Re: Number sequence characterization

On Tue, 6 Feb 2007, mathedman@xxxxxxxxxxxxxxx wrote:

These kinds of questions are psychology questions NOT math questions!
There are infinitely many sequences which have any given finite
number of terms and each is as correct mathematically as any oyher.
So, the "correct" answer is the one the questioner expects to see!

I agree fully, and yet such quizzes *can* make sense. When the numbers in
the sequence are the values of a well-defined (but not by simple
expression or by recursion formula) function, for instance the solution to
a combinatorial problem, solving such a quiz could be the first step for
finding a more useful representation of that function - of course one has
to prove afterwards that it is indeed the same function.

And one can even make a reasonable test for a person's skill of such a
quiz: find not only the next number but give also the underlying law.
More than one solution is possible, but it is not easy to come up with a
solution that fits and is not arbitrary (i.e., would have worked with any
other continuation as well).

--
Helmut Richter
.

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