Christmas Puzzle 1999
Description
of the puzzle
Reactions
I presented the 1999 Christmas puzzle in an article in
ChessBase Magazine 73 and offered a special prize –
a book signed by some of the world's top players, confirming
that the winner is the greatest. The article was posted
on a number of internet chess forums, where people immediately
launched concerted efforts to solve it.
On Christmas day 1999 I posted the article on my favourite
site, the geek watering-hole Slashdot
(“News for Nerds”). The URL is http://slashdot.org
and you should definitely pay the site regular visits if
you are interested in science, technology, computers, programming
and weird stuff in general. There are new reports there
every day, each with an attached discussion forum where
you can air your views on the subject. They have approximately
120,000 unique visitors and about 1 million page views per
day.
Just a few hours after the slashdot posting all hell broke
lose. A lot of emails had been coming in from CBM subscribers
and the chess forum crowd, but the ones from Slashdot were
like a tsunami and swept everything else away. I received
a total of well over a thousand messages, and even many
months later, after the solution had been published, they
kept coming.
Initially, on Christmas day and immediately thereafter,
only a very small number of correct solutions were submitted
to me by email. One interesting phenomenon was that a numerical
majority of these came from East German grandmasters. Apparently
the puzzle was known in the chess schools there. And I got
correct answers from a couple of Russian players, like now
US champion Anjelina Belakovskaia, who wrote: “Are
you joking or what? I have the puzzle in a book I wrote
in 1990 and give it to my students from time to time. It
is one of the tricks I learned in the 'School for Russian
Stars' by A. Panchenko. Don't forget I am from Soviet Chess
School!”
But an overwhelming number of messages had the wrong solution.
The most common error was that the contestants would overlook
a check, and the most common line (by far) was 1.e4 Nc6
2.a4 Nb4 3.Ra3 Nxc2+ 4.Rd3 (??) Nb4 5.Ne2 Nxd3#. Of course
4.Rd3 is illegal since it ignores a check. Ben Lin knew
that he was doing this and wrote: “My solution only
works if certain lightning chess rules are used, i.e. one
is allowed to overlook checks. Does it count?” Nope,
it doesn't, Ben.
Another very common solution involved interpreting the
puzzle in a way that one could use an extra ply. Frank Weed
II wrote: “Ok, I'm convinced this is a matter of semantics,
and that the 'fifth move' refers to the fifth move after
1.e4, which means the game really ends on the sixth move
(I hope, I hope, I hope). Then the solution is 1.e4 g5 2.Qh5
h6 3.Nf3 Nc6 4.Nxg5 b6 5.Nxf7 a5 6.Nxh8#”. Another
common six-mover was 1.e4 f6 2.Nf3 g5 3.Ne5 a6 4.Ng6 a5
5.Qh5 a4 6.Nxh8#. Another imaginative try was to follow
up 1.e4 with a second white move and get an extra ply that
way.
A number of readers decided that on the fifth move a knight
takes a rook and a mate occurs (not by the same side), for
instance 1.e4 Nf6 2.Nf3 Nxe4 3.Ng5 e6 4.Nxf7 Qh4 5.Nxh8
Qxf2#. Matthew O'Connor wrote: “The phrase 'knight
takes rook mate' can be interpreted two ways: 1. The canonical
way. On the fifth move one of white or black a knight takes
one of the opponent's rooks, thus placing the opponent in
checkmate. 2. As a word puzzle. On the fifth move a knight
captures a rook and then a checkmate occurs. These two events
are independent of each other.” Another imaginative
try in this vein: 1.e4 Nc6 2.Qf3 Na5 3.e5 Nb3 4.e6 Nxa1
5.exf7#, sent in by the members of a retirement centre in
the US.
Many submissions, especially from the non-chess Slashdot
site, contained mates that were not mates. Here's a typical
example, in the original form in which I received it:
E2 - E4 (starting move required by white)
D7 - D6 (black queen's pawn)
F2 - F4 (white king's pawn)
G8 - F6 (black king's knight)
E1 - F2 (white king)
F6 - G4 (black king's knight - check)
F2 - G3 (white king)
G4 - F2 (black king's knight)
G1 - F3 (white king's knight)
F2 - H1 (black king's knight takes white king's rook - checkmate)
This translates to 1.e4 d6 2.f4 Nf6 3.Kf2 Ng4+ 4.Kg3 Nf2
5.Nf3 Nxh1+. Unfortunately White has 6.Kh4 and the final
position is not mate. Similarly solutions like 1.e4 d6 2.Nh3
f6 3.Nf4 Kf7 4.Ng6 Qe8 5.Nxh8+ fail because the king can
escape (5...Ke6).
