Certainly a valid homework problem would be one that includes the algebraic
work as suggested. However, the goal of that particular Matter &
Interactions homework problem was also valid. It was intended to address
another important aspect of critical thinking like a physicist, namely that
starting from a few powerful fundamental principles rather than
formula-grabbing it is possible to analyze new situations never previously
encountered, in this case an arcane particle reaction. The intent of
omitting the algebraic solution was to make this point stand out in high
relief. This form of a problem also addresses the strong learned tendency
of students to think that the algebra is the only important part of a
problem, rather than setting up the problem (and checking the result, an
additional point not addressed in this particular problem).
I don't agree that the original problem was of the type that "don't require
much reasoning." It's a big step for students to progress from "I don't
have any idea where to start because I've never seen this problem before"
to "I guess I could see what momentum and energy conservation might bring
to bear on this problem, even though I don't initially see what."