William Henry Harrison Trivia

This week we continue our chronological look as US presidents with a look at our ninth president, William Henry Harrison. He is a good president for trivia purposes, and probably largely forgotten otherwise, as you shall soon see. However, as usual, we start with our weekly logic puzzle. The answer and solution appear at the end of the column.

Logic Puzzle

Adam and Bob wish to play Russian roulette. Here are the rules:

1. The gun has six chambers.
2. One to five bullets must be placed in the gun at all times. This can be adjusted before each pull.
3. The gun must pass back and forth after every turn.
4. No other methods of randomization can be introduced like spinning the gun or flipping a coin.

 

How can they achieve a fair game in which each player has a 50% chance to survive?

William Henry Harrison Trivia

Following is my hand-picked trivia about William Henry Harrison.

1. • Harrison had the shortest presidency in US history at just 30 days (3/4/1841 – 4/4/1841)
2. • Last president to be born a British subject
3. • First of eight presidents to die in office
4. • Founding member of the “Curse of Tippecanoe,” in which presidents elected in years evenly divisible by 20 tend to die in office. Members of this club with year elected president are: William Henry Harrison (1840), Lincoln (1860), Garfield (1880), McKinley (1900), Harding (1920) and Franklin Roosevelt (1940) and Kennedy (1960).
5. • Grandfather to 23rd president, Benjamin Harrison
6. • Delivered the longest inaugural address at 8,445 words, which took nearly two hours to read.
7. • A likely contributing cause to his death was the length inaugural address, delivered on a cold and rainy day, without a coat nor hat. The likely final cause of death was septic shock (something I personally have had).
8. • After his death, there was a constitutional crisis about the next steps. The Constitution states that in the event of a presidential death the vice president takes over the Powers and Duties of the Office, but is unclear if the vice president actually becomes president or just assumes the duties.
9. • Originally, he wanted to be a doctor, but dropped out of the Pennsylvania Medical School because he couldn’t afford the tuition.
10. • Was 68 years old when assuming the presidency, the oldest to date at the time.
11. • Fathered ten confirmed children, ranking him second among all presidents. There were also six more alleged children he fathered.
12. • Had a pet goat as president.

 

Logic Puzzle Answer

1. Player 1 puts two bullets in the gun and pulls. If he survives to go step 2.
2. Player 2 puts three bullets in the gun and pulls. If he survives, go back to step 1.

 

In the first two rounds, the chances that player 1 and 2 losing should be the same. If they both survive, you just repeat the process, so it’s all fair. Let’s let:

p = Probability player 1 dies in round 1

q = Probability player 2 dies, assuming he must pull the trigger.

For the chances of dying in the first two turns to be the same we set:

p = (1-p) q

p = q – pq

p + pq = q

p (1 + q) = q

p = q/(1+q)

With only six chambers, there are only six viable values for q. Let’s start with q = 1/6. That leads us to p = 1/7. Since the gun doesn’t have 7 chambers, this won’t work.

Let’s try q = 2/6 = 1/3. Then p = 1/4. That won’t work with a six chamber gun.

Let’s try q = 3/6 = 1/2. That leads to p = 1/3. That works with two of the six chambers. So, the first player must use two bullets and the second player three.

In case you’re wondering, a value of q = 4/6 = 2/3 leads to p=2/5, which doesn’t work.

A value of q = 5/6 leads to p=5/11, which doesn’t work.

A value of q = 6/6 does lead to p = 1 / 2, however it was stated in the rules there must always be at least one empty chamber.