Some of the Slashdot mail came from people who couldn't
read chess notation. It is astonishing how they invented
readable scores. “This is going to look like a pretty
nasty hack, since I don't know how to transcribe chess moves.
I'm going to assume the lower left corner is a1 and just
give start and end coordinates...” wrote Jeff Braciak
and submitted perfectly readable notation (“1. White:
e2 - e4, Black: a7 - a6 2. White: c2 - c3 Black:
b8 - a6” etc.). Others simply invented their
own descriptive notation: “Black moves king's bishop
pawn forward one, queen fills king's position; queen's knight
moves twice to be alongside white's advanced pawn and then
moves next to blacks advanced pawn...”
A lot of readers carefully parsed the puzzle, looking for
linguistic tricks. A couple of readers sent me a sequence
of moves ending in 5.NxR and interpreted the puzzle as requiring
"Knight takes rook, mate" (“mate” in
the sense of “buddy”). David McCuiston wrote:
“Is there a word trick to this problem? I mean after
thinking I had solved it I was disappointed and considered
it a trick problem. I would certainly hope that it's a brilliant
solution instead of a gimmick or trick.” Mike Carson
made an earnest appeal to my conscience: “I have been
working on this puzzle for ages, and I still am. I am determined
to work on it until I solve it. Just one little note: if
it is a play on words of some sort, or a riddle, not a chess
problem, I will be upset at you for ruining my life. I am
only 23 and I still have some time left to enjoy. So if
it is a play on words, please tell me now.”
A very imaginative solution came from Gerhard Josten, who
confronted me with the following: 1.e4 f6 2.Nf3 Kf7 3.Nh4
Qe8 4.Ng6 Be6 5.Nxh8#. Huh, 4...Be6?? Ah, Josten explains,
the piece is the historical Alfil, which was the bishop
in the original version of the game. At the time the bishop
could jump two squares diagonally. “You only said 'a
game starts with 1.e4...'. My analysis leads me to conclude
that it is an original game from medieval Arab times, with
an Alfil on the board.” Robin Smith argued in a similar
vein: “How about this solution. The game was played
several hundred years ago, when the bishop could only hop
two squares diagonally. So the moves are 1.e4 Nf6 2.Ne2
Nh5 3.g3 Nf4 4.Rg1 a6 5.Rg2 Nxg2 mate.” I am almost
inclined to recognise these as a correct solutions.
One reaction I received quite often is exemplified in the
following messages: “This is Francois from Paris. I
think this problem is: The greater chess swindle. There
is no solution on the board.” Carlo Wood wrote: “I
tried this problem for many hours. And my conclusion is
that it is not
possible. I think you and Gary Kasparov made an error. Please
recheck your solution for intermediate checks that are ignored. I found several 'solutions' that I thought at first were okay,
and only after entering them in xboard my computer told
me that one of the moves was illegal.” A number of
readers sent in proofs for the impossibility, and some were
quite compelling. James Puccio wrote: “Although I hate
to submit this as an answer, but I must state that the scenario
of knight takes rook mate is not possible. I will try to
explain why I believe it is so in less than 100 pages.”
Which he dutifully did. I'm sure if I had not known the
solution James would have convinced me.
Letters
As I said I received many hundreds of emails in response
to the puzzle, and I actually answered most of them. The
family didn't appreciate this highly unusual Christmas activity,
but I was reading some very interesting stuff and making
new friends all over the world. Naturally I soon created
a small library of responses which I could copy into the
body of my replies, since most of the emails has similar
themes. From the over 600 messages I filed away here are
some short excerpts.
Valentin
Pepelea: Thank you Frederic for this opportunity
to show off and gloat. What a wonderful Christmas present!
As you can see, I am sending this email to all my friends,
so that they will be the first to know, that I am The Greatest.
:-). [The
solution was incorrect, and a while later I got a second
mail from Valentin, who had discovered this by himself].
Fred, I still want the book signed by Gary Kasparov and
Ken Thompson, but let them acknowledge me as The Greatest
Delusionist.
Hein-Jan
Leliveld: Your Christmas puzzle kept me and my
father thinking for a long time, but we couldn't solve it.
As usual, unsolveable puzzles are very interesting especially
without an answer. You can't help thinking about it. I tried
to apply the second law of Newton, but it didn't help me.
