A Presidential Trivia Question, how I tried to solve it

       

A friend of mine told me that in the last six months, the last grandchild of one of our former presidents (who had already passed away) died.

I tried to  deduce who it was without checking the web directly. For example, I  looked up when various presidents were born to narrow it down, but try not to search for the answer itself.

I could look this up easily. However, by spending time thinking about it and exploring related questions, I might learn things I  didn’t know before.

Things I care about? Maybe.

I now have a lot of white space, so you can think about the answer yourself and perhaps make a guess, then my reasoning process and the answer.

Before answering, I’ll walk through the reasoning I used for my educated guess.
Assume the president was born in year x.

ADDED LATER: In the original version of this post (and its still there) I would make comments like: 

                           Warren G. Harding- why is the G always mentioned.

A commenter pointed out that middle names and initials are an American thing. This made me wonder why some of them didn't use their middle initial. Hence I have ADDED information about that. I won't bother writing ADDED LATER for those late adds. 

END OF ADDED LATER

Assume the president’s youngest child is born in approximately year x+35.

Assume that child’s youngest child is born in approximately year x+70.

Assume the grandchild lives 80 years, so dies in approximately year x+150.

Then x+150=2025, so x=1875.

Since this is an approximation, I looked at all presidents born between 1850 and 1900. The website I consulted tells us the answer. What would we do without the internet? (Maybe spend more time offline tightening our bounds on the polynomial van der Waerden numbers.)
Here are all the presidents who were born in a year in [1850,1900].

Theodore Roosevelt — born 1858. Formal name: Theodore Roosevelt Jr. No middle name. 

William Howard Taft — born 1857. He seems to have his full name mentioned. Why? 

Woodrow Wilson — born 1856. Formal name: Thomas Woodrow Wilson. So it would be impossible to use a middle initial unless you do what David Dwight Eisenhower did and swith the two names, so then he would be Woodrow T. Wilson. 

Warren G. Harding — born 1865

Calvin Coolidge — born 1872. Formal name: John Calvin Coolidge Jr. Similar to Woodrow Wilson.  Cal's dad was John Calvin Coolidge Sr.  Naming your kid after yourself, including the middle name, coud be a mistake, see here.

Herbert Hoover — born 1874. Formal name: Herbert Clark Hoover. I am surprised he wasn't called Herbert C. Hoover. Maybe Herbert Hoover was better because its alliterative. 

Franklin D. Roosevelt — born 1882

Harry S Truman — born 1884 (There really is no period after the S. Both chatty and Wikipedia get that wrong.)

Dwight D. Eisenhower — born 1890 (born David Dwight Eisenhower; he preferred to be called Dwight).

When I was asked the question, I guessed Harry S. Truman. I was wrong.

In fact, none of the presidents on that list is the one. 

The correct answer is John Tyler, who was born in 1790.

My rule-of-thumb assumptions (35 years to have a child; an 80-year lifespan) were  large underestimates for this case. John Tyler had sixteen children. The third-to-last was Lyon Tyler, born in 1853 — John Tyler was 63 at the time, which is 28 years more than my estimate of 35. Lyon Tyler had six children; the second-to-last was Harrison Tyler, born in 1928 — Lyon was 75, which is 40 years more than my estimate of 35.

(In 1840 William Henry Harrison and John Tyler were elected Prez and Veep. WHH died after giving his inaugural speech in the cold rain, and Tyler became president. Lyon Tyler names his son Harrison. My thought was: Did Lyon name his son after WHH? I asked Google 

Why did Lyon Tyler name his son Harrison? 

The AI Overview said:

Lyon Tyler named his son Harrison because his own mother, Julia Gardiner, was a member of the Harrison family of Virginia, making Harrison a great-grandson of both President John Tyler and William Henry Harrison, the president whom John Tyler succeeded. Naming his son Harrison was a way for Lyon Tyler to honor the family connection to both presidents, particularly the presidential connection. 

Thats not quite right- Harrison is John Tyler's grandson, not great-grandson. 

I didn't know that John Tyler's grandchild was named Harrison.

I didn't know that John Tyler's grandchild was also related to WHH.

)


Harrison Tyler died in 2025 at the age of 96, which is 16 years more than my estimate of 80.

So my point (do my posts need a point?) is that I made an approximation but was still way off. John Tyler is an outlier, which is hard to account for.

Let’s say I assumed 60-year-old fathers and the grandson lives to 90. Then we would have:

x + 210 = 2025
x = 1815

This is an approximation, so I would look at presidents born between 1790 and 1840:

John Tyler: 1790. No middle name. 

James K. Polk: 1790. Why is the K always mentioned?

Zachary Taylor: 1784. No middle name. 

Millard Fillmore: 1800. No middle name. 

James Buchanan: 179. He never had kids. That’s just as well, since his children would have had the stigma of their father being one of the worst presidents of all time by most accounts.

Abraham Lincoln: 1809. Born February 12, 1809 — the same day and year Charles Darwin was born. No middle name. 

Andrew Johnson: 1808. No middle name. 

Ulysses S. Grant: 1822.  Born Hiram Ulysses Grant, but he didn’t like that the initials were H.U.G.

Rutherford B. Hayes: 1822. Why is the B always mentioned?

James Garfield: 1831. James Abram Garfield. I sometimes see the A initial and sometimes not. 

Chester Arthur: 1829. My Darling’s favorite president — really! Formal name Chester Arthur which I have seen written, though not as much as the others. Perhaps I just didn't notice him as much as my Darling did. 

Grover Cleveland: 1837. Formal name: Stephen Grover Clevelant. 

Three points:

1) When I picked 60–60–90, I did not know that John Tyler would actually make it onto the list.

2) He just barely made the list.

3) I would not have picked 60–60–90 unless I had already learned that 35–35–80 was far too small.