One-Space Notchers
One-space notchers are groups that consist of a chain on the second line, interrupted by a notch of one empty space on the second line and one stone on the third. The term was invented by James Davies. See also Notchers, Two-Space Notchers and Three-Space Notchers.
The rule for one space notchers is: "Four die, Seven live". You may also remember this as: "Five and Six are unsettled".
Here's the proof that "Four die". Even if Black plays first, White always has an answer to keep his group dead. Black 1 is answered by White 2 and vice versa.
Here's proof that "Seven live". Even if White plays first, Black always has an answer to keep his group alive. The diagram shows one white attack that fails. You can verify for yourself that it doesn't matter where the notch is located. You can also verify that five- and six-space notchers are unsettled, i.e. that the black group is alive if Black plays first and dead if White plays first. If you don't know how to verify unsettled cases, look in the discussion of two space notchers.
Classification
Classification
See notcher code for the coding.
- All of 111xx, 112xx are dead and not worth discussing
- All of 1xxWW are dead until 133WW. 133WW can make a ko. From 134WW onward it can live by connecting the stone in atari:
122
All 122 can live, except 122WW and 122WN which are dead
123
(...)
All 123 can live, except for 123WW, dead, and, 123WN and 123NW, where Black can make a ko.
133
(...)
133WW makes ko. 133WN can make life. All other 133xx live
116SW
The status of 116SW depends on outside liberties.
See table of notchers.