Now I can't sleep until I have found the answer. Very, very,
very annoying!! [Hein-Jan is a physicist].
Jim
Puccio: Frederic, I am going nuts still trying
to solve this thing. When and where you will be posting
the solution. I won't be able to quit until I know the answer.
“Mastroid”:
have discovered a truly marvellous solution to this problem,
which however this textbox is not large enough to contain.
[This
is one of my favourites].
Uri
Blass: Are you sure that there is a solution
when the same side who takes the rook does the mate? The
only solution that I can find is in case that white takes
the rook and black does the mate. For example 1.e4 e5 2.Nc3
Bc5 3.Nb5 Qh4 4.Nxc7+ Kd8 5.Nxa8 Qxf2# or 1.e4 e6 2.Nf3
Bc5 3.Ne5 Nc6 4.Nxf7 Qf6 5.Nxh8 Qxf2#. I tried many ideas
when the same side takes the rook and does the mate but
they failed. Examples: 1.e4 Nf6 2.Be2 Ng4 3.Kf1 Nxh2 4.Qe1
Ng4 5.Rh2 Nxh2# when the only problem is that 4.Qe1 is illegal.
1.e4 Nc6 2.Ne2 Nb4 3.c4 Nxa2 4.Ra3 Nb4 5.Rd3 Nxd3# (4.Ra3
is illegal). 1.e4 Nc6 2.d4 Nb4 3.a4 c5 4.Ra3 Qa5 5.Rd3 Nxd3+
is not mate. 1.e4 f6 2.Ne2 Kf7 3.Nf4 Qe8 4.Ng6 Be6 5.Nxh8#
(Be6 is illegal). 1.e4 c6 2.Qe2 h5 3.Nc3 Rh6 4.Nb5 Rd6 5.NXd6+
is not mate. 1.e4 f6 2.Nf3 Kf7 3.Ng5+ Kg6 4.Nf7 Nh6 5.Nxh8+
is not mate. I even thought about underpromotion (the only
pawn that has time to do it is e4) but found no way.
Daniel
Rodgers: I SOLVED IT! The day after Christmas
I had noticed the problem on slashdot. I got started working
on it at around midnight between Monday and Tuesday. The
problem seemed easy, and I tried a few simple moves, but
I soon began to see that normal strategy had nothing to
do with it. I soon came to the realisation that the puzzle
was impossible. It was obviously a joke to get people all
worked up for nothing.
Then suddenly, I realized that the article had not said
who had to actually mate who. So I tried to get black to
mate white, and saw that just maybe, there could be a possible
solution. First, I tried not moving the king, then I tried
moving the king and not the rook, then moving both. Next,
I tried a nifty discovered/double check using the black
queen and knight, which worked handily in six moves, or
if the first move was 1.d4 instead of 1.e4. Next, I went
to slashdot and read all of the entries for clues. Next,
I went to google.com and searched for obsolete notations. No luck. I also searched the internet for the outright solution,
with no luck at all. I turned off the computer and prepared
for bed, frustrated, but challenged. Then a thought stirred.
Maybe white could do the checkmating, after all. Since e4
is forced as the first move, maybe I could use that to my
advantage to trot out my white rather than my black queen
and do a discovered check on black. I vowed that I would
never do anything bad again if I could figure this out.
It didn't work. I stared at the chess board, my mind in
that creative frame of mind – that frame of mind where
the teacher says: chuck out everything you've been doing,
and come up with a lesson that really works. The main problem
was getting that damn white rook out, but the pawn in front
of it was in the way.
The thought naturally followed, 'what if the black
knight takes the pawn, rather than having white move it.'
I tried it, and to my stupefication, it worked. I
began laughing hysterically – 'I did what Kasparov
couldn't do! I
did what the grandmasters couldn't do!' My hands still haven't
stopped shaking. [Daniel's
solution was 1.e4 Nh6 2.Be2 Ng4 3.Kf1 Nxh2+ 4.Qe1 Ng4 5.Rh2
Nxh2 mate. Perfect, except that 4.Qe1 ignores a check].
Manuel
Rodriguez: My English is regular but I have a
few words for John Nunn. I have one of his excellents books
(Secrets of Minor-Piece Endings) and I already know the
deep of his thought, but now i consider him a big
creative genius. I like to know how he find this
wonderful and amazing puzzle. I have seen a lot chess problems
including some amazing from retrograde chess. But this puzzle
take clear first!! Now I am already one winner, because
now I know that beauty. I have three friends of mine with
the puzzle, they call me every instand jejeje, but I will
let them a month without tell they the answer if they don't
find it first. [Manuel is from Higuey, tourist pole of the
Dominican Republic. I have a standing invitation to come
visit].
