> Second, the article suggests that the problem should be introduced to children by casting in in terms of several rules of exchange ("For Alice, the transition vector (−1, −1, 1, 0) would represent the exchange of an apple and a banana for a cantaloupe."). But that would make the problem trivial: you start at the origin; without a rule of "exchange" in which the other party gives you as much as you want of something for free, you're never going to leave it.

I'm not sure what point you're trying to make here? That specific transition vector would be one such vector among several in a given ruleset. You're correct that for any ruleset, if I don't have at least one vector that can get me away from the origin, I'm stuck there, but then I also have to consider that I still might not be able to get to where I want to go. If I have the ruleset [(2, 0), (-4, 2)] I still can't get to (3, 5).