Each issue Jerry, O4R's puzzle guy, brings you a set of puzzles. As always, the answers will be published in the next issue. They are now posted here as well! Questions and discussion may be directed to Jerry.

**PROBLEM 1**
A bear walks a mile South, a mile West, a mile North and returns to her
starting point. Identify the places from which she could have started. (Due
to Paul Halmos, mathematician extraordinaire.)

**PROBLEM 2**
Why don't they build 200 story buildings?

**ANSWERS**

**Problem 1.** This is a fun problem because almost always some, or all, of the
recipients will insist they know the answer-the North Pole. On a percentage
(or measure) basis you don't get much, in fact you get zero for that
correct answer.
Now, hie thee-self South till you are near the South Pole. Stop when
circumnavigation of the Pole is exactly one mile, and you have another
starting place. Go a bit closer, till you can make two circles around the
pole before returning to your starting place. Obviously, you can continue
this process for 3, 4, ......n. So, here we have as many answers for
starting places as there are integers. But even with all of these, you
still have zero percent of the answers. For along each circle, you could
have started at any point whatsoever, and it turns out that all the
integers can't hold a candle to all the points on a line (or curve)
segment. (c.f. any elementary text on set theory and check on orders of
infinity).

**Problem 2.** Answer: People will only wait so long for an elevator, or walk so far to an
alternate bank, before they take their business elsewhere when possible.
This means that approximately every ten floors requires another elevator.
(Actually, you probably don't know of a ten-story building with only one
elevator.) Now, of course, elevators that only go from floor A to floor B
speed things up for those passengers; but alas, we then need roughly the
same number of elevators for each equivalent set of deleted floors. For 200
floors (with a footprint small enough so one bank of elevators suffices),
you'd need more than 20 elevators and, if you count the areas of the
elevators and approaches, there will be precious little (or zero) space
remaining for whatever purposes people were taking the elevator in the
first place.
Incidentally, when Peter Cooper built the five-story Cooper Union in New
York (in 1855) he was sure someone would invent a means of vertical assent
and included a cylindrical shaft five stories tall. It is still used today.