![]() RecentChanges Paths Referenced by
|
Notchers
"Notcher" is terminology borrowed from James Davies?' excellent book on life and death, which is called, well, "Life and Death". There are now separate pages on OneSpaceNotchers, TwoSpaceNotchers and ThreeSpaceNotchers. One day, my son, this will all be ... WikiMasterEditet --Dieter One space notchersThe following is a one space notcher that is six spaces long (meaning: from end to end the black group is six points wide).
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 below in the discussion of two space notchers. Two space notchers
The rule for two space notchers is, depending on how you want to formulate it, either "Five die, Seven live" or "Six is unsettled". This time we'll leave proof of the two extremes to you and demonstrate the unsettled case.
If Black goes first, he can live. White is again rather stuborn to keep trying with 2 and 4, but after 5 Black has completely constructed the two eyes he needs to live.
White can start her attack with a hane at 1. (Reducing your opponent's eye space like this should always be the very first option you consider when examining the status of one of his groups, by the way. See also the article on approaching a life and death problem the right way). Even if Black were to resist, White can keep his group dead. unkx80: See also Two Space Notchers Not Fully Connected. I am expanding this topic in response of Stefan's note below. Three space notchers
The rule for a three space notcher is either "Four die, Six live" or "Five is unsettled". Verify for yourself that Black can live and White can kill by playing at 'a' in the diagram. For this reason 'a' is called the "vital point" of this formation. --Stefan
note: expand later with some examples of connecting points missing in the group under investigation.
A systematic approach to NotchersSuppose the notcher is black and the surrounding group white.
Marked points: possible weaknesses
We put this information into a code nklxx where n, k, l take numerical values and the x-es can be either W, N or S. Status abbreviationsLet's define the following abbreviations:
L: alive even if attacker plays first TablesSee OneSpaceNotchers, TwoSpaceNotchers and ThreeSpaceNotchers CriticalNotchers are notchers that represent a critical point in the notcher space. An example is the weak FlyingSaucerShape 222WW, which is dead. Anything weaker is obviously also dead. Anything stronger, however, is either unsettled or alive. Here is the TableOfNotchers. This is a copy of the living page "Notchers" at Sensei's Library. (C) the Authors, published under the OpenContent License V1.0. |