Month: January 2009

Timely Trivia Question

One person administered the presidential oath of office nine times (a record). Who was that person, and to which presidents did he administer the oath? Scroll down for the answer.

John Marshall, Chief Justice of the United States from 1801 to 1835, administered the oath to Thomas Jefferson in 1801 and 1805, James Madison in 1809 and 1813, James Monroe in 1817 and 1821, John Quincy Adams in 1825, and Andrew Jackson in 1829 and 1833.

Roger B. Taney, Marshall’s successor as Chief Justice (1836 to 1864), administered the oath of office seven times. Warren E. Burger (Chief Justice from 1969 to 1986) administered the oath six times.

For more trivia about inauguration day, go here.

Math Puzzler

Here is the problem (from Misha Lemeshko, via Eugene Volokh):

8809 = 6
7111 = 0
2172 = 0
6666 = 4
1111 = 0
3213 = 0
7662 = 2
9312 = 1
0000 = 4
2222 = 0
3333 = 0
5555 = 0
8193 = 3
8096 = 5
7777 = 0
9999 = 4
7756 = 1
6855 = 3
9881 = 5
5531 = 0

2581 = ?

I found the general and specific solutions to the problem after pondering it for about 15 minutes. Can you do it?

If you’ve given up, or want to check your answers against mine, scroll down.

Specific solution: 2581 = 2, because…

General solution: The value of a string of numbers comprising the integers 0, 1, 2, 3, 5, 6, 7, 8, 9 is equal to the sum of the values of the integers contained in the string, where the value assigned to each integer is equal to the number of closed curves contained in it. Thus: 0 = 1, 2 = 0, 3 = 0, 5 = 0, 6 = 1, 7 = 0, 8 = 2, and 9 = 1. Therefore, for example, 0000 = 4 because each integer in the string has 1 closed curve; that is, 1 + 1 + 1 + 1 = 4.

Note that the preceding general solution omits the integer 4. Why? There is no way of determining the value of 4 because it doesn’t occur in Lemeshko’s list of strings. If, however, the value of 4 were known to be 0 (e.g., 8884 = 6, 1114 = 0), the general solution would be as follows: The value of a string of numbers comprising the integers 0 through 9 is equal to the sum of the values of the integers contained in the string, where the value assigned to each integer is equal to the number of closed curves contained in it. Thus: 0 = 1, 2 = 0, 3 = 0, 4 = 0, 5 = 0, 6 = 1, 7 = 0, 8 = 2, and 9 = 1. Therefore, for example, 4444 = 0 (0 + 0 + 0 + 0 = 0) because 4 (in standard typography) contains a closed area but not a closed curve.

If, however, the value of 4 were known to be 1 (e.g., 8884 = 7, or 1114 =1), the general solution would be as follows: The value of a string of numbers comprising the integers 0 through 9 is equal to the sum of the values of the integers contained in the string, where the value assigned to each integer is equal to the number of closed areas contained in it. Thus: 0 = 1, 2 = 0, 3 = 0, 4 = 1, 5 = 0, 6 = 1, 7 = 0, 8 = 2, and 9 = 1. Therefore, for example, 4444 = 4 because each integer in the string has 1 closed area; that is, 1 + 1 + 1 + 1 = 4.

A Logical Fallacy

The sub-hed of an article at City Journal asks “If human beings are naturally risk-averse, then what the heck happened on Wall Street?” The question can be expressed in the following syllogism:

Major premise: All humans are risk-averse.

Minor premise: Humans work on Wall Street (i.e., financial markets).

Conclusion: The humans who work on Wall Street are risk-averse.

It should be obvious to the casual observer that both the major premise and conclusion are false.

The article, by the way, is spot-on. Don’t be deceived by its flawed sub-hed.