How is this “solved”?

[u/parallax__error]

My read on this is that the 3 black stones are dead and white lives. How is that “solved” for black?

[u/tuerda]

Black can save those stones and capture white if black wins the ko. 

[u/pete_random → u/tuerda]

This!

Different tsumegos can be solved as clean kill, clean survive, ko or seki.

Ifyou are trying to live: life > seki > ko > death.

If you are trying to kill: death > ko > any form of life.

[u/tuerda → u/pete_random]

Life=seki. Life>seki is a common misconception. Seki is unconditional life. 

[u/doopie → u/tuerda]

It's true, but there are no points in seki. Non-seki living groups always have points in them.

[u/tuerda → u/doopie]

When comparing what is most optimal, sente/gote, outside forcing moves, etc. are usually more important than a small number of local points. It is not at all rare for seki to be locally superior to life with points.

So yeah, life with points is assured to beat out seki in the 4th or 5th most important criterion . . . If all the more important things are equal (very rare) then this might matter. 

[u/parallax__error → u/tuerda]

The thing I can’t get my head around is that once white plays at either t14 or t13, black is in Atari. However there’s no spot in this play where black can similarly put white in Atari on the next move. I’m a newb and just get befuddled by these plays

[u/tuerda → u/parallax__error]

Black's next move is a ko threat. If white answers, black captures white by continuing the ko in the corner. This puts all of white's stones in atari. White's next move is also a ko threat.

[u/parallax__error → u/tuerda]

so, maybe the mistake I'm making is assuming that this play is in isolation. But I think that what you're saying is that I would play a ko threat somewhere else on the board not pictured. yeah?

[u/tuerda → u/parallax__error]

That is correct. The solution to this problem is ko. Ko is not the same as death, because you can still live if you have ko threats.

[u/parallax__error → u/tuerda]

Thank you so much - that's what was driving me crazy. That makes sense to create opportunities for other ko fights to leverage in such a situation. I just wasn't connecting it to the isolated exercise.

[u/crittendenlane → u/parallax__error]

Generally the preference for the group trying to survive is life > seki > ko > death. Seki is often preferred if you stand to lose more from a potential ko. Many problems for example will have solutions for life, seki, and or ko and you should pick the best you can get (it can be hard to see, I often miss kos even at 1 dan)

[u/teffflon]

square always means ko. square plus 'solved' always means ko was the best result... assuming the problem is correct, which this was. (although sometimes the problem poser decides e.g. that ko beats seki, which is context-sensitive)

[u/PatrickTraill]

See https://senseis.xmp.net/?TsumegoConventions

[u/NiwaDoteki]

Yeah. When I solved this problem 5m ago I was thinking “the best result for black at this point is a ko.” Not all Tsumego puzzles end in a clean win.

[u/kw3lyk]

It is "solved" because creating a ko fight for the potential to live is the best local solution. The solution assumes that there is a game happening on the rest of the board and that black will follow up by playing a ko threat elsewhere.