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  • $\begingroup$ Would it help if you split your Tuples[{1,0},n] into two Tuples[{1,0},n/2] lists and work through each combination of the two lists, joining elements as you go? $\endgroup$ Commented Jul 7, 2013 at 8:26
  • $\begingroup$ Refer the algorithm to find subsets using "lattice of subsets" which actually starts for small number of promising subsets and than using them together to generate bigger subsets automatically ignoring irrelevant subsets. $\endgroup$ Commented Jul 7, 2013 at 9:11
  • $\begingroup$ How large is n typically in your cases? I mean with n=30 you have 2^30 tuples which is a number too large to do even the simplest loop Do[Null, {i, 2^30}];. $\endgroup$ Commented Jul 7, 2013 at 13:01
  • $\begingroup$ @halirutan n=30 is fairly easily achieved in 'small' examples. A particular example I've tried to compute that ran into a memory error had about n=24 to n=28 on each of 5 sets of equations. $\endgroup$ Commented Jul 7, 2013 at 16:41
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    $\begingroup$ @Zibadawa Preferably, one should be able to copy and paste code blocks into Mathematica and test out the code. TeX code is not functional when pasted into Mma. For big or long problems, a simplified example that illustrates the problem is acceptable (and preferred). You can also use d[i] as your variable and have it formatted as a subscript. See this and perhaps point 4 in this. $\endgroup$ Commented Jul 7, 2013 at 20:48