugurated on the normally allotted day for the same reason - however he died in office.

9. Eleven presidents have served exactly two full terms in office. One of them served a different number of days than the other 10. Who and why?

George Washington. His first inauguration was in April.

10. If Ted Kennedy had been elected president in 1980, he and George Washington would have had in common something that only two actual presidents do. What and who?

An older brother in the Navy. (Lawrence Washington was in the Royal Navy, and Jack Kennedy was also in the Navy).

The others I haven't figured out.

Regards, Ivan