Matrixes and Randomization in Excel

The size of the limit variable would have a dependence on the size of the set, but its a statistical dependence on the variance in the set coupled with the number of solutions you want to retain, not just the total numbers (at least for reasonably small groups). You could probably do something like take the average variance of the numbers or a multiple of the standard deviation as your limit. Edit: Actually thinking more about the math, stdev ends up rather huge.

However, there's really no point if you just want the closest combo, as you can brute force a converging limit by taking the difference on each try, storing it as a min difference, and then discarding anything that doesn't meet that min. No guesswork on what to throw away, and it converges quite fast.

Jam it back in, in the dark.

If you want a long list of potential matches, then the limit depends on: the length of the list, the variance of the list, and how many matches you want. More than that, I can't say, as its complex.

If you want one match, then just do a brute force.

if( tolerance > LastTotal1Diff ){
tolerance = LastTotal1Diff;
}

which will end up with the closest match for your first sum if you assign Total1Diff to LastTotal1Diff at the end of each successful loop.

You could also do minima of the total difference for both sets if they weren't going to add up to such a close set of numbers.

You can also solve this in Excel using packrat's general strategy, if you don't like coding. X columns for the bit mask, X columns for your numbers, summary columns that give the totals, columns for the differences, and a column for the difference total. In a simple form with three numbers.

Target 1	Target 2									
100000		20000									
Bit 1	Bit 2	Bit 3	30405	2103	128923	Sum 1	Sum 2	Diff 1	Diff 2	Diff Total
0	0	0	0	0	0	0	161431	100000	141431	241431
0	0	1	0	0	128923	128923	32508	28923	12508	41431
0	1	0	0	2103	0	2103	159328	97897	139328	237225
0	1	1	0	2103	128923	131026	30405	31026	10405	41431
1	0	0	30405	0	0	30405	131026	69595	111026	180621
1	0	1	30405	0	128923	159328	2103	59328	17897	77225
1	1	0	30405	2103	0	32508	128923	67492	108923	176415
1	1	1	30405	2103	128923	161431	0	61431	20000	81431

There's nowhere I can't reach.