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Feb 8th, 2016
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  1. mids[c_] := Table[Total[Take[c, i - 1]] + (c[[i]] + 1)/2, {i, Length[c]}]
  2. midgoodQ[p_] := [Not] IntersectingQ @@ Map[mids, p]
  3.  
  4. midgoodQ[{{4}, {1, 3}}]
  5.  
  6. During evaluation of In[56]:= Part::take: Cannot take positions 1 through 3 in {4}. >>
  7.  
  8. Out[56]= True
  9.  
  10. [Not] IntersectingQ @@ Map[mids, {{4}, {1, 3}}]
  11.  
  12. Out[57]= True
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