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Kevin Bonham
18-07-2008, 09:24 PM
Saw this rather striking position in an interschool today

n1b5/P7/1PK5/6k1/8/8/8/8 b - - 0 1

Black played 1...Nxb6 and after 2.Kxb6 black couldn't stop the a-pawn and white duly queened and (despite the low skill level of the comp in question) converted.

What is the outcome with correct play and why? Any solutions in white text please to give others time to have a look.

Zwischenzug
18-07-2008, 09:29 PM
First thing that pops into my head is 1..Bh3 (though it doesn't need to go all the way to h3, g4 or f5 probably is just as good), with the idea of skewering the king to the pawn if white plays 2.b6.

eclectic
18-07-2008, 09:32 PM
white text please ;)

CameronD
19-07-2008, 12:00 AM
1... Bg4 {0} 2. Kb7 Bf3+ 3. Ka6 Nxb6 4. Kxb6 *

black
19-07-2008, 12:22 AM
Draw after the bishop retreats beyond e6, along the c8-h3 diagonal.

I am using 1...Bh3, although the range of correct answers were stated above:

1...Bh3 2.Kb7 Nxb6 [2...Bg2+ 3.Ka6! Bf1+! 4.Kb7 {4.Ka5 Bg2 5.Ka6=} Bg2+! 5.Ka6 =] 3.Kxb6! Bg2! = and the bishop holds the a8-h1 diagonal forever, stopping white from being able to make progress with his final pawn.

Alternatively, white can play 2.Kb5 which also draws after:
2...Bg2 3.Ka6 = (as above)
2...Nxb6 3.Kxb6 Bg2 = (as above)
2...Bf1+ 3.Ka5! Bg2 (3...Nxb6 4.Kxb6 Bg2 =) 4.Ka6 =
2...Bc8 3.Kc6 (initial position)

I think that's all right. Distracted by hunger. Time for dinner.

Kevin Bonham
19-07-2008, 12:43 AM
Now here's a little variation (above answers are quite correct of course).

Suppose it was like this:

n1b5/P7/1PK5/8/8/k7/8/8 b - - 0 1

Black to move again, what result this time?

black
19-07-2008, 01:44 AM
The position is the same except that white's best play from the previous diagram no longer draws due to a mating net. Very cute.

I am using 1...Bh3 but 1...Bf5 and 1...Bg4 work also. (As in the last diagram)

1...Bh3 2.Kb7 Bg2+ 3.Ka6 Ka4 (or 3...Kb4) 4.b7 Bf1#

Same if white tries to get to a6 via 2.Kb5 Bg2 3.Ka6

Kevin Bonham
23-07-2008, 07:03 PM
First position - as noted by various solvers black needs to drop the bishop back on the diagonal to one of h3, g4 or f5. Now b7 doesn't work for white because after the bishop check the white king can no longer defend b7 as the dead knight in the corner is covering both squares. White can instead try Kb7 but after the bishop checks white cannot go to b8 threatening to push pawn to b7, because black has ...Nxb6 winning. However white can go to a6, which draws. (Kb5 instead of Kb7 also draws).

Second position - obviously black's problem in the first diagram is that the king is too far away to do anything so I tried entering some different king positions in Fritz to see how close it needed to be for Black to win. I expected there would be a few squares near the pawns where Black could win but was surprised that Black wins if the Black king can reach a4 or b4 in one move. As noted by black (poster) the reason for this is a mate - 1...Bh3/g4/f5 2.Kb7 B+ on long diagonal 3.Ka6 Ka4/b4 4.b7 (only legal move) B mates (with a bit of help from the dead knight again)

I find that mate rather nifty since in a position with KNB v KPP usually one is thinking about how to block the pawns and clean them up. It reminds me of a remarkable game I had once against Peter Lucas where I had KRPP vs KNB, made an error in time trouble and had to allow a perpetual to avoid being mated!