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Golomb's Puzzle Column 
Number 32:
Finding Examples
Solomon W. Golomb
- The product of three distinct integers in arithmetic progression
[which can be written
] is the fourth power of a
non-zero integer. What are the possible solutions, if any?
- A and B are similar
matrices of integers,
yet AB is not similar to BA. How is this possible?
- A pentagon (i.e. a plane figure bounded by 5 straight line
segments) can be partitioned into four regions which are congruent
to each other, and similar to the original figure. Can you find
this pentagon?
- Is it possible to ``complete'' the
array
to form a 
Latin square?
- Suppose that
is one of four distinct complex roots
of 
(where a and b are real
constants). Express the other roots of 
in terms of
. (You don't have to ``solve'' the quartic!)
Ramesh Rao
Sun Oct 22 16:54:28 PDT 1995