-> the algebra (which presumes no restraint of location, no matter  
-> how the problem is worded) - and the logic of geometry.... 
 
-> Case 1 - Setting the total area to 36 
 
-> Thrice coverage - set logic = 1.18, geo-prog = 7.3 and my  
-> eyeballing a scribble = 5ish. 
  
I am convinced that, geometrically, if Circle = 20 and Total = 36, 
Triple can have any value between 4.0 and 7.3, depending on exactly how 
the circles are arranged. 4.0 corresponds to the arrangement with two 
circles superimposed and the third partially overlapping them. 7.3 
corresponds to the arrangement with the centres of the circles at the 
vertices of an equilateral triangle. It would be possible to "slide" 
the circles from one of these arrangements to the other while keeping 
Total constant at 36, so I imagine that Triple would smoothly move from 
one end of its range to the other, covering all possibilities in 
between. It may possibly go outside the stated range, but I doubt it. 
  
So if the teacher had, say, just stated Triple to be 6 instead of 3, 
the thing would have been perfectly possible. 
  
                             dow 
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