-> Accepting the 20cm^2 circles must cover 36cms^2 only gets you.... 
 
-> Cover  Segment Cm^2  Total Cm^2 
 
-> Thrice  1.1572999     1.1572999 
-> Twice   7.2284667    21.6854002 
-> Once    4.3857666    13.1572999 
->         Totalling... 36.0000000  
 
-> Setting the thrice to 3 cm^2 then has the total coverage rise.... 
 
-> Thrice  3             3.0 
-> Twice   1.0237947     3.0713841 
-> Once   14.952411     44.857233 
->         Totalling... 50.9286171 
 
-> Neither of these optimums fit the specifications given. 
 
-> I'd conclude that the problem is geometrically impossible... 
  
You've lost me... 
  
                          dow 
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