From: Calvin Ashmore (coa@andrew.cmu.edu)
Date: Sat Feb 28 2004 - 17:37:19 MST
> the funny thing is that the woman who put together this puzzle book calls
> herself the 'human computer'...
>
> how will you write a computer program to get the solution for this
problem?
I wish I had jumped on this thread earlier, but since equation manipulation
and generation is one of my "things", I'll add on to this:
The funny things about computers is that they're very very fast and
powerful, but very stupid and foolish when it comes down to it. For a human
to solve these sorts of puzzles, the process is usually built around
objectives, like getting the right digit in the 100's place and such.
Computers won't have any conception of this unless you spend a lot of time
teaching them.
The easiest way to get solutions to this is to actually solve it with brute
force, I think. For instance, one can define +, -, *, /, as binary
operators, and also bracket things with ( and ), and then just iteratively
construct every possible tree out of those symbols, where each of the leaves
may only be 8, 88, 888, or .8, etc., and there may be only eight leaf nodes.
There are a finite number of possible trees, and a decent program could
probably go through all of them (excluding things that won't produce
anything useful) in a matter of a couple of minutes.
I've played around with equation generation in a small program of mine-
http://www.icosilune.com/icosilune/cgraph/index.html
Which generates equations that will supposedly produce "interesting" images.
The key to it is to basically abstract the equation, that it is basically a
tree. One of the intriguing things about the way we solve problems is that
often we make these kinds of abstractions without really realizing it...
-Calvin
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