3 L&D problems from an ancient Chinese game

hiyayang · #1

Taken from a year-old post at Tom Weiqi Forum (http://club.weiqi.tom.com/item_111_1456663_0_7.html).

It was an H3 game between Zang Nianxuan (W) and Fang Zuozhou in Qing Dynasty (circa 1700 AD).

Problem #1. Level: Easy (for SDKs?)

Click Here To Show Diagram Code: [go]$$Wc Position at move 94 $$ --------------------------------------- $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . X . . . . . . . . . . . | $$ | . X X . X X . . O . O . X . . . . O . | $$ | . . O , . O O . . , . . . . X X . X X | $$ | . . . O . . . . . . O . X X O . X O . | $$ | . . . . . . . . . O X X . O O . O O . | $$ | . . . . . . . . . X X . O . . . . . . | $$ | . . . . . . . . . X O O . O O . O X . | $$ | . . X . . . . . . . . X O X O . O X . | $$ | . . . , . . . . . X X X X X O O X X . | $$ | . . . . . . . . . . X X O O X O O X . | $$ | . . X . . . . . . . . O . . X X X . . | $$ | . . . . . . . . . . . . . O . O X a . | $$ | . . O . O . . . . . . . . . . X O X . | $$ | . . . . . . . . . . . . . O O . O O . | $$ | . . . X . . . . . , . . O X O , O . . | $$ | . . . . . . X . O . . X . X X X O . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ ---------------------------------------[/go]

White to play. What's the status of the black group on the right side? Specifically, if white plays 'a', can black live?

Gresil · #2

A nice problem!

I can't find anything.

Click Here To Show Diagram Code: [go]$$Wc Position at move 94 $$ --------------------------------------- $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . X . . . . . . . . . . . | $$ | . X X . X X . . O . O . X . . . . O . | $$ | . . O , . O O . . , . . . . X X . X X | $$ | . . . O . . . . . . O . X X O . X O . | $$ | . . . . . . . . . O X X . O O . O O . | $$ | . . . . . . . . . X X . O . . . . . . | $$ | . . . . . . . . . X O O . O O . O X . | $$ | . . X . . . . . . . . X O X O . O X . | $$ | . . . , . . . . . X X X X X O O X X . | $$ | . . . . . . . . . . X X O O X O O X . | $$ | . . X . . . . . . . 9 O 5 4 X X X 2 . | $$ | . . . . . . . . . . . 8 6 O . O X 1 . | $$ | . . O . O . . . . . . . . 7 . X O X 3 | $$ | . . . . . . . . . . . . . O O . O O . | $$ | . . . X . . . . . , . . O X O , O . . | $$ | . . . . . . X . O . . X . X X X O . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ ---------------------------------------[/go]

Not this

—the ladder doesn't work.

Click Here To Show Diagram Code: [go]$$Wc Position at move 94 $$ --------------------------------------- $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . X . . . . . . . . . . . | $$ | . X X . X X . . O . O . X . . . . O . | $$ | . . O , . O O . . , . . . . X X . X X | $$ | . . . O . . . . . . O . X X O . X O . | $$ | . . . . . . . . . O X X . O O . O O . | $$ | . . . . . . . . . X X . O . . . . . . | $$ | . . . . . . . . . X O O . O O . O X . | $$ | . . X . . . . . . . . X O X O . O X . | $$ | . . . , . . . . . X X X X X O O X X . | $$ | . . . . . . . . . . X X O O X O O X . | $$ | . . X . . . . . . . . O 4 5 X X X 2 . | $$ | . . . . . . . . . . . . 9 O 7 O X 1 . | $$ | . . O . O . . . . . . . . 8 6 X O X 3 | $$ | . . . . . . . . . . . . . O O . O O . | $$ | . . . X . . . . . , . . O X O , O . . | $$ | . . . . . . X . O . . X . X X X O . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ ---------------------------------------[/go]

Not this

either.

Click Here To Show Diagram Code: [go]$$Bc Position at move 94 $$ --------------------------------------- $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . X . . . . . . . . . . . | $$ | . X X . X X . . O . O . X . . . . O . | $$ | . . O , . O O . . , . . . . X X . X X | $$ | . . . O . . . . . . O . X X O . X O . | $$ | . . . . . . . . . O X X . O O . O O . | $$ | . . . . . . . . . X X . O . . . . . . | $$ | . . . . . . . . . X O O . O O . O X . | $$ | . . X . . . . . . . . X O X O . O X . | $$ | . . . , . . . . . X X X X X O O X X . | $$ | . . . . . . . . . . X X O O X O O X . | $$ | . . X . . . . . . . . O 4 3 X X X X . | $$ | . . . . . . . . . . . . 1 O . O X O . | $$ | . . O . O . . . . . . . . 2 . X O . O | $$ | . . . . . . . . . . . . . O O . O O . | $$ | . . . X . . . . . , . . O X O , O . . | $$ | . . . . . . X . O . . X . X X X O . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ ---------------------------------------[/go]

Transposes to the ladder.

