-> To me,  the original problem was crafted using set logic,  
-> expecting geometricity to follow - unjustifiably. 
  
No. I suspect the teacher fell into the trap of providing *too much* 
information, not realizing that he had made the problem 
self-contradictory. 
  
If he had just used the words "closed figures" instead of
"circles", 
there would have been no difficulty. Alternatively, if he had given the 
total area *or* the triple-overlap area, but *not* both, the question 
would have been consistent, although probably not soluble by the kids 
to whom it was given. But, by stating "circles" and giving both areas, 
he unknowingly postulated an impossibility. 
  
I did the same a few times, when I was a math teacher. It's an easy 
trap to fall into. 
  
                            dow 
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