After a too brief look at Trinagon, a guy told me : "Hey, why don't you 'just' compute all the possibilities ... " 
... hinting that this would lead to the obvious solutions.

Well. Sure. Not that the first would be so hard. But the other ?

So. After making the not extremely big effort to calculate all those permutations on the puzzles, the conclusion is :
There are often too many for our limited resources to compute : Septillions or so (a trillion trillions). 
These puzzles often DO have more permutations than the rubiks cube does.

Fortunately, this is not always the case, some puzzles have just a few hundred, or thousands or hundred thousands.
In that space, it is possihble to find perfect solutions, by letting the computer play (with medium algorithmic intelligence)
So. Now there are real absolutely perfect solutions for many puzzles available ! 
Does this give a clue to how hard they are : NO, not really. Its not that straightforward.
but  that's another story ...