Click Here To Show Diagram Code: [go]$$Bc Position at move 94 $$ --------------------------------------- $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . X . . . . . . . . . . . | $$ | . X X . X X . . O . O . X . . . . O . | $$ | . . O , . O O . . , . . . . X X . X X | $$ | . . . O . . . . . . O . X X O . X O . | $$ | . . . . . . . . . O X X . O O . O O . | $$ | . . . . . . . . . X X . O . . . . . . | $$ | . . . . . . . . . X O O . O O . O X . | $$ | . . X . . . . . . . . X O X O . O X . | $$ | . . . , . . . . . X X X X X O O X X . | $$ | . . . . . . . . . . X X O O X O O X . | $$ | . . X . . . . . . . . O 4 3 X X X X . | $$ | . . . . . . . . . . . . 5 O 1 O X O . | $$ | . . O . O . . . . . . . . 6 2 X O . O | $$ | . . . . . . . . . . . . . O O . O O . | $$ | . . . X . . . . . , . . O X O , O . . | $$ | . . . . . . X . O . . X . X X X O . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ ---------------------------------------[/go]

The same ladder again.

Click Here To Show Diagram Code: [go]$$Bc Position at move 94 $$ --------------------------------------- $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . X . . . . . . . . . . . | $$ | . X X . X X . . O . O . X . . . . O . | $$ | . . O , . O O . . , . . . . X X . X X | $$ | . . . O . . . . . . O . X X O . X O . | $$ | . . . . . . . . . O X X . O O . O O . | $$ | . . . . . . . . . X X . O . . . . . . | $$ | . . . . . . . . . X O O . O O . O X . | $$ | . . X . . . . . . . . X O X O . O X . | $$ | . . . , . . . . . X X X X X O O X X . | $$ | . . . . . . . . . . X X O O X O O X . | $$ | . . X . . . . . . . . O . . X X X X . | $$ | . . . . . . . . . . . . 4 O . O X O . | $$ | . . O . O . . . . . . . 3 1 2 X O . O | $$ | . . . . . . . . . . . . . O O . O O . | $$ | . . . X . . . . . , . . O X O , O . . | $$ | . . . . . . X . O . . X . X X X O . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ ---------------------------------------[/go]

Nah.

Numsgil · #3

@Gresil

Gresil · #4

Whoops.

hiyayang · #5

Nice job, Numsgil and Gresil! Gresil was just one move away from the solution, but he saved me a lot of work posting the variations.

For beginners, here is a variation that most people first thought about and that didn't work (with a correction to one of Gresil's variations):

Click Here To Show Diagram Code: [go]$$Bc Black fails, after white captures the black stone at S6 $$ --------------------------------------- $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . X . . . . . . . . . . . | $$ | . X X . X X . . O . O . X . . . . O . | $$ | . . O , . O O . . , . . . . X X . X X | $$ | . . . O . . . . . . O . X X O . X O . | $$ | . . . . . . . . . O X X . O O . O O . | $$ | . . . . . . . . . X X . O . . . . . . | $$ | . . . . . . . . . X O O . O O . O X . | $$ | . . X . . . . . . . . X O X O . O X . | $$ | . . . , . . . . . X X X X X O O X X . | $$ | . . . . . . . . . . X X O O X O O X . | $$ | . . X . . . . . . a 8 O 4 3 X X X X . | $$ | . . . . . . . . . b . 7 5 O 1 O X O . | $$ | . . O . O . . . . . . . 6 . 2 X O . O | $$ | . . . . . . . . . . . . . O O . O O . | $$ | . . . X . . . . . , . . O X O , O . . | $$ | . . . . . . X . O . . X . X X X O . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ ---------------------------------------[/go]

At this point, neither 'a' nor 'b' works for black.

