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Solutions and Feedback
January 5th, 2004 |
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Dear Christmas Puzzle solvers,
Here, after some delay, are the solutions to all the Christmas
puzzles we published from December 25 2003 to January 1st
2004. We have included some of the feedback we got from
our readers – just a microscopic selection of letters,
since the column would otherwise become unreadable.
At the bottom of this page you will find a link to our
Javascript replay board. It contains all the positions
quoted in the articles, including the ones for which solutions
were already given. Remember that you can replay the moves
of each solution either with the recorder buttons just
below the board or by clicking on the moves in the notation.
On Sunday, January 11th, at 18:00h MET (= 9 a.m. California,
12:00 noon NY, 17:00h London, 22:30h Delhi, 02:00h Tokya)
we will be giving you details of our Christmas Puzzle competition,
in which you can win a copy of Fritz autographed by Garry
Kasparov, as well as other valuable gifts (for the chess
section). The competition will include a prize contest
by John Nunn for Gambit books and a Repton section with
prizes donated by Superior Software.
J. Vancura, Ceske Slovo 1922
White to play and win
At the World Microcomputer Chess Championship in Budapest
in 1983 I recorded the tries of a number of different players:
-
GM István Bilek initially
showed me 1.Bf1! Ke3 2.Bd3! Kf4 3.Kd4! Kg5 4.Ke5! Kh4
5.Bf5 and wins (the exclamation marks are taken from
the way he plonked down the pieces). But I showed him
2...Kf3! 3.Kd4 (3.h3 Kg3! 4.Bf5 Kf4 draw) 3...Kg4 draw.
Bilek reexamined the position together with an IM colleague
and, moving piece on the board, found the correct move
in a total of 15 minutes.
-
The most interesting try by the Polgar infants
was 1.Be6 Ke3 2.h4 Ke4 3.h5 Ke5 4.h6 Kf6 5.Bf5! Kf7
6.Bh7. The king is cut off and cannot reach the drawing
corner. It took me a minute to find the refutation:
6...Kf6! 7.Kd4 Kg5 and draw. Sophie and Judit sighed
and went back to work, giving me the full solution
in 22 minutes
- Both Zsuzsa Polgar and Mikhail
Botvinnik both needed 17 minutes to find the
correct solution, without moving the pieces on the board.
The only move to secure the win is 1.Bd7!
and now White can reliably shut out the enemy king: 1...Ke3
2.h4 Ke4 3.h5 Ke5 4.h6 Kf6 5.Be8! winning.
Jonathan Berry from Canada wrote: "It
took me a while to find 1.Bd7 (to have access to e8), but
then I already knew I wasn't a Bilek or a Botvinnik or
a Polgar. After looking at it for about half an hour on
the screen, I took out a pocket set and from there it was
only about 10 minutes. Which might reinforce the (prejudice?)
that screens are less effective to figure chess. A nice
study by
Vancura."
One reader from Windsor, On, Canada, wrote: "Not
too hard, thanks to your fine lesson. After considering
a couple of drawn lines, I found 1.Kd4! Kf3 2. Ke5! and
the way to h8 is blocked (it's a matter of blocking the
access to the dark squares e3 and f4). My time was 8.5
minutes. Can I say I beat, in a virtual duel, 7-year-old
Polgar?" Sorry, no. Black simply picks up the
pawn with 1...Kg1. Maybe our lesson was not so fine after
all?!
V. Kosek, Ceskoslovensky Sach,
1930
White to play and win
The solution is very profound and fairly complex: 1.Kh5
g5! [1...Kf7 2.Bd5+ Kf6 3.h4 Kf5 4.Bf7 Kf6 5.Be6!
Kxe6 6.Kg6] 2.Kh6 g4! [2...Kf5 3.h3 Kf6
( 3...Kf4 4.Kg6) 4.Bd5 Kf5 5.Kg7] 3.Bd5! Ke5! 4.Bb7!
Kf5! 5.Bc6! Ke5 [5...Kf6 6.Bd7 Kf7 7.Kh7] 6.Kg6!
Ke6 7.Be4! Ke5 8.Bb7! Kf4 9.Kf6! g3 10.h3 g2 11.Bxg2 Kg3
12.Kg5 1-0.
Mika Korhonen, Suomen Tehtäväniekat
1979
White to play and draw
1.Ka5!! This is the remarkable move you
had to find. Nothing else works: 1.Kc6? Kd4 2.Kd7 Ke5!
