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 Discussion: Circle 3 tool Topic: Re: Circle 3 Related Item: http://mathforum.org/mathtools/tool/3033/

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 Subject: Re: Circle 3 Author: mmckelve Date: Feb 8 2004
Jeanette,

The lowest-to-highest number strategy was the same one I used, and it
seemed to work really well.  I also recommend starting with circles having high
numbers close to each other, so you have less assumptions to make.  So,
combining these strategies you have 2 circles with their middle numbers filled
in (both preferably greater than 1)--start with the lowest number available,
put that in the circles' intersection, and see if you can make the circles add
up to 3 in the 3rd part of the circle.  If you can't, you can discard that
smallest number as a possibility for that spot and keep moving up to higher
numbers, until you eventually reach one that works in that spot.  This has a
high probability of being right.  Here's an example of a solved puzzle:
http://www.mste.uiuc.edu/courses/ci336sp04/folders/mmckelve/images/circle3.jpg
In this puzzle, I started with the circles containing numbers 1.3 & 1.4.  I
tried 0.4 first, but it didn't work, then 0.5 did work, and I had the 0.5, 1.1,
and 1.2 placed.  I then moved to the 0.7 and 0.9 circles.  I think I started
high in that case, since the numbers were low, and it seems probable that lower
numbers will share a high number (though this is by no means guaranteed).  Once
you get 4 circles filled in like that, you can quickly see whether you've been
wrong and if so, start working backwards, taking out piece by piece and seeing
of something else would've worked instead.  This method can be very quick,
especially if you happen upon the right numbers right off the bat.  Even if you
have to backtrack some, it should be a lot faster than random guessing :)  Best
of luck!

--Michael--

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