Interesting go problem from Daiki Komatsu twitter

[oren]

https://twitter.com/daiki__0417/status/ ... 0487126018

How many moves does white need to live inside?

[Kirby]

Nice problem... One of the comments seems to suggest 7, but I don't see it, yet.

[HermanHiddema]

Copyable diagram, for those who want to post an attempt:

$$ How many :white: to live?
$$ . . . . . . . |
$$ . X X X X X X |
$$ . X . . . . X |
$$ . X . . . . . |
$$ . X . . . . . |
$$ . X . X . . . |
$$ . X X X X X X |
$$ . . . . . . . |

Click Here To Show Diagram Code

[go]$$ How many :white: to live?
$$ . . . . . . . |
$$ . X X X X X X |
$$ . X . . . . X |
$$ . X . . . . . |
$$ . X . . . . . |
$$ . X . X . . . |
$$ . X X X X X X |
$$ . . . . . . . |[/go]

My solution:

$$ 7 stones needed
$$ . . . . . . . |
$$ . X X X X X X |
$$ . X . . O O X |
$$ . X . . . . O |
$$ . X . O . O . |
$$ . X . X . O O |
$$ . X X X X X X |
$$ . . . . . . . |

Click Here To Show Diagram Code

[go]$$ 7 stones needed
$$ . . . . . . . |
$$ . X X X X X X |
$$ . X . . O O X |
$$ . X . . . . O |
$$ . X . O . O . |
$$ . X . X . O O |
$$ . X X X X X X |
$$ . . . . . . . |[/go]

[Uberdude]

I was thinking it might be a bit of a trick question in that you can use fewer white moves by also adding black moves as below, but such shapes probably require too much connection. Could be a nice idea for composing another problem though.

$$B
$$ . . . . . . .
$$ . . O O O O .
$$ . O . O . O .
$$ . O O O O . .
$$ . . . . . . .

Click Here To Show Diagram Code

[go]$$B
$$ . . . . . . .
$$ . . O O O O .
$$ . O . O . O .
$$ . O O O O . .
$$ . . . . . . .[/go]

vs

$$B
$$ . . . . . . .
$$ . . O O O O .
$$ . O X . X O .
$$ . O O O O . .
$$ . . . . . . .

Click Here To Show Diagram Code

[go]$$B
$$ . . . . . . .
$$ . . O O O O .
$$ . O X . X O .
$$ . O O O O . .
$$ . . . . . . .[/go]

[Cassandra]

$$
$$ . . . . . . . |
$$ . X X X X X X |
$$ . X O O O . X |
$$ . X O . O O . |
$$ . X . O . O . |
$$ . X . X O O . |
$$ . X X X X X X |
$$ . . . . . . . |

Click Here To Show Diagram Code

[go]$$
$$ . . . . . . . |
$$ . X X X X X X |
$$ . X O O O . X |
$$ . X O . O O . |
$$ . X . O . O . |
$$ . X . X O O . |
$$ . X X X X X X |
$$ . . . . . . . |[/go]

The minimum size for a living group in the centre with "closed borders" is 10 stones.
>>> No chance to create an "open borders" shape with less stones.

$$
$$ . . . . . . . |
$$ . X X X X X X |
$$ . X . . O O X |
$$ . X . . O . O |
$$ . X . . O O . |
$$ . X . X . O O |
$$ . X X X X X X |
$$ . . . . . . . |

Click Here To Show Diagram Code

[go]$$
$$ . . . . . . . |
$$ . X X X X X X |
$$ . X . . O O X |
$$ . X . . O . O |
$$ . X . . O O . |
$$ . X . X . O O |
$$ . X X X X X X |
$$ . . . . . . . |[/go]

The minimum size for a living group at the edge of the board with "closed borders" is 8 stones.

$$
$$ . . . . . . . |
$$ . X X X X X X |
$$ . X . . O O X |
$$ . X . . O . O |
$$ . X . . P O . |
$$ . X . X . O O |
$$ . X X X X X X |
$$ . . . . . . . |

Click Here To Show Diagram Code

[go]$$
$$ . . . . . . . |
$$ . X X X X X X |
$$ . X . . O O X |
$$ . X . . O . O |
$$ . X . . P O . |
$$ . X . X . O O |
$$ . X X X X X X |
$$ . . . . . . . |[/go]

The marked white covers a potential cutting point.

$$
$$ . . . . . . . |
$$ . X X X X X X |
$$ . X . . O O X |
$$ . X . . O . O |
$$ . X . O . O . |
$$ . X . X . O O |
$$ . X X X X X X |
$$ . . . . . . . |

Click Here To Show Diagram Code

[go]$$
$$ . . . . . . . |
$$ . X X X X X X |
$$ . X . . O O X |
$$ . X . . O . O |
$$ . X . O . O . |
$$ . X . X . O O |
$$ . X X X X X X |
$$ . . . . . . . |[/go]

No option left for Black to cut.

$$
$$ . . . . . . . |
$$ . X X X X X X |
$$ . X . . O O X |
$$ . X . . P . O |
$$ . X . O . O . |
$$ . X . X . O O |
$$ . X X X X X X |
$$ . . . . . . . |

Click Here To Show Diagram Code

[go]$$
$$ . . . . . . . |
$$ . X X X X X X |
$$ . X . . O O X |
$$ . X . . P . O |
$$ . X . O . O . |
$$ . X . X . O O |
$$ . X X X X X X |
$$ . . . . . . . |[/go]

The marked stone is not necessary any longer.

$$
$$ . . . . . . . |
$$ . X X X X X X |
$$ . X . . O O X |
$$ . X . . . . O |
$$ . X . O . O . |
$$ . X . X . O O |
$$ . X X X X X X |
$$ . . . . . . . |

Click Here To Show Diagram Code

[go]$$
$$ . . . . . . . |
$$ . X X X X X X |
$$ . X . . O O X |
$$ . X . . . . O |
$$ . X . O . O . |
$$ . X . X . O O |
$$ . X X X X X X |
$$ . . . . . . . |[/go]

>>> 7 stones