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The initial moves are 1.g3 2.g9 3.i9 4.i5 5.e7 6.f7 7.g6 8.g12 9.b10
Black to move and win. Standard rules apply, which means links never cross, but you are allowed to remove your own links as desired on your move prior to placing any.
The unique key move is 10.c12 with four variations:
-- 11.c13 12.d10 13.d9 14.f11 15.b11 16.c11The only way
white can block black's a10 threat is to play at c9,
removing the b10/d9 link and adding the b11/c9 link.
As of this posting this site has no way to implement such
a move, so use your imagination. 17.c9 18.c8 this
should be linked to d10. Now from here there are four
variations for the battle on the right.
--++ 19.k8 20.i11 21.k12 22.h7 23.k4 24.L8 black wins
--++ 19.m8 20.h7 21.k4 22.l6 23.l7 24.k8 black wins
--++ 19.m9 20.h7 21.m5 22.k5 23.k4 24.m6 black wins
--++ 19.l8 20.h7 21.l4 22.k4 black wins
-- 11.c11 12.a11 13.d13 14.d8 15.c8 16.c10 and the battle on
the right is the same, black wins
-- 11.g10 12.f11 13.e13 14.e11 and the battle on the right is the
same, black wins
-- 11.k8 12.i11 13.k12 14.h7 15.k4 16.L8 is a different move
order, black wins
FALSE STARTS four variations:
-- 10.d10 11.d9 12.c12 13.e11 14.e13 15.j11 two variations:
--++ 16.h7 17.g10 white wins
--++ 16.f11 17.j7 18.k4 19.h6 white wins
-- 10.c10 11.d9 12.d12 13.g10 two variations:
--++ 14.f11 15.e13 16.a11 17.j7 18.i11 19.f12 white wins
--++ 14.i11 15.f12 16.f11 17.e13 18.a11 19.j7 white wins
-- 10.g4 11.b6 two variations:
--++ 12.e5 13.c4 two variations:
--++-- 14.c8 15.d9 16.d7 17.c7 18.c5 19.b7 20.b5 draw
--++-- 14.c12 15.c13 16.d10 17.d9 18.f11 19.b11 20.c11 21.c9 removing a link 22.c8 linking to d10 23.b7 24.d3 25.d2 26.d6 27.c5 28.b3 29.e6 30.d4 draw
--++ 12.c12 13.c13 14.d10 15.d9 16.f11 17.b11 18.c11 19.c9 removing a link 20.c8 linking to d10 21.b7 22.d6 23.d5 24.c5 draw
-- 10.h3 11.c8 12.f4 13.b4 14.d4 15.d3 white wins
-- 10.e5 11.b6 two variations:
--++ 12.g4 13.c4 transposes into the 10.g4 line. draw
--++ 12.c6 13.c8 white wins
-- 10.e3 11.b6 12.g4 13.c4 is essentially the same as the 10.g4 line. draw
-- 13.f5 14.c12 15.c13 16.d10 17.d9 18.f11 19.b11 20.c11 21.c9 removing a link 22.c8 linking to d10 23.b7 24.d6 black wins
--13.c3 14.d2 15.b5 16.b3 17.f5 18.c12 is the same, black wins
I can dumb down the puzzle a bit by moving the G3 peg over to E3. Now the initial moves are 1.e3 2.g9 3.i9 4.i5 5.e7 6.f7 7.g6 8.g12 9.b10 black to move and win. Now such moves as 10.h3 or 10.g4 or 10.e5 do not even deserve mention, and there are no drawing lines. But that's a small price to pay to avoid an alternate winning key move.