Roger
Fischer: Naturally after spending many hours
brooding over the problem I hadn't found a solution. Then
I committed the very serious error of showing it to my colleagues
at the chess club. They, too, invested many hours and now,
just like the students in the Botvinnik school, they are
demanding that I show them the solution (they are convinced
that there is none). Please send it to me immediately, otherwise
I am in big trouble. I'm sure that is not your intention.
[Roger
did not receive the solution from me. I told him I was physically
incapable of revealing it before I was absolutely forced
to do so.]
Ken
Boucher: 'Frederic, all of Slashdot went nuts
thanks to you. When your puzzle was posted there I and many
others lost all productivity until someone managed to solve
it. Brilliant sir, Brilliant. Thanks for a reminder of why
I used to play.
Ken Boucher also posted an incredible
sendup on the problem, to be sung to the tune of "One
night in Bangkok" from the musical Chess.
Picking a winner from all the correct solutions
I received was not an easy task. One of the problems was
that someone posted the solution on the internet, and immediately
after this had occurred I started getting a dozen or so
correct answers per day, up from one every three days before
then. So I picked David
Bellows, who gave me a vivid and plausible description
of his thought process almost exactly at the time the solution
first appeared in the forums. “It was an amazingly
difficult and enjoyable problem, and I spent a total of
eight hours working on it (divided into two days)”,
he wrote
| As a prize David receives
a beautiful book, “Chess Highlights of the 20th
Century” (by Graham Burgess, Gambit Publications
1999). On the first page there is a commemoration, certifying
that David Bellow is the greatest. It is signed by Garry
Kasparov, Vishy Anand, Vladimir Kramnik, Alexander Morosevich,
Peter Leko, Michael Adams, Judit Polgar and a number
of other players (from the super-tournament in Wijk
aan Zee). David is a webmastr and music composer living
in Atlanta, Georgia. |
 |
Here are a few more reactions from successful solvers.
Peter
Svidler: From Peter I got two mails. The first
was at 23:15 PM and read: “The hell of it – I
used to know the solution :-( ”. Then at 23:35 PM:
“I do :-) ”.
Jürgen
Schmitz-Jordan: After spending countless hours
on countless days I have at last succeeded. The solution
came after all attempts ended in six move mates. I was convinced
that it was impossible, but then I suddenly realised that
a pawn has to be removed in order to bring the queen into
play. I'm glad I am now relieved of this madness. However,
thanks for the very fine occupational therapy.
V.
Saravanan: Well, you wouldn't believe this, but
I found the solution in about 20 minutes of time!! (No disrespect
to Garry, I adore him). I opened the CD, and was going thru
the multimedia section first, as usual, and came across
the puzzle. I just had a look initially for about a few
minutes, and understood that it would be difficult for White
to mate with the move Nxh8 on the 5th move, as Black cannot
arrange his pieces accordingly in just five moves before
that (for example, 1.e4 f6 2.Nf3 Kf7 3.Ng5 Kg6 4.Nf7 'pass'
and 5.Nh8 leaves out the h6 and g5 squares). Then I stopped
trying, and went thru the story in the magazine booklet.
When I read the lines 'When I told him the solution on the
phone I could hear Mikhail Botvinnik gasp in the background'!
After that, it was quite easy. It took another ten minutes
to find the solution. [The
solution was correct. Turns out that Saravanan is an IM
from India, Elo 2429, living a stone's throw away from Vishy
Anand's home in Madras].
Alex
Kundin: “I've solved the puzzle just before
falling asleep and enjoyed it very much. It took me about
three hours overall. But it was a really tough challenge!
I just couldn't let it go and kept thinking deep into the
night, considering calling my trainer Alterman the next
day. But then it struck me...” [Boris
Alterman, as you will remember, was one of the students
at the Botvinnik school who had bugged Kasparov for the
solution].
Sami
Hämäläinen: I had to write you immediately after
I found the solution, although it is 3 a.m. in the night
here in Finland. It took me about three hours, without breaks,
could not leave the board on my computer screen! Of course
I had all the peace and quietness (wife and baby are sleeping
and only sound around me was some mild humming from the
computer). Suddenly
I saw it!! At first I thought that this puzzle
was awful, a real pain in the ... But now it is just a wonderful
and beautiful puzzle, which I can hardly wait
to show to my chess friends – to be solved with much
pain and sleepless (k)nights, of course.