3.Kxe7 Kf4 4.Nh1 Kxe4 5.Kf6 Kf3 6.Kf5 Kg2 7.Kf4 Kxh1 8.Kf3
Kg1–+; 1.e5? Kd5 (1...Kd4? 2.e6 Ke5 3.Kc5 Kf4 4.Nh1
Kf3 5.Kd4 Kg2 6.Ke3 Kxh1 7.Kf2=) 2.e6 Kxe6 3.Kc5 Ke5 4.Nh1
Ke4 5.Kc4 Kf3 6.Kd3 Kg2 7.Ke2 Kxh1 8.Kf2 e5–+.
1...Kd4 [1...e6 2.Ka4 e5 3.Ka5! Kc3 4.Kb5
Kc2 5.Kc4 Kd1 6.Kd3 Ke1 7.Ke3 Kd1+–; 1...Kd3 2.Kb4
Kc2 3.Kc4 Kd1 4.Kd3 Ke1 5.Ke3 e6 6.Kf3+–] 2.Kb4
Ke5 3.Kc3 Kf4 4.Nh1 Kxe4 [4...Kf3 5.Kd2 Kg2 6.Ke3
Kxh1 7.Kf2 e6 8.e5=] 5.Kd2 Kf3 6.Ke1 Kg2
[6...e6 7.Kf1 e5 8.Nf2 e4 9.Ke1 e3 10.Kf1! e2+ 11.Ke1=]
7.Nf2 Kf3 8.Kf1 e6! 9.Nh1 e5 10.Nf2 e4 11.Nh1 e3
12.Nf2! e2+ [12...exf2=] 13.Ke1 draw.
Brian Stewart of San Jose, Ca, wrote:
I finally figured this one out! The correct first move
is 1. Nf5. Then, after 1... h1Q 2. Nxe7, White will, according
to the endgame tablebases, lose in the next nine moves.
Which would be much less stressful than trying to find
the real answer to this @#$% impossible puzzle! Seriously,
though, I'm pretty sure the first move is 1. Nh1. Then,
if 1...Kd3 2. Ng3 and the Black king can't get any closer
to the h1 corner. If either 2... Ke3 or 2... Kd2, then
3. Nf1+ forks king and pawn. Alternatively, if 1...Kd4,
then 2. Nf2 and again the Black king is cut off from the
h1 corner. Both 2...Ke3 and 2... Ke5 allow Ng4+, again
forking king and pawn. The only stumbling block I've come
across is, what if after 1...Kd3 2.Ng3, Black plays 2...Kd4?
It seems from there that there's no way for White to prevent
Black from queening his h-pawn, or to queen his own pawn
in time. Ah well. The new year can't come soon enough for
some of us.
F. Dedrle, Ceskoslovensky Sach,
1921
White to play and win
1.Kb1! Again, not the first move you
tend to look at. But the more "reasonable" 1.Kc3?
allows Black to draw: 1...a3! 2.b4 Ke5 3.Kb3 Kd5 4.Kxa3
Kc6 5.Ka4 Kb6
1...a3 [1...Ke5 2.Ka2 Kd5 3.Ka3 Kc5 4.Kxa4
Kb6 5.Kb4] 2.b3! Ke5 3.Ka2 Kd5 4.Kxa3 Kc6 5.Ka4!
Kb6 6.Kb4 1-0.
Igor Freiberger of Porto Alegre, Brazil
wrote: "A great, very entertaining article! It seems
that Mr. Nunn is so good with words as with the black side
of the KID. Hope we could see more Nunn fictions in a near
future." So do we, Igor. So do we.
John Nunn, The Problemist, 1991
White to play and mate in 24
To solve the problem we advised you to remove the four
black h-pawns and then try to solve the problem. It turns
out that White can then play the waiting move 1.Bh1. Black
is in deadly zugzwang and has only 1...Bg2 2.Bxg2 Ngf7
3.Be4 (threatening 4.Bc2#) 3...Nxe5+ 4.dxe5 and mate on
the next move. With the black pawns on the h-file White
must make 18 (!) waiting moves.
1.Bh1 h3 2.Ba8 h2 3.Bh1 h4 4.Ba8 h1Q 5.Bxh1 h3
6.Ba8 h2 7.Bh1 h5 8.Ba8 h1Q 9.Bxh1 h4 10.Ba8 h3 11.Bh1
h2 12.Ba8 h1Q 13.Bxh1 h6 14.Ba8 h5 15.Bh1 h4 16.Ba8 h3
17.Bh1 h2 18.Ba8 Nb7 [18...h1Q 19.Bxh1 Bg2 20.Bxg2
Ngf7 21.Bb4 (or 21.Be4 Nxe5+ 22.dxe5 Nf7 23.Bc6#) 21...Nxe5+
22.dxe5 e1Q 23.b3#] 19.Bxb7 h1Q 20.Bxh1 Bg2 21.Bxg2
Ne4 22.Bb4 Nd2+ 23.Bxd2 e1Q 24.Bc6# 1-0.
