For lessons, as well as threads about specific moves, and anything else worth studying.
SmoothOper
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by SmoothOper Wed Dec 11, 2013 3:04 pm
I wonder if any one has solved the fewest stones to break all ladders problem. This is probably pretty vague, maybe just any ladder from the third or forth line going inwards. I am thinking sort of analogously to the queens problem, placing 8 queens such that they weren't mutually attacking.
mitsun
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by mitsun Wed Dec 11, 2013 3:06 pm
Useful factoid: san-ren-sei (three star points) breaks all ladders.
HermanHiddema
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by HermanHiddema Wed Dec 11, 2013 3:10 pm
mitsun wrote: Useful factoid: san-ren-sei (three star points) breaks all ladders.
Yes. The handicap points are exactly at the maximum distance from each other so that they break all ladders. If the space between them were one wider, a ladder could pass though the gap.
Therefore, 8 stones on the corner and side star points break all ladders going up from anywhere.
Note that the stones need to be on the fourth line for this to work. On the third line:
$$W White can bend the ladder at the last moment.
Click Here To Show Diagram Code [go]$$W White can bend the ladder at the last moment.
SmoothOper
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by SmoothOper Wed Dec 11, 2013 3:17 pm
mitsun wrote: Useful factoid: san-ren-sei (three star points) breaks all ladders.
breaks all ladders going one direction.
DrStraw
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by DrStraw Wed Dec 11, 2013 4:52 pm
So an 8 stone handicap breaks all ladders? If W plays tengen first does that enable them all?
Still officially AGA 5d but I play so irregularly these days that I am probably only 3d or 4d over the board (but hopefully still 5d in terms of knowledge, theory and the ability to contribute).
Solomon
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by Solomon Wed Dec 11, 2013 9:24 pm
$$c
Click Here To Show Diagram Code [go]$$c
Bill Spight
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by Bill Spight Wed Dec 11, 2013 10:14 pm
The Adkins Principle:At some point, doesn't thinking have to go on?
ez4u
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by ez4u Fri Dec 13, 2013 3:07 am
Probably we can all agree the first diagram is a ladder. If so, we can't use stones on the third line....
$$Wc A Ladder
Click Here To Show Diagram Code [go]$$Wc A Ladder
If the next diagram is also a 'ladder' we can't use the 3-2 point.
$$Wc A Ladder?
Click Here To Show Diagram Code [go]$$Wc A Ladder?
However, it seems to my eye that filling the second row with alternate stones as below will break all ladders. This requires four rows of eight stones or 32 stones in total.
$$Bc All Ladders Broken?
Click Here To Show Diagram Code [go]$$Bc All Ladders Broken?
Dave Sigaty
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- Marcus Aurelius; Meditations, VIII 21
Bill Spight
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by Bill Spight Fri Dec 13, 2013 6:48 am
$$Wc All Ladders Broken?
Click Here To Show Diagram Code [go]$$Wc All Ladders Broken?
The Adkins Principle:At some point, doesn't thinking have to go on?
ez4u
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by ez4u Fri Dec 13, 2013 7:10 am
So where do we go from here?
$$Wc All Ladders Broken?
Click Here To Show Diagram Code [go]$$Wc All Ladders Broken?
I'm assuming a rather different idea about the role of ladder breakers.
Edit: OK, I think I see your point, mine isn't a ladder. So we can't really get away from the first line?
Dave Sigaty
"Short-lived are both the praiser and the praised, and rememberer and the remembered..."
- Marcus Aurelius; Meditations, VIII 21
SmoothOper
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by SmoothOper Fri Dec 13, 2013 7:25 am
I was thinking about posing a subtly different question. What placement of stones gives maximal ladder breakage for X stones. The easy case I think would be for one stone, at tengen. Two stones? Three stones etc.
hyperpape
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by hyperpape Fri Dec 13, 2013 7:37 am
We could consider some kind of minimal ladders, for instance a bend, block, bend pattern.
$$Wc A Minimal Ladder?
Click Here To Show Diagram Code [go]$$Wc A Minimal Ladder?
I'm not saying that's the "true" meaning of ladder or anything like that. But it might be an interesting question, and perhaps we can avoid having to put as many stones on the board as Bill had to
SmoothOper
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by SmoothOper Fri Dec 13, 2013 8:36 am
$$c
Click Here To Show Diagram Code [go]$$c $$c
Click Here To Show Diagram Code [go]$$c
For more stones I think directionality and edge cases might come into play, as well as overlap.
SmoothOper
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by SmoothOper Fri Dec 13, 2013 10:36 am
Here is a configuration for three with minimum overlap, I would have to count to figure out the optimum centering.
$$c
Click Here To Show Diagram Code [go]$$c
SmoothOper
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by SmoothOper Fri Dec 13, 2013 10:49 am
$$c
Click Here To Show Diagram Code [go]$$c
There that is better. Every position is covered for ladders in some direction, a majority of the board is covered in two directions. I suspect tengen would work its way back into the picture at five stones and triple directional coverage.
