Solid lines mean multiply. Dashes mean add.
Place numbers in the empty circles so all the calculations work out correctly.
Solving this puzzle is equivalent to factoring 6x^2 + 17x + 12.
EDIT: Here’s a version based on jd2718’s comment below.
The whole point of my expressing this as a puzzle is it can be generalized into other puzzles which have nothing to do with factoring, for example:
I was planning a worksheet that started out with only 3 circles and then worked its way up to more complex puzzles. (ADD: See files below.)
It’s also possible to express factoring a cubic this way! It’s a messy diagram but I’ll see if I can get it up this week. (ADD: Post is here.)
ADDED Jan. 31 2012: These were part of a presentation I gave at a conference. The puzzles in “Puzzles 3” are all equivalent to factoring a quadratic.