Last week I posed a wee question on social media: Who was both the oldest former President of the United States, and the oldest former Vice-President, but not at the same time?

Lots of people scratched their heads over this, which was gratifying, and the answer is admittedly a bit obscure.

Below is the full list of people who were the oldest former President of the United States, and the oldest former Vice-President, at all times since the terms of the first holders of both offices ended on 4 March 1797. I have put in bold the cases where a President or Veep who was older than all their living predecessors (if any) left office at the end of their term. In all other cases, the distinction is transmitted through mortality.

You'll see that since 1797, there have been five intervals when there were no living former Presidents, and two when there were no living former Vice-Presidents. There were no living ex-Presidents 1) between the death of Washington and the end of John Adams' term; 2) between the death of Andrew Johnson and the end of Grant's term; 3) between the death of Cleveland and the end of Theodore Roosevelt's term; 4) between the death of Coolidge and the end of Hoover's term; and 5) between the death of Lyndon Johnson and Nixon's resignation.

More obscurely, there were no living Vice-Presidents between 1) the death of Hannibal Hamlin and the end of Levi P. Morton's term, and 2) between the death of Levi P. Morton and the end of Thomas R. Marshall's term.

John Adams, Martin Van Buren, Millard Fillmore, Andrew Johnson, Harry Truman, Lyndon Johnson, Richard Nixon, Gerald Ford and the elder George Bush were all both the oldest former President of the United States, and the oldest former Vice-President, at the same time. (In all cases except Nixon, they held both distinctions at the time of their deaths.)

John Quincy Adams, William Howard Taft and Charles G.Dawes all appear twice in their respective columns, having been succeeded in their offices by older men who they then outlived.

The otherwise rather obscure Levi P. Morton outlived six younger successors as Vice-President. I think that is a record.

And the answer to the question, "Who was both the oldest former President of the United States, and the oldest former Vice-President, but not at the same time?"

It's Calvin Coolidge.

He was elected Vice-President on the same ticket as Warren Harding in 1920, and took office in 1921. When Harding died in 1923, Coolidge became president and the only other living former vice-president was his immediate predecessor Thomas R. Marshall, who was older than him. Marshall died in 1925, making Coolidge not just the oldest living former vice-president but the only one. Coolidge's own vice-president, Charles G. Dawes, was older than him, so when their term ended in 1929, Dawes took over the mantle of oldest former Vice-President from him.

At that point the only living former presidents were Coolidge himself and William Howard Taft. When Taft died in 1930, Coolidge became the oldest former president until his own death in 1933, after which there were no living former presidents until Herbert Hoover's term ended two months later. (Hoover lived another thirty years.)

If you spot any mistakes below, please yell.