Degenerate means something dumb, trivial, quick and short, in a logical context. Part of this is laziness and part of this is actually a good algorithm. If an obvious/previous strategy doesn't quite work, the question is how to tweak it so it does?
Another example of a degenerate solution is
x^2-y^3=1
Degenerate solutions are x,y = 1,0 -1,0 and 0,-1. You can see why people always look for those first. They do give a boost for other things.
Regenerated may be the next step--but basically, experienced puzzle gamers try to cheat up to find easy ways through the board, or ways they'd already seen. If a strategy that worked on level 7 works on level 28--even if 28 just sort of repeats 7 a few times--then level 28 doesn't count as a "new" level and is really just 7 repeated. Then it does not add to the depth of the game.
ETA: an example of a degenerate solution of a review would be:
I played Block Busters for ten minutes. I got to level 5. Up to four was hella easy but I think you need a new button or something for level 5. No way! That gets in the way of pure thinking. Plus there was no cool colorfull tutorial?! 1/10.
My principal said, 'Emo, Emo, Emo.'
I said 'I'm the one in the middle, you lousy drunk!'
-- Emo Phillips