## Math for Figger Filbert*

*October 19, 2011 at 8:05 pm* *
2 comments *

A well-known problem:

A man walks 1 mile south, 1 mile east, and 1 mile north. He arrives at the same place where he started, and then he sees a bear. What color is the bear?

The answer, of course, is white. It’s a polar bear. These three moves will let a person return to the same place if he starts at the North Pole. (The person could also return to the same place if he starts at an infinite number of points near the South Pole, too. He could start at a point so that when he walks 1 mile south, he is at a point such that the east-west circle on which he is standing has a circumference of 1 mile. Then, he can walk 1 mile east to return to the same spot. Finally, he can walk 1 mile north, and he’s back where he started. Then again, he could also start at a point so that he can walk 1 mile south to a point where the circumference of the east-west circle is 1/2 mile, do that loop twice, then walk 1 mile north. Or find points where the cicumference is 1/3 mile, 1/4 mile, 1/5 mile, etc. You get the idea. However, since there are no bears in Antarctica, the answer to my original question is still correct.)

Two points about this:

- In answer to the question, “Are there polar bears in Antarctica?” there is only one correct answer:
*Only if they are bipolar.* - I really don’t care to receive silly comments about how a bear trapper could capture a grizzly and take him to Antarctica, or how a brown bear might mistakenly meander north to the Arctic Circle.

Here is a similar question:

A man runs 90 feet, turns left, runs another 90 feet, turns left, runs another 90 feet, and turns left. He is now headed home, and two men with masks are waiting for him. Who are they?

If you don’t know the answer to this riddle, remember that today is the first day of the World Series. My prediction? The Rangers will win easily. It’s not really a fair fight. I mean, members of the Lone Star State’s law enforcement agency with opposable thumbs and automatic weaponry versus defenseless birds? Seriously, if the Rangers don’t win, then we need to seriously reconsider the theory of natural selection.

If you watch the first game of the World Series tonight, remember to enjoy the game. Please don’t get caught up trying to figure out if it converges or diverges.

Here are a few baseball-related math puzzles:

- A baseball player has four at-bats in a game. At three different times during the game, his batting averages for the entire season (rounded to three decimal places) have no digits in common. What was his average at the end of the game?
- During a little league game, the visiting team scored 1 run per inning, and the home team scored 2 runs per inning. What is the final score of this seven-inning game?
- During the first half of the season, Derek batted .100, but his average was .300 during the second half of the season. Similarly, Alex batted .200 the first half of the season and .400 the second half of the season. Both players ended up with the same number of total at-bats, yet Derek had a higher batting average for the entire season. How is this possible?

* *Figger Filbert* is a term for baseball fans who are obsessed with statistics. Such fans are easily identified; they will make statements like, “Did you know that Albert Pujols is batting .275 when facing married pitchers in suburban ballparks that only sell popcorn on the mezzanine level?” It is a synonym for *number nut*.

Entry filed under: Uncategorized. Tags: average, baseball, Cardinals, polar bear, postaweek2011, Rangers, St. Louis, Texas, walk, World Series.

1.Joshua | October 20, 2011 at 3:39 amThe polar bear question makes me think you’ve been reading Numberplay recently: http://wordplay.blogs.nytimes.com/2011/10/17/numberplay-what-color-was-the-bear/

And your very last question makes me wonder whether you read an earlier Numberplay column featuring yours truly: http://wordplay.blogs.nytimes.com/2011/07/25/numberplay-bart-and-lisa-paradox/

2.venneblock | October 23, 2011 at 8:29 amI’ve seen the polar bear question in many venues. Didn’t see the Numberplay version. I mainly included it in my blog as an analog (and red herring) to the baseball problem.