I see the distinction and also think Trivial was right.

Just wanted to say that the switch in constraints from case 1 to case 3 (empty bags are first allowed, then not) in her original post may led to Yongcheng's comment.

I agree the latter cases seem too much for high school students. Physics is a good application, and thanks for illustrating the problem there. But I'd say that the underlying abstract problem may turn out to be easier to understand ... :)

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