->  DW> So if the teacher had, say, just stated Triple to be 6 instead of 3, 
->  DW> the thing would have been perfectly possible. 
 
-> Agreed. 
 
-> The sticking point then would be how that might be achieved and  
-> checked by a student...geometrically. 
 
-> I can now also see easier ways of checking the coverage of any 3  
-> circles in any 3 locations virtually - and I guess then altering  
-> location to search for an outcome - but requiring effort well  
-> beyond normal homework. 
 
-> I look forward to reading what you get from the teacher.... 
  
"The student" would just do the algebra. I think we've done it 
previously. If the *total* double-overlap area is X, and the *total* 
single-coverage area is Y then: 
  
X + Y + 3 = 36     (total area covered = 36) 
Y + 2X + 9 = 60    (total area of circles) 
  
Subtract top from bottom: 
  
X + 6 = 24 
X = 18 
  
which we know is the answer. This method makes no assumptions as to how 
the circles are arranged. 
  
Normally, the class would be in session right now. It meets on Sunday 
mornings. But this weekend is the Thanksgiving holiday here in Canada 
(strictly, it's tomorrow, Monday, but a lot of people go away for the 
whole weekend), so the today's class has been cancelled. We'll have to 
wait another week before I can tackle the teacher. 
  
                               dow 
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