Martin Van Buren Trivia

This week we honor the eighth president of the United States, Martin Van Buren. As usual, we salute him with some trivia. However, before we get to that, I present our weekly logic puzzle.

Logic Puzzle

Five pirates come upon a treasure of 1,000 gold coins. The pirates are all of different rank. Per pirate law, the pirate of the highest rank gets to make a suggestion of how to distribute the coins among all remaining pirates. Then that suggestion will be voted on by all pirates, including the one making the suggestion. If it gets more than half the vote, then the suggested division shall be carried out. Otherwise, that pirate who made the suggestion must walk the plank. In that event, the next pirate in rank order will make a suggestion. This process continues until a suggestion is approved.

Here are the pirates’ goals, in priority order, starting with the first.

1. Get as many coins as possible.
2. Watch other pirates walk the plank (because pirates are bloodthirsty).
3. Stay alive.

 

All pirates are perfect logicians. What is the maximum number of coins the first pirate can get?

Martin Van Buren Trivia

1. Van Buren spoke Dutch as his primary language. The only president to not have English as his primary language.
2. Van Buren was the first president born a US citizen.
3. Van Buren was only 5’6” tall, making him tied (with Benjamin Harrison) for second shortest president. James Madison was the shortest at 5’4”.
4. Nicknames include “Little Magician”, “Red Fox”, “Old Kinderhook” and “Martin Van Ruin” by his critics.
5. One of five presidents to have red hair. The others were Washington, Jefferson, Jackson and Coolidge. Interesting that four out of the first eight presidents were redheads.
6. One of four presidents who were already widowed before becoming president. The other three were Jefferson, Jackson and Arthur. Three others become widowers while serving as president. Van Buren’s daughter-in-law served as First Lady during his term.
7. Some say the origin of the expression “OK” was a campaign slogan for Van Buren, who was known as “Old Kinderhook.” However, there are other theories. I tend to not believe this one.
8. Said the two best days of his life here his first and last as president.
9. Favored peace with Great Britian and settled the border between Maine and Canada.
10. Only president to have neither a college degree nor be a commissioned officer in the military.

 

Answer to Logic Puzzle

997

Solution to Logic Puzzle

This is the kind of puzzle that should be solved recursively by starting the simplest case of one pirate and moving back from there. Let's label the pirates 1 to 5, according to their rank, with pirate 1 the highest.

Only pirate 5 left: He would suggest giving himself all 1000 coins, vote in favor and keepall of them.

Pirates 4 and 5 left: Pirate 4 may as well walk the plank without making a suggestion. Even if he gave pirate 5 everything, pirate 5 would still vote "no." A 1-1 split vote is not more than 50%, so this situation is hopeless for pirate 4.

Pirates 3 to 5 left: Pirate 3 knows that pirate4's vote will be easy to buy, since pirate4 will die if pirate 3 dies. He won't need pirate 5's vote. So his suggestion would be:

Pirate 5 gets 0

Pirate 4 gets 1

Pirate 3 gets 999

This would pass with "yes" votes from pirates 3 and 4.

Note that he has to offer pirate 4 at least one coin. If he offered him 0, pirate 4 would vote "no," just for the pleasure of watching pirate 3 walk the plank, even at the cost of his own life next.

Pirates 2 to 5 left: Getting the votes of pirates 4 and 5 will be cheap. He can suggest one to pirate 5 and two to pirate 4. They make out better by voting "yes" than "no." He doesn't need pirate 3's vote, so can offer him nothing. Thus, pirate 4 should suggest:

Pirate 5 gets 1

Pirate 4 gets 2

Pirate 3 gets 0

Pirate 2 gets 997

This would pass with "yes" votes from pirates 2, 4 and 5.

All pirates left: Getting the votes of pirates 3, 4 and 5 will be cheap. In fact, he needs only two of them, so the cheapest votes to buy will be 1 coin to pirate 3 and 2 coins to pirate 5. They make out better by voting "yes" than "no." He doesn't need the votes of pirates 2 or 4. Thus, pirate 5 should suggest:

Pirate 5 gets 2

Pirate 4 gets 0

Pirate 3 gets 1

Pirate 2 gets 0

Pirate 1 gets 997

This would pass with "yes" votes from pirates 1, 3 and 5.

So, the answer is pirate 1 can get 997 coins.