The theme of the composition tourney was to force the
largest number of long bishop moves. John Nunn won it with
18 of the longest possible bishop moves.
Mark Jordan of Bellingham, Wa, wrote:
"I think I solved John's puzzle. I used Fritz 8 to
help me though. Without those four pawns there was a forced
mate after Bh1. Fritz could not find anything with the
pawns on the board though, and declared White was losing.
I figured out though those pawns were just doing tempo
moves and eventually black ran out of pawn moves. Black
cannot move any of his pieces or white can mate him. He
cannot move his king either. So after he moves those four
pawns down the board, he has to move one of his pieces
and then you can mate him."
F. Amelung, Düna-Zeitung,
1897
White to play and mate in two moves
In this problem we have to step back and consider: what
was Black's last move? In Solving
in Style
John Nunn writes: The last move must have been by the
g5 pawn or the black king. If by the king, it must have
come from g7, but in this case White's f6 pawn has no square
from which it could have departed to deliver check to the
king. Thus the last move was made by the g5 pawn; it could
not have come from g6, in which case White's king was in
illegal check, so the last move was indeed ...g7-g5. Thus
the solution 1.hxg6 Kh5 2.Rxh7 is perfectly
valid.
Ron K. Fenton, Christmas 2003
Helpmate in five moves by RxN# (duplex)
Here both sides must cooperate to achieve the goal, i.e.
to mate in five with rook takes knight. The "duplex"
indicates that it works both ways, i.e. in the above position
White can start and help Black to mate him, and Black can
also start and, with White's assistance, lose in five moves,
in each case with rook takes knight being the final move.
The solutions are
- 1.Nc5 d5 2.Ne6 a5 3.e4 Ra6 4.exd5 Qxd5 5.Ke2
Rxe6#
- 1.d5 c4 2.dxc4 a3 3.Nc6 Ra2 4.Qxd2+ Rxd2 5.Nd8
Rxd8#
In both cases there are numerous transpositions that lead
to the same mate.
A.A.Troitzky, Ceske Slovo, 1924
White to play and win
1.h7 [1.Kxd6 Bf5 is simply a draw] 1...Rg5+
2.Kxd6 Rxh5 3.Kc7 [threatens Ra2#. 3.Kxd7? Rxh7+
is a draw] 3...Be6 4.Kb8 [threatens Rd6#]
4...Bd5! 5.Rxd5 Rxd5 6.h8R! [6.h8Q? Rd8+
7.Qxd8 is stalemate] 6...Rd6 7.Kc7 and
Black must give up the rook to avoid mate. 1-0.
V. Platov, Rigaer Tageblatt 1905
White to play and draw
1.f4! The threat is 2.Be1#. 1...Bxh3
2.Be1+ Kg4 3.Bxh3+ Kxf4 4.Bd2+. If the king moves
onto the long diagonal, Bg2+ wins the queen. 4...Ke5
5.Bc3+ Kd6 6.Bb4+ Kc7 7.Ba5+ Kb8 8.Bg2 ½-½.
The decisive position: the black queen is trapped in a
very amusing way.
Gyula Neukomm, Magyar Sakkvilág
1945
Black to play, helpmate in four
A: Diagram; B: wKh6 => h5
In helpmates Black starts and both sides cooperate to
mate him in the stipulated number of moves. The problem
by Neukomm is a "twin". After you have solved
the diagram position you must move the white king from
h6 to h5 and solve that position, in each case constructing
a mate in four moves. The solutions are:
- [wkh6]: 1.Kb5 Qh7 2.Kc6 Kg7 3.Kd7 Kf6+ 4.Ke8
Qe7 mate
- [wkh6]: 1.Kb3 Qf4 2.Kc2 Kg4 3.Kd1 Kf3 4.Ke1
Qc1 mate
Kari Heber of Okinawa, Japan wrote: Thank
you, Frederic Friedel, for helping me finally find the
enjoyment of helpmates. I had previously attempted some
but always found them to be ugly and counterintuitive because
I had viewed them as black purposely throwing the game.
"Why would black want to lose on purpose?" I
asked myself. However, I caught the vision with Neukomm's
twin puzzles. After doing them I followed the links to
last
years puzzles, and although I never solved Korhonen's
twins, I was finally able to solve yours. I was even
able to realize that if you had started the black king
on b4 the rooks could move to either c or e files before
moving into final position, thus making alternate moves
possible. I now realize that the answer to enjoying helpmates
is to quit thinking of them as a chess game (unlike traditional
mate problems). Helpmates are puzzles that use the medium
of chess pieces and board, like traditional blacksmith
puzzles made from nails or horseshoes, or the wood, rope
and ring puzzles that I love to solve. From a chess player
whom Tim Krabbe could truthfully describe as mediocre,
thank you.
