Submissions and Requests
As a puzzlesite owner, I get an occasional request for help on one problem
or another. When they're especially interesting, I usually turn them into
a POTW quickly. Though some may not be completely applicable to a POTW,
they're still interesting. Here are a few questions I've received,
followed by a few puzzle submissions I've received.
Requests for help

An interior designer has an intriguing dilemma. She has to move an amazingly
heavy armchair, but the only possible movement is to rotate it through ninety
degrees about any of its corners. Can it be moved so it is exactly beside its
starting position and facing the same way? [Update 9/18: One reader suggested
this problem should be attacked without requiring the angle of rotation
always be 90 degrees. Consider this as part (b) of this problem.]

An angus is anchored to a 6 meter rope. The rope is attached to the outside
corner of a shed measuring 4 meters by 5 meters in a rolling grassy meadow with
varying elavations. What area of grass can the cow graze in 1.5 hrs?

Prove that: Within a set of triangles having a constant base and constant
perimeter,
the isosceles triangle has the maximum area.

What is the missing number ?
30
26 34
22 ? 26
11 18 27 31

You have 6 pool balls, all identical in size though differently numbered.
5 balls are of the same weight, the 6th is different (i.e. heavier or
lighter).
You have a set of balancing scales and, using the scales twice only, you
have to identify the rogue ball.
Small Submissions

S     S
Enter a 4 letter word, divisible by 2, to get odd numbers.

14 people are eating at their hotel's restaurant. They are seated at
two tables which hold 8 and 6 people. If they are seated at these tables
for every meal, how many meals are needed to assure that every pair of
people sit at the same table at least once? What if the tables instead
hold 9 and 5 people?

a/b + b/c + c/a = 1
Does a solution exist for a, b, and c belonging to the set of
negative and positive integers?
Does any solution exist? If so, show a simple example.

Simplify the infinite product
(1+x)(1+x^2)(1+x^4)(1+x^8)(1+x^16)..., given x < 1.
Source: Many sources. Submissions from Denis Borris and Ravi Subramanian.
Solution
Mail to Ken