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Constraint Partitioning

aminzoll at ece.tamu.edu 
Dear all,
  I appreciate to let me know if there is any method in R to find all  
the possible solutions (non-negative integers) to the following  
constraint partitioning problem:

  X_1+X_2+...+X_(2k)=N
   X_1+X_2<=r_1
   X_3+X_4<=r_2
   X_5+X_6<=r_3
   .....
   X(2k-1)+X(2k)=r_k

  Thank you,
  Amin Zollanvari