Any name for "focusing on the problem, not on the solution"

Solution 1:

Thinking out of/outside the box

is a metaphor that means to think differently, unconventionally, or from a new perspective. This phrase often refers to novel or creative thinking. The term is thought to derive from management consultants in the 1970s and 1980s challenging their clients to solve the "nine dots" puzzle, whose solution requires some lateral thinking.

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References

• Wikipedia
• Wiktionary
• The free Dictionary

Previous answer, kept for relevance

When I first read the question I believed you were referring to the XY-problem which is referred at meta.stackoverflow.com

The X-Y Problem, as it is sometimes called, is a mental block which leads to enormous amounts of wasted time and energy, both on the part of people asking for help, and on the part of those providing help. It often goes something like this:

• User wants to do X.
• User doesn't know how to do X, but thinks they can fumble their way to a solution if they can just manage to do Y.
• User doesn't know how to do Y either.
• User asks for help with Y.
• Others try to help user with Y, but are confused because Y seems like a strange problem to want to solve.

After much interaction and wasted time, it finally becomes clear that the user really wants help with X, and that Y wasn't even a suitable solution for X.

Solution 2:

There are many interpretations of this.

• A management consultant might like Goal-oriented (-directed, -driven etc.).
• The second solution in your story was, in the engineering sense elegant.
• How about enterprising: 2. characterized by great imagination or initiative
• Or even resourceful: able to deal skillfully and promptly with new situations, difficulties, etc.

In contrast simply "focusing on the problem" (or at least dwelling on the negative aspects of it) could be construed as pessimistic.