Re: What is next in the series? 2 more Q
- From: "The Qurqirish Dragon" <qurqirishd@xxxxxxx>
- Date: 23 Jun 2006 07:19:48 -0700
Pubkeybreaker wrote:
Ben Rudiak-Gould wrote:
Dave L. Renfro wrote:
Iamaskingu wrote:
11, 100, 9, 64, 7, _
as I can justify answer (b), I think I'm absolutely right to invoke Occam's
razor and claim that (b) is the /correct/ answer.
I can invoke Occam's razor to get yet another simple answer.
The pattern is odd, even, odd, even, ... where the odd numbers
decrease by 2 and the even numbers decrease by 36. This gives
28 as the next number....
If you want to insist that the correct answer has to be among those
given,
then I can claim 48 is the correct answer, where the rule is now:
The odd numbers decrease by 2, but the even numbers just decrease
*by any amount*.
Or I could say the the correct answer is 8. The pattern (with
extension
to the left) is
.... 48 13 100 11 100 9 64 7 8 5 -52 ......
Where the even numbers are decreased by 4K * previous odd number
as k =...-1, 0,1,2,3,4,...
100 = 48 - 13 * -4
100 = 100 - 11* 0
64 = 100 - 9*4
8 = 64 - 7*8
-52 = 8 - 5*12
etc.
Your assumption that the even numbers are squares imposes
additional requirments on the sequence. My sequence might
be taken as "simpler" than yours because I impose no structure
on the even numbers.
Until one can give a METRIC which defines what it means for one
answer to be "simpler" than another, Occam's razor is not applicable.
These kinds of questions are ridiculous.
This is why I am careful with these on exams.
When I introduce sequences in class, it is important for the students
to be able to recognize or find patterns, to come up with a general
rule. When I give such a problem, I *never* make it a multiple choice
question.
Rather, I say "provide the next 3 values, and explain how you
determined them"
Every problem I have given has an "obvious" answer (usually of the form
a_n=nx+a_0 or a_n=x^n*a_0 for beginning classes), but if someone gave a
true reasoning for another pattern (such as those polynomials in an
earlier post), then I would accept it.
I even tell the students about how to create a general polynomial to
fit any pattern of numbers- but that is usually too much work to
complete and still have time for the rest of the exam.
.
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