posted 8 years ago
Well, the knapsack interpretation is more exciting than Paul's "buy nothing" interpretation, which yields an extremely trivial problem. (Which of course is his point.) I believe the difference is in how we interpret "keep the difference [between two values] to a minimum". Steve is implicitly assuming that what is meant here is to keep the absolute value of the difference to a minimum. While Paul is happy to let the magnitude of the number get as large as possible, as long as it's negative. Paul's interpretation may be literally correct, but I think it's pretty ambiguous. What does "difference between A and B" mean? Is it A-B? Or B-A? Depending on the answer, the solution might be to pick all of the players, rather than none. At least if we take the absolute value, that ambiguity doesn't matter, and it does yield a more interesting problem - albeit one that's already discussed extensively in the literature.