White can also play :b6:

at

, to the same effect. Actually, there is a bonus question derived from this:

Click Here To Show Diagram Code: [go]$$Bc $$ --------------------------------------- $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . X . . . . . . . . . . . | $$ | . X X . X X . . O . O . X . . . . O . | $$ | . . O , . O O . . , . . . . X X . X X | $$ | . . . O . . . . . . O . X X O . X O . | $$ | . . . . . . . . . O X X . O O . O O . | $$ | . . . . . . . . . X X . O . . . . . . | $$ | . . . . . . . . . X O O . O O . O X . | $$ | . . X . . . . . . . . X O X O . O X . | $$ | . . . , . . . . . X X X X X O O X X . | $$ | . . . . . . . . . . X X O O X O O X . | $$ | . . X . . . . . . a . O 4 3 X X X X . | $$ | . . . . . . . . . . . 6 5 O 1 O X O . | $$ | . . O . O . . . . . . 9 7 8 2 X O . O | $$ | . . . . . . . . . . . . . O O . O O . | $$ | . . . X . . . . . , . . O X O , O . . | $$ | . . . . . . X . O . . X . X X X O . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ ---------------------------------------[/go]

How does white escape? Does 'a' work?

hiyayang · #6

Spoiler alert: Stop here if you want to work on the first problem, as the diagram below contains the spoiler.

Problem #2. Level: Medium

Click Here To Show Diagram Code: [go]$$Bc Position at move 157 $$ --------------------------------------- $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . X X . . . . . . . . . . . | $$ | . X X . X X . X O . O . X . . . . O . | $$ | . . O , X . . X . , . . . . X X . X X | $$ | . X . O O X X X O . O . X X O . X O . | $$ | . . . . . O O O . O X X . O O . O O . | $$ | . . . X O . . . . X X . O . . . . . . | $$ | . . . . . . . . . X O O . O O . O X . | $$ | . . X . O . . . . . . X O X O . O X . | $$ | . . . , . . . . . X X X X X O O X X . | $$ | . . . . . . . . O . X X O O X O O X . | $$ | . O X . . O . X X O O O O X X X X . . | $$ | . . . . . . O O X X X O X O . O X . . | $$ | . O O . O O X . O . . . . . . X O X . | $$ | . O X . . X X . O X X O . O O . O O . | $$ | O X X X . . . X O O X X O X O , O . . | $$ | . O O X . X X . O . O X . X X X O . . | $$ | . . . . X O O . . . O X . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ ---------------------------------------[/go]

Black to play. How does the black group extending from lower-right corner to center live? Hint: Running out is not an option.

Gresil · #7

This

seems to work:

Click Here To Show Diagram Code: [go]$$Bc Position at move 157 $$ --------------------------------------- $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . X X . . . . . . . . . . . | $$ | . X X . X X . X O . O . X . . . . O . | $$ | . . O , X . . X . , . . . . X X . X X | $$ | . X . O O X X X O . O . X X O . X O . | $$ | . . . . . O O O . O X X . O O . O O . | $$ | . . . X O . . . . X X . O . . . . . . | $$ | . . . . . . . . . X O O . O O . O X . | $$ | . . X . O . . . . . . X O X O . O X . | $$ | . . . , . . . . . X X X X X O O X X . | $$ | . . . . . . . . O . X X O O X O O X . | $$ | . O X . . O . X X O O O O X X X X . . | $$ | . . . . . . O O X X X O X O . O X . . | $$ | . O O . O O X . O . . 5 6 . . X O X . | $$ | . O X . . X X . O X X O 7 O O . O O . | $$ | O X X X . . . X O O X X O X O , O . . | $$ | . O O X . X X . O . O X 1 X X X O . . | $$ | . . . . X O O . . . O X . . 3 2 4 . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ ---------------------------------------[/go]

Without it black only gets a ko from the atari of M6:

Click Here To Show Diagram Code: [go]$$Bc Position at move 157 $$ --------------------------------------- $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . X X . . . . . . . . . . . | $$ | . X X . X X . X O . O . X . . . . O . | $$ | . . O , X . . X . , . . . . X X . X X | $$ | . X . O O X X X O . O . X X O . X O . | $$ | . . . . . O O O . O X X . O O . O O . | $$ | . . . X O . . . . X X . O . . . . . . | $$ | . . . . . . . . . X O O . O O . O X . | $$ | . . X . O . . . . . . X O X O . O X . | $$ | . . . , . . . . . X X X X X O O X X . | $$ | . . . . . . . . O . X X O O X O O X . | $$ | . O X . . O . X X O O O O X X X X . . | $$ | . . . . . . O O X X X O X O . O X . . | $$ | . O O . O O X . O . . 1 2 . . X O X . | $$ | . O X . . X X . O X X O 3 O O . O O . | $$ | O X X X . . . X O O X X O X O , O . . | $$ | . O O X . X X . O . O X . X X X O . . | $$ | . . . . X O O . . . O X . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ ---------------------------------------[/go]

But can't black live by just extending his eyespace? Does white have a more severe attack than than this :w2:

?

