Puzzle Solution
Eden: #1 #2 #3 #4
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Eden Puzzle - General Solution

Solution #4 (General) -- submitted by Khaled Hammouda.


These kinds of problems could be easily formulated using first-order
predicate logic, which is originally an area of mathematical logic but
heavily used in artificial intelligence. The problem solution usually
involves writing what is called "well-formed formulas" (wff's) that
represent the facts in the puzzle. These wff's are then put in a normalized
form where we can use them for a procedure known as "resolution" and

You start with the goal (in this case the goal is the predicate: "X" ate the
apple) and then try to do the resolution by eliminating and merging wff's
together in a chain manner, until you reach a contradiction, then you
back-track and try another path, until you finally eliminate all wff's.
Along the way you do substitution of variables (including the variable "X"
above). If we reach the end point of the resolution, then we take the
substituted value of X to be the solution (in this case the value would be

Of course doing resolution by hand is good for problems with a few number of
wff's. For the Eden puzzle it's not practical to do it by hand. A very small
program written in Prolog will solve it right away, no sweat, you just need
to know a bit of Prolog to write it. For the solution I sent you earlier, I
just used an ad-hoc technique, nothing formal there :)

Thanks again for the puzzles, I really enjoyed solving them :)



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