I've found similar problems to be challenging in the past, because there are two places where Black can sacrifice a stone, the correct answer is probably to play one of those then the other, and these things tend to be sensitive to move order. When White has at least two plausible replies to each Black move, it adds up to a lot of variations!

Click Here To Show Diagram Code

[go]$$c Black to play and connect
$$ | . . O , . . . . . ,
$$ | . . . . . . . . . .
$$ | . . O . . . . . . .
$$ | . X O . O . X . O .
$$ | . X O . . . . . . .
$$ | . . X O O . X . O .
$$ | . . X . b . . . . ,
$$ | . , X . O . X . O .
$$ | . . . . a . . . . .
$$ | . . . . . . . . . .
$$ ---------------------[/go]

In this case I have trouble choosing between 'a' and 'b' because it looks like they both fail! The book is no help: all three answer diagrams show the same first black move, and one of them is labelled "variation" but appears to show black not connecting. When I try to dummy up a full-board position in which 'a' and 'b' are the biggest moves, all three of KataGo, ELF and LZ-242 rate 'a' and 'b' about equally, and prefer to sacrifice the black stones on the right even in variations where connecting would be possible.

So what's going on here? Is either move better than the other? Is a real tesuji to be found in this position?

Generally I'm finding these books to be clear-cut, useful and enjoyable. There's just the odd one or two problems in each book that are much harder to understand than the rest (or that are hitting my blind spots much more strongly)!

Difference game.

Click Here To Show Diagram Code

[go]$$c Who wins, playing first?
$$ | . . O , . . . . . , . . . . . , X . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . O . . . . . . . . . . . . . X . . |
$$ | . X O . O . X . O . X . O . X . X O . |
$$ | . X O . . . . . . . . . . . . . X O . |
$$ | . . X O O . X . O . X . O . X X O . . |
$$ | . . X . . . . . . , . . . . W , O . . |
$$ | . , X . O . X . O . X . O . X . O . . |
$$ | . . . . B . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ----------------------------------------[/go]

A difference game may be used to compare plays, if no ko fights arise. The positions must be independent, so in this case no player may play on the K file. (If that becomes necessary then we'll have to alter the setup.)

On the left side Black has played , on the right White has played . Although the problem is to connect, the difference game is about who wins, playing first. A tie is counted as a win for the second player.

Edit: This is the basic difference game setup. I see that we may have to alter that because of reversal. See https://lifein19x19.com/viewtopic.php?p=198894#p198894 and https://senseis.xmp.net/?Reversible .

_________________
The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins

Visualize whirled peas.

Everything with love. Stay safe.

I haven't spent too much time on it so maybe I'm missing a white's response, but a seems to work.

First b indeed seems to fail :



But a seems to succeed :

Right. Your second and third diagrams are what bothers me, or more simply:

Black can connect the corner group to one of the outside stones, but can't connect up without most of the outside group being cut off.

Funny, today when I put down some more stones and ask KataGo to look at the whole board, it's actually keen to connect. The other day, with a slightly different context, it definitely preferred not to. Unfortunately I didn't keep a record of the full board position. Looks like the best option is context dependent!

I suppose that this is a modern composition, Classical problems, while not looking for the best play on an otherwise empty board, still allowed for the fight to spill out into the rest of the board. Modern problems, by contrast, do not make that assumption, and often rely upon ill defined boundaries for the play. That's why I guessed that no plays should be made on the K file. I also guess that the White stones on the J file are all safe.



Should that be Black instead of White?

_________________
The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins

Visualize whirled peas.

Everything with love. Stay safe.

Ah, the other white. Fixed. Thanks.

Interesting link, thanks.

Hmmm. The bit about port and starboard makes me wonder how they arose. Maybe it had to do with ocean going ship traffic close to the shore way back when (long before radar), especially at night, when it was hard to see. If everybody kept the land (port) to the left and the night sky (stars) to the right, collisions would be less likely.

Edit: Wrong again.

_________________
The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins

Visualize whirled peas.

Everything with love. Stay safe.

Indeed, this is a great link!

_________________
Dave Sigaty
"Short-lived are both the praiser and the praised, and rememberer and the remembered..."
- Marcus Aurelius; Meditations, VIII 21