[majelix]

Yes, if you can't solve a problem, you certainly can't solve a problem in a supportable manner.

Agile has the concept of Spikes (http://www.scaledagileframework.com/spikes/) for researching new problems. The key point that code is thrown away after completion -- this gives you the freedom to ignore normal methodologies and not have to worry about technical debt.

Presumably, you then go back with this new knowledge and only now concern yourself with writing supportable code.