Click Here To Show Diagram Code: [go]$$Bc Position at move 157 $$ --------------------------------------- $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . X X . . . . . . . . . . . | $$ | . X X . X X . X O . O . X . . . . O . | $$ | . . O , X . . X . , . . . . X X . X X | $$ | . X . O O X X X O . O . X X O . X O . | $$ | . . . . . O O O . O X X . O O . O O . | $$ | . . . X O . . . . X X . O . . . . . . | $$ | . . . . . . . . . X O O . O O . O X . | $$ | . . X . O . . . . . . X O X O . O X . | $$ | . . . , . . . . . X X X X X O O X X . | $$ | . . . . . . . . O . X X O O X O O X . | $$ | . O X . . O . X X O O O O X X X X . . | $$ | . . . . . . O O X X X O X O . O X . . | $$ | . O O . O O X . O . . . . . . X O X . | $$ | . O X . . X X . O X X O . O O . O O . | $$ | O X X X . . . X O O X X O X O , O . . | $$ | . O O X . X X . O . O X 3 X X X O . . | $$ | . . . . X O O . . . O X 2 5 . . 1 9 . | $$ | . . . . . . . . . . 8 4 6 7 . . . . . | $$ ---------------------------------------[/go]

hiyayang · #8

Hint (and @ Gresil):

hiyayang · #9

@Gresil:

hiyayang · **#10**

Solution to Problem #2: In the actual game the following moves were played, which are believed to be optimal --

Click Here To Show Diagram Code: [go]$$Bc Moves 158 to 167, black to live with ko $$ --------------------------------------- $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . X X . . . . . . . . . . . | $$ | . X X . X X . X O . O . X . . . . O . | $$ | . . O , X . . X . , . . . . X X . X X | $$ | . X . O O X X X O . O . X X O . X O . | $$ | . . . . . O O O . O X X . O O . O O . | $$ | . . . X O . . . . X X . O . . . . . . | $$ | . . . . . . . . . X O O . O O . O X . | $$ | . . X . O . . . . . . X O X O . O X . | $$ | . . . , . . . . . X X X X X O O X X . | $$ | . . . . . . . . O . X X O O X O O X . | $$ | . O X . . O . X X O O O O X X X X . . | $$ | . . . . . . O O X X X O X O . O X . . | $$ | . O O . O O X 0 O . . . . . . X O X . | $$ | . O X . . X X . O X X O . O O . O O . | $$ | O X X X . . . X O O X X O X O , O . . | $$ | . O O X . X X . O . O X . X X X O . . | $$ | . . . . X O O 7 8 . O X . . . 4 1 2 . | $$ | . . . . . 9 . . . . . . . . . 5 6 3 . | $$ ---------------------------------------[/go]

Click Here To Show Diagram Code: [go]$$B Moves 168 to 177, 9 at 1 $$ --------------------------------------- $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . X X . . . . . . . . . . . | $$ | . X X . X X . X O . O . X . . . . O . | $$ | . . O , X . . X . , . . . . X X . X X | $$ | . X . O O X X X O . O . X X O . X O . | $$ | . . . . . O O O . O X X . O O . O O . | $$ | . . . X O . . . . X X . O . . . . . . | $$ | . . . . . . . . . X O O . O O . O X . | $$ | . . X . O . . . . 7 . X O X O . O X . | $$ | . . . , . . . 8 6 X X X X X O O X X . | $$ | . . . . . . . 5 O . X X O O X O O X . | $$ | . O X . . O . X X O O O O X X X X 3 . | $$ | . . . . . . O O X X X O X O . O X 2 . | $$ | . O O . O O X O O . . . . . . X O X 0 | $$ | . O X . . X X . O X X O . O O . O O . | $$ | O X X X . . . X O O X X O X O , O . . | $$ | . O O X . X X . O . O X . X X X O . . | $$ | . . . . X O O X O . O X . . . O 1 O . | $$ | . . . . . X . . . . . . . . . X 4 X . | $$ ---------------------------------------[/go]

