1, 4, 9, 16, 25, ?
of course, everyone (well, almost) would say "these are just the square-numbers; the next one is 36".
but as a mathematician you know that every number sequence
a_1, a_2, a_3, a_4, a_5, ...
has a infinite number of functions f which satisfy
f(1)=a_1, f(2)=a_2, f(3)=a_3, f(4)=a_4, f(5)=a_5. the values f(6) can be different as well. you could even conclude, that every number x is a continuation of the sequence, because you could find a function satisfying f(6)=x.
therefore there is not a "single" correct answer to number sequences.
now you could say: "you should always find the easiest/most simple function of all these". but what do you define as simple?
as a mathematician you would say "its very easy to calculate _polynomials_ to solve number sequences" (you just have to solve a system of linear equations).
so the main question is: how should you evalue/rate possible solutions to number sequences? or should you rather rate the corresponding function found?
2006-07-08
22:32:20
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9 answers
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asked by
yushoor
1