We would like to remind you that the real point
of helpmates is that they demonstrate the most beautiful
and surprising checkmate motifs you will ever see. None
of these would ever occur in chess (which is, by the
way, about checkmate), because both sides in a regular
chess game are doing everything they can to prevent them
from occurring. Listen to the following readers tell
it:
Themis Argirakopoulos, Athens, Greece:
Dear Frederic, I don't know about the other readers, but
after reading last year articles, I got addicted to helpmates!
Trying to solve them is something different. There are
no threats, no strategic plans, nothing in common with
the over the board play (except piece movement and checking
rules). Probably, even the most "mediocre" ;-)
player on earth, is going to annotate every Black move
with a double interrogation mark. But this is the point:
You have to struggle to switch off your "direct chess
vision", to find that strange combination, the only
one which can solve the problem! Precision needed too,
it is not enough to get Fritz evaluating the position as
+–. Everything in time, like listening to a concert,
watching a ballet or trying to solve Repton!
Brian Stewart of San Jose, Ca, wrote:
Maybe you remember the comments I made last year regarding
helpmates. Now, you haven't converted me into a helpmate
fanatic just yet. I'm not rubbing my hands together waiting
for you to put up another one. But I can say that I appreciate
the logic of the approach that it takes to solve a helpmate.
You can always make observations that help you narrow down
your search. For example, in this problem by Neukomm. Observation:
There are only so many mating patterns that involve a king
and queen vs. a lone king, and they all involve the black
king being on the edge of the board. Conclusion: The black
king must make its way to an edge of the board. It doesn't
have enough moves to reach the right edge, nor white's
king to the left edge, so they must meet at the top or
bottom edge. Observation: For the black king to reach the
edge, the queen must move once to clear a path. Since there's
no way for the king to unscreen a mating position, the
queen must move again to mate the black king. Conclusion:
At least two moves must involve the queen, leaving at most
two for the white king. Therefore, the king must be within
a two-square radius of its starting square. Observation:
If the white king to be within two squares of its starting
position, the farthest it can get is the f-file. Meanwhile,
the black king can only go as far as the e-file. Conclusion:
The only mates that are achievable are where white's king
is on f6, black's king on e8 and the queen either on c8
or e7, or the symmetrical position with the black king
on e1.
Those three conclusions were enough for me to solve part
2 of the puzzle. But I still struggled with the first part.
I knew the white king couldn't make it to f3, so it had
to go to f6. But I couldn't figure out where to put the
queen so that a) the black king had a straight shot to
e8, and b) the queen could get to e7 or c8 in one move.
Only after I thought about it for a while did I get the
idea of the white king screening the queen on the seventh
rank, to allow the black king to pass, and then everything
fell into place.
Incidentally, I was so intent on solving this puzzle that
I forgot to check the score of the Rose Bowl game, which
I had fallen asleep halfway through earlier in the day.
I grew up in Michigan, and I have two brothers who graduated
from U of M, so I felt honor-bound to watch and root on
my Wolverines. But midway through the second quarter, I
couldn't keep my eyes open any longer, so I went to bed.
I now know that they lost 28-14. Ah well, better luck next
year. Maybe by then I'll feel up to "tackling"
another helpmate.
One more remark: a number of grandmaster friends
spent time solving Neukomm's helpmate and called or wrote
to comment. All thought it was quite incredible that
one could compose something as difficult at this problem
with just three pieces. One, a top-twenty player, needed
12 minutes to solve the problem. "It's just a queen
mate you have to find. How can it be so hard to do that?"
Gyula Neukomm, Christmas card 1948
White to play and mate in ten
If the pawn on b5 were not pinned White could deliver
mate immediately with b5-b6#. His aim is to release the
pin and avoid the checks by the black rook.
1.Kg4 Rxa4+. Now if there was no white
knight on a1 the mate would be quite easy: 2.Kg5 Ra5 3.Ra1!
Rxa1 4.b6#. White must get rid of the knight and does so
by forcing Black to capture it: 2.Kg3 Ra3+ 3.Kg2
Ra2+ 4.Kg1 Rxa1+ 5.Kg2 Ra2+ 6.Kg3 Ra3+ 7.Kg4 Ra4+ 8.Kg5
Ra5 9.Ra1 Rxa1 10.b6 mate.
Frederic Friedel
Click
here to replay and download the solutions to all puzzles.
The solutions can be replayed on our Javascript board.
The page contains all the positions quoted in the articles,
including the ones for which solutions were already given.
Remember that you can replay the moves of each solution
either with the recorder buttons just below the board or
by clicking on the moves in the notation.
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