That's been the topic of several spirited discussions over the years. :-)

The administrator's answer is "find the best move (or line of moves)".

Of course, there can be some debate over how one defines "best", or even if it indeed has a consistent definition that works in all cases.

In one sense, it's a moot point, since some people solve it in their heads, some set it up on a board (real or virtual) and move pieces around. Besides that, we're (almost) all anonymous and there's nobody keeping score and nobody to make sure we're not "cheating".

So, IMHO, you're free to make your own definition! Your definition should be whatever makes puzzle solving enjoyable for you (that is, after all, the real goal). Naturally, if you make your definition more demanding, it becomes more difficult, but also more rewarding in terms of improving your chess skills.

Here's mine: I analyze the puzzle in my head (as if I arrived at this position OTB). I decide what the best possible outcome should be (win or sometimes draw), and then try to find a way to make that outcome fairly obvious. That is, I try to bring clarity to the position.

I am generally not so concerned about finding the "fastest" solution. A win is a win, whether it's mate in 5 or mate in 25 (and sometimes the longer mate is easier to see, more fun, and provokes a quicker resignation). When done, I write up my experience, for better or worse.

To elaborate on <zb2cr>'s excellent advice, I define "a decisive material edge" as the equivalent of a clear P ahead. This definition is essentially Kotov's advice for terminating calculation of the variations, and some of the puzzles result in just a P advantage. Some might disagree, but I consider such puzzles as quite legitimate.

Also, <zb2cr>, thanks for reminding me of the direct ways of breaking a attack on a piece: (1) capture the attacker; (2) block the line; or (3) move the attacked piece.

Spouge in re zb2cr and the list of options when attacked -- <(1) capture the attacker; (2) block the line; or (3) move the attacked piece.>

Isn't there an item (4)? Make more pressing counterthreat which demands reaction? (there should be a more succinct way to say this)

Isn't there an item (4)? Make more pressing counterthreat which demands reaction?>

Hi, <JG27Pyth>. When you get beyond fantasizing about mere belligerent mutant albino penguins and achieve rapture, you too will find ways of defending yourself against the nitpickers that frequent this site.

My exact statement was: <thanks for reminding me of the <<>direct> ways of breaking a attack on a piece>.

You will note the presence of the weaselly word "direct" in the statement, a compositional technique I learned principally from negative experiences on chessgames.com :)

I felt unready to enumerate defenses to an attack. In spirit, you are quite correct, of course, so here is my best shot at defenses to an attack, in typical but not infallible order of desirability:

(A) counter-attack

(B) direct defense:

...insert my previous list...(1) (2) (3)

only half points today then I guess.

The queen check and fork of a loose piece is one of the easiest, most useful, and least appreciated tactics in chess.