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From: hall@aplcenmp.apl.jhu.edu (Marty Hall)
Subject: Re: A General Theory of Patterns?
Message-ID: <DCyFCu.9MB@aplcenmp.apl.jhu.edu>
Organization: JHU/APL AI Lab, Hopkins P/T CS Faculty
References: <403do0$p46@Venus.mcs.com>
Date: Mon, 7 Aug 1995 18:58:06 GMT
Lines: 28



In article <403do0$p46@Venus.mcs.com> jorn@mcs.com writes:
>
>Has anybody ever built an AI for solving the sort of IQ-test problems
>that involve *mathematical sequences*?
>
>Like: 1, 1, 2, 3, 5, ...?

When I was an undergrad we were given such an assignment. I recall
that the way we did it just came down to simple search looking for
repeated operations between neighboring numbers until you reduced the
entire sequence to just one number. 

1, 2, 3, 4, 5  --- subtract each number from the previous one to get 1's.
1, 4, 9, 16, 25 -- subtract each number from the previous one
                   to get 3, 5, 7, 9. Then do it again to get 2's.

You then reversed the operations to get the next number.

You could put in a lot of cases that found Fibonacci sequences, etc,
and the program would try a bunch and then use the shortest such
sequence of operations to pick the "right" answer. Lots of fun and
amazing to an undergrad how seemingly well it did, but just a toy
application, esp considering the definition of the "right" answer is
pretty subjective in many (most? all?) cases. 
							- Marty
(proclaim '(inline skates))
