The Perils of Predicting Patterns

Date: 11/02/2003 at 07:19:27
From: Su
Subject: number pattern

What is the next number in the pattern 1,3,6,10 ___?  

If the pattern is to add 2, 3, 4, and then 2, 3, 4 again and again, it
should be 12.  But if the pattern is to add 2, 3, 4, 5, and so on,
then it should be 15.  Which is correct?

Date: 11/02/2003 at 09:40:07
From: Doctor Tom
Subject: Re: number pattern

Hello Su,

There can't be a single "correct answer" for any question like this,
since no matter what list of numbers you give me, I can find a formula
that will fit them to any following number.

Usually what is desired is the "simplest" answer, and unfortunately,
different people's definition of what it means to be "simple" varies.

Obviously, adding 2, then 3, then 4, then 2, then 3, then 4, then 2,
and so on, is one way to extend the sequence; and adding 2, then 3,
then 4, then 5, then 6 is another.

To my mind, the second is slightly simpler but only because the
pattern presented so far does not give us any reason to think that
we should go back to adding 2 to obtain the next number.

These sorts of patterns are used in intelligence tests, and the
"correct" answer is "whatever very intelligent people think the
correct answer is".  That's not much help, is it?

I remember a wonderful example shown to me once that illustrated
how silly this sort of question is.  Here it is:

  What comes next in this sequence?

  33, 23, 14, 9, ___

The answer is "Christopher Street".  The reason is that the numbers
are the exits of the 6th Avenue subway in New York City.

- Doctor Tom, The Math Forum
  http://mathforum.org/dr.math/