I'm confused by this problem because I don't see any "win" for black. The program's stated answer is shown below as 1-3.

My objection is 4 & 6.

Click Here To Show Diagram Code

[go]$$B Corner
$$ ------------------
$$ | . O X 1 4 X 2 . .
$$ | . O X 6 X O . . .
$$ | 3 O X X O O . . .
$$ | . X O O O . . . .
$$ | . X . . . . . . .
$$ | . . X . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .[/go]

Is the problem in error? Or am I missing something terribly obvious?

Yes you are missing
After the situation turns into a Ko. Living without Ko is usually better than Ko, but Ko is better than plain dying. So the answer is "Black can make Ko with 1 and 3".
Just for comparison, this is what happens when white can play first:

Click Here To Show Diagram Code

[go]$$B Corner
$$ ------------------
$$ | . O X 2 . X 4 . .
$$ | . O X 3 X O . . .
$$ | . O X X O O . . .
$$ | . X O O O . . . .
$$ | . X . . . . . . .
$$ | . . X . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .[/go]

Now black can't connect because it is self-atari, so black is outright dead.

_________________
Magics way up the hill (personal study journal)

Black 3 is Self-Atari, so White 4 should capture !

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The really most difficult Go problem ever: https://igohatsuyoron120.de/index.htm
Igo Hatsuyōron #120 (really solved by KataGo)

I don't understand how this makes ko. What I see is elsewhere and killing all the group and taking the 6 stones. The reader is supposed to assume that is a sufficiently large ko threat played elsewhere on the board to make playing at the key point a bad decision? Couldn't you use that logic to solve every tsumego?!?

Hi Drew, it's B's turn to play, so:
Where can B play locally, and what are the different results, locally ?

Can you see, and do you agree, that if B does not play at the solution (x),
but anywhere else, then W can kill at least ?

Click Here To Show Diagram Code

[go]$$B not at (x)
$$ ------------------
$$ | . O Y x . X . . .
$$ | . O Y . X O . . .
$$ | . O Y Y O O . . .
$$ | . X O O O . . . .
$$ | . X . . . . . . .
$$ | . . X . . . . . .
$$ | . . . . . . . . .[/go]

Sorry, what you said is a bit unclear:
does the program show the solution only up to ?
Or does it also include and ?Same question: does the program include , removing the 6 B stones, or is that your continuation ?

After hane, starts the ko.
Suppose is a ko threat elsewhere, and W replies with (also elsewhere).
Then B can re-take the local ko with , which gains an important liberty for B --
now the big B group momentarily has 2 liberties:

Click Here To Show Diagram Code

[go]$$B , elsewhere
$$ ------------------
$$ | . O X 1 4 7 2 . .
$$ | a O X . X O . . .
$$ | 3 O X X O O . . .
$$ | . X O O O . . . .
$$ | . X . . . . . . .
$$ | . . X . . . . . .
$$ | . . . . . . . . .[/go]

This means that if -- an important if --
B has the chance to play at (a) while the 6 B stones are not in atari,
then B kills W here, and B lives.

Which is better than simply dead for B.

This is why the solution is a ko.If your program includes removing the 6 B stones,
it's showing the local result when W wins the local ko.

White should not play 4. No need to. He should ignore it.

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Still officially AGA 5d but I play so irregularly these days that I am probably only 3d or 4d over the board (but hopefully still 5d in terms of knowledge, theory and the ability to contribute).

Hi Ed,

It stops at and marks itself solved. I meant that was played elsewhere because I didn't see how it could possibly stave of locally, which is because I didn't consider the possibility of a ko threat outside the scope of the problem.

I can understand how the ko is possible now, thank you. Just too inexperienced with tsumego to understand what they were after.

Hi Drew, you're welcome.

Yes, these are standard conventions: when a tsumego shows you only the local situation:
- if a ko develops, you have to look at all the local threats (if any), and we don't know about the global threats, because they depend on the rest of the board.
- usually you can assume all global ladders (not shown) are good for B, unless explicitly specified otherwise.