Click Here To Show Diagram Code: [go]$$B Moves 178 to 187, 8 at 2 $$ --------------------------------------- $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . X X . . . . . . . . . . . | $$ | . X X . X X . X O . O . X . . . . O . | $$ | . . O , X . . X . , . . . . X X . X X | $$ | . X . O O X X X O . O . X X O . X O . | $$ | . . . . . O O O . O X X . O O . O O . | $$ | . . . X O . . . . X X . O . . . . . . | $$ | . . . . . . . . . X O O . O O . O X . | $$ | . . X . O . . 0 . X . X O X O . O X . | $$ | . . . , 4 . 9 O O X X X X X O O X X . | $$ | . . . . . . 3 X O . X X O O X O O X . | $$ | . O X . . O . X X O O O O X X X X X . | $$ | . . . . . . O O X X X O X O 7 O X O . | $$ | . O O . O O X O O . . . 6 . 1 X O . O | $$ | . O X . . X X . O X X O . O O . O O . | $$ | O X X X . . . X O O X X O X O , O . . | $$ | . O O X . X X . O . O X . X X X O . . | $$ | . . . . X O O X O . O X . . . O 5 O . | $$ | . . . . . X . . . . . . . . . X 2 X . | $$ ---------------------------------------[/go]

I will post some variations next.

hiyayang · **#11**

Assessment of the situation:

hiyayang · **#12**

Black failure #1:

Trying to live without ko, B ends up getting his group killed --

Click Here To Show Diagram Code: [go]$$Bc Black group dies $$ --------------------------------------- $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . X X . . . . . . . . . . . | $$ | . X X . X X . X O . O . X . . . . O . | $$ | . . O , X . . X . , . . . . X X . X X | $$ | . X . O O X X X O . O . X X O . X O . | $$ | . . . . . O O O . O X X . O O . O O . | $$ | . . . X O . . . . X X . O . . . . . . | $$ | . . . . . . . . . X O O . O O . O X . | $$ | . . X . O . . . . . . X O X O . O X . | $$ | . . . , . . . . . X X X X X O O X X . | $$ | . . . . . . . . O . X X O O X O O X . | $$ | . O X . . O . X X O O O O X X X X . . | $$ | . . . . . . O O X X X O X O . O X 3 . | $$ | . O O . O O X . O . . . 2 . . X O X . | $$ | . O X . . X X . O X X O d O O . O O . | $$ | O X X X . . . X O O X X O X O , O . . | $$ | . O O X . X X . O . O X c X X X O . . | $$ | . . . . X O O . b . O X . . 9 6 X O . | $$ | . . . . . . . . . . a 0 e 8 5 7 1 4 . | $$ ---------------------------------------[/go]

Note:

1. B 'a' is not sente (because W 'b' is), otherwise W :w8:

would be unable to go home.

2. It is important that B 'c' does not force W 'd', otherwise B could throw in at 'e' to live. Therefore, W has to be careful with :w2:

, as he would get an inferior result by playing this way:

Click Here To Show Diagram Code: [go]$$Bc White fails $$ --------------------------------------- $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . X X . . . . . . . . . . . | $$ | . X X . X X . X O . O . X . . . . O . | $$ | . . O , X . . X . , . . . . X X . X X | $$ | . X . O O X X X O . O . X X O . X O . | $$ | . . . . . O O O . O X X . O O . O O . | $$ | . . . X O . . . . X X . O . . . . . . | $$ | . . . . . . . . . X O O . O O . O X . | $$ | . . X . O . . . . . . X O X O . O X . | $$ | . . . , . . . . . X X X X X O O X X . | $$ | . . . . . . . . O . X X O O X O O X . | $$ | . O X . . O . X X O O O O X X X X 3 . | $$ | . . . . . . O O X X X O X O . O X 2 . | $$ | . O O . O O X . O . . . 6 7 5 X O X 4 | $$ | . O X . . X X . O X X O b O O . O O . | $$ | O X X X . . . X O O X X O X O , O . . | $$ | . O O X . X X . O . O X a X X X O . . | $$ | . . . . X O O . . . O X . . . . X O . | $$ | . . . . . . . . . . . . c . 9 . 1 8 . | $$ ---------------------------------------[/go]

Later B 'a' would enable a ko at 'b' or a throw-in at 'c' as described above.

hiyayang · **#13**

Variation #1:

So double hane to live with ko is the best result B can hope for in this situation.

