Without giving it much thought (therefore I may most certainly be wrong), I think it's a question of 3 or 4 variables and combinations
You choose wxyz
substract zwxy (let's say xwyz is bigger)
You have 4 pairs of substractions:
z-y
y-x (+1)
x-w (+1)
w-z (+1)
Then you give the following information:
How many of the results are 0 and a number of results for these equations.
You choose w-z(+1) for example (which is not zero).
I think the program can calculate in no time what combination of results/equations can be valid (and having different numbers grants there'll be no two valid combinations) and take the correct value for wxyz, therefore guessing the missing equation.
Just guessing here, didn't pick up a paper so my assumption may be completely off the mark.
Daniel