John
Watson: Right after I saw the problem in ChessBase
Magazine thinking: “This will be easy!”, I went
to my computer and worked nonstop in full concentration
for about three hours, and went to bed having achieved nothing
(no genius here, sorry!). I did what I'm sure are all the
usual things, but I also thought, because of the wording
of the problem, that maybe White was doing the mating, despite
the tempo less, perhaps because Black didn't have the disadvantageous
e4 in. I spent a humiliating amount of time on that idea
before I rejected it. Here's the interesting part: today,
I woke up and did errands until the early afternoon, flipped
on the computer, and within three minutes I got the answer!
They say we mull these things over in our subconscious,
so maybe that was it, but I was also very lucky. When I
was young I used to wake up and quickly find solutions to
math problems that I'd spent hours on the night before,
so I do think there's something to the subconscious theory.
Anyway, thanks for the extremely fun (and frustrating!)
problem. [John
is a ChessBase contributor and translator].
Richard
Meisel: Mr. Friedel, finally! Absolutely amazing!
I've spent weeks looking at this problem. I must have tried
every possible position NxR could have occurred on the 5th
move of White or Black; thought it was impossible a couple
of times, but I believed you when you wrote me that it was
honest, no tricks. And then it finally just came to me,
looking at the board while watching “Indiana Jones
and the Temple Of Doom” on TV. No wonder Botvinnik
gasped. It's nice to know I found this, something even Kasparov
and Karpov missed!
Anonymous
Coward [this is the default name Slashdot allocates
to people who do not identify themselves]: Frederic, thanks
for adding this great beauty for us to puzzle over and eventually
admire. It is humbling for us humans to think that even
the grandmasters did not see this solution for so long,
and that computers are not that much better. But when the
Aha!
insight floods the mind and the puzzle is solved, it is
that great creative moment when things are all so beautiful
and delicious. It must be the same with chess, with programming
computers, and with all great art, like the state of being
in love. This is the moment when we stop thinking of chess
as a combat between two people, or of programming as a combat
between a machine and a person, but rather we realise that
this must be the way God thinks and sometimes we get a flash
of it. We should thank God we are provided that flash a
few times in our life! And thanks again, Frederic, for helping
us see it.
David
Lowy: “I figured it out by cheating –
I used a computer. Do I still qualify for the prize? :-)
Thanks for your puzzle, and for all your good work.”
I wrote back “You will qualify for a special prize
if you can tell me exactly how you were able to use a computer
to solve the problem. Now that's
really interesting.” Dave's reply: “Sure, I'll
tell you how I used my computer: I pointed my browser to
slashdot.org and the rest is pretty much academic!”
This was after the solution was published.
Heiner
Marxen actually solved the problem with the help
of a computer program: “I modified my problem solving
program Chest
slightly to do a brute force search, and especially to prove
that there are no alternate solutions (except for the fact
that the second and third moves of White can be exchanged).
Chest
claims after over a week of computing there are no cooks
and especially no shorter solutions. It found the correct
solution before I did, so the honour belongs to the computer
and only indirectly to the program author. Such is life.
The solution is very beautiful.”
Marc
Boulé: I gave this unique chess problem an hour
of thought and after that, concluded it was a task for a
computer. I have been programming my own chess engine for
over two years now. I decided to try and solve the Christmas
Puzzle with my program. I quickly realized that, in its
current state, it was not possible to do so. Most of the
algorithms and heuristics are a result of both sides playing
their best moves. Because of the nature of the problem,
many modifications were needed. With the help of my friend
we devised a few optimizations that, once implemented in
the program, would yield calculation times that were feasible
(with no optimizations, a Pentium 200 would have taken a
few years to compute the solution!). We occupied a programming
lab at our university to do the calculations. A total of
19 Pentium3 500MHz computers were used to calculate an eight
ply search after 1.e4 and each of black's possible moves
(we guessed it was black that delivers the mate). We started
all the machines on a Saturday night and the next morning,
all had finished their tasks. It is with great satisfaction
we give to you the solution. [The
solution was correct. Marc's letter arrived just as I was
finishing this article].
The solution
Ah, naturally I'm not going to reveal it here. There will
be many new visitors who do not know the problem, and it
must not be spoiled for them. If you have great difficulties
finding the solution then write
to me. But don't expect to receive the solution without
a fight!
|