Now W has a choice. If W avoids the ko, B lives:

Click Here To Show Diagram Code: [go]$$Bc White backs off; Black lives $$ --------------------------------------- $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . X X . . . . . . . . . . . | $$ | . X X . X X . X O . O . X . . . . O . | $$ | . . O , X . . X . , . . . . X X . X X | $$ | . X . O O X X X O . O . X X O . X O . | $$ | . . . . . O O O . O X X . O O . O O . | $$ | . . . X O . . . . X X . O . . . . . . | $$ | . . . . . . . . . X O O . O O . O X . | $$ | . . X . O . . . . f . X O X O . O X . | $$ | . . . , . . . . . X X X X X O O X X . | $$ | . . . . . . . . O . X X O O X O O X . | $$ | . O X . . O . X X O O O O X X X X . . | $$ | . . . . . . O O X X X O X O . O X 5 . | $$ | . O O . O O X . O . . . 4 . . X O X . | $$ | . O X . . X X . O X X O . O O . O O . | $$ | O X X X . . . X O O X X O X O , O . . | $$ | . O O X . X X . O . O X 9 X X X O 2 . | $$ | . . . . X O O . . . O X 8 a . . X O . | $$ | . . . . . . . . . . . 6 7 0 3 . . 1 . | $$ ---------------------------------------[/go]

Then B 'a' lives.

But why should W be afraid of the ko fight? He has virtually nothing to lose here -- even if B won the ko fight, the W group in the LR corner is still alive:

Click Here To Show Diagram Code: [go]$$B Moves 190 to 191 $$ --------------------------------------- $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . X X . . . . . . 2 . . . . | $$ | . X X . X X . X O . O . X . . . O O . | $$ | . . O , X . . X . , . . . . X X . X X | $$ | . X . O O X X X O . O . X X O . X O . | $$ | . . . . . O O O . O X X . O O . O O . | $$ | . . . X O . . . . X X . O . . . . . . | $$ | . . . . . . . . . X O O . O O . O X . | $$ | . . X . O . . O . X . X O X O . O X . | $$ | . . . , O . X O O X X X X X O O X X . | $$ | . . . . . . X X O b X X O O X O O X . | $$ | . O X . . O . X X O O O O X X X X X . | $$ | . . . . . . O O X X X O . O a O X O . | $$ | . O O . O O X O O . . . O B X X O . O | $$ | . O X . . X X . O X X O . O O . O O c | $$ | O X X X . . . X O O X X O X O , O . d | $$ | . O O X . X X . O . O X . X X X O 3 4 | $$ | . . . . X O O X O . O X . . 1 O X O . | $$ | . . . . . X . . . . . . . . . X . X . | $$ ---------------------------------------[/go]

That is, even if W got cut at 'b' and B played the circled stone (to destroy W's eye) instead of the actual game move 'a' (to give W fewer ko threats). Then, whether B plays :b3:

or 'd',

secures the eye at 'c'.

W just has to make sure he gets compensated elsewhere for the loss of the ko fight.

hiyayang · **#14**

Black failure #2:

hiyayang · **#15**

Variation #2:

hiyayang · **#16**

Spoiler Alert: The diagram below contains answers to previous problems!

Problem #3. Level: Difficult

The black group extending from the upper-right corner to center is surrounded. Can it live?

Click Here To Show Diagram Code: [go]$$Bc Position at move 195, Black to play $$ --------------------------------------- $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . X X . . . . . X O . . . . | $$ | . X X . X X . X O . O . X X O . O O . | $$ | . . O , X . . X . , . . . . X X O X X | $$ | . X . O O X X X O . O . X X O . X O . | $$ | . . . . . O O O . O X X . O O . O O . | $$ | . . . X O . . . . X X . O . . . . . . | $$ | . . . . . . . . . X O O . O O . O X . | $$ | . . X . O . . O . X . X O X O . O X . | $$ | . . . , O . X O O X X X X X O O X X . | $$ | . . . . . . X X O . X X O O X O O X . | $$ | . O X . . O . X X O O O O X X X X X . | $$ | . . . . . . O O X X X O . O X . X O . | $$ | . O O . O O X O O . . . O . X X O . O | $$ | . O X . . X X . O X X O . O O . O O . | $$ | O X X X . . . X O O X X O X O , O . . | $$ | . O O X . X X . O . O X . X X X O . . | $$ | . . . . X O O X O . O X . . X . X O . | $$ | . . . . . X . . . . . . . . . X . X . | $$ ---------------------------------------[/go]

3 L&D problems from an ancient Chinese game

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