Hope to see you there!
The boy on the show was Xaver Neuhäusler from the state of Bavaria, and the bet was that this young lad could complete a "knight's tour" of the chessboard, completely in his head, starting from any square on the board.
A "knight's tour" is a sequence of 64 knight moves executed in such a way that each square of the board is visited exactly once. Xaver was blindfolded and a starting square was called out to him. Without much ad the lad dictated a sequence of 64 squares that comprised a perfect knight tour.
The reaction to this feat in Germany was overwhelming. Newspapers were full of it, people discussed it on trains and busses, in offices and schools, and we received dozens of calls asking us to tell the story on our web site.
Well this is what we are doing. And it leads to a small dilemma. Should we not simply report the story, one that has produced such universal interest for a chess-related subject? Should we join the speculation that we might have encountered a future chess world champion, or at least been witness to an prodigious feat of pure genius? Or should one look deeper? Even if it detracts from a moment of glory for a nine-year-old child? Will anyone cheer if we shoot down a legend that has moved a nation? Our decision can be seen at the end of the article. But first let us take a look at the mechanics of the knight's tour.
A "Knight's Tour" of the chessboard, as originally proposed, is a sequence of moves by a knight such that each square of the board is visited exactly once. The questions raised were: can the knight indeed make such a tour; and if it can, how many different knight tours are there? A comprehensive history of the knight's tour is to be found on
The first question was answered in a ninth century Arabic manuscript by Abu Zakariya Yahya ben Ibrahim al-Hakim. The author give two tours, one by Ali C. Mani, an otherwise unknown chess player, and the other by al-Adli ar-Rumi, who flourished around 840 and is known to have written a book on Shatranj (the form of chess then popular).
A "closed tour" is one in which the square at the end of a knight's tour is a knight move away from the first square, as in the second example above. The master of Shatranj as-Suli, who based his works on those of al-Adli (which he criticised), published the following two closed tours:
The first example shows perfect axial symmetry on the left halfboard, the second is composed of two quasi-symmetrical half-board tours.
The first comprehensive mathematical analysis of the knight's tour was presented by the eighteenth century mathematician Leonhard Euler (1707–1783) to the Academy of Sciences at Berlin in 1759. The Academy had proposed a prize of 4000 francs for the best memoir on the problem, but that the prize was never awarded, probably since Euler was at that time Director of Mathematics at the Berlin Academy and presumably ineligible.
If you want to learn a closed knight's tour by heart pick one of the above by Leonhard Euler. Learning a closed tour had the important advantage of allowing you to start from any square on the board and complete the tour from there.
How many knight's tours are there?
The number of knight's tours that are possible on a normal chessboard is surprisingly big. Actually it is so big that simple counting of tours is out of reach even for the fast computers of today. The problem has to be tackled in other ways. In 1995 Martin Löbbing and Ingo Wegener proclaimed that "the number of knight's tours equals 33,439,123,484,294". They obtained this result by running 20 Sun workstations for four months.
In 1997 Brendan McKay used another method (splitting the board into two halves) and got the result 13,267,364,410,532. To give you an idea of the magnitude of these numbers, a computer searching and finding tours at a speed of one million tours per minute would need more than 25 years to calculate the number of tours given by McKay.
The Magic Knight's Tour
If you really want to show off you should not just learn one of the closed tours given above, you should go for a "magic knight's tour".
In a magic knight's tour the steps, if numbered, make amagic square. This is an arrangement of the numbers from 1 to n in a matrix, with each number occurring exactly once, and such that the sum of the entries of any row, any column, or any main diagonal is the same.
Full magic knight's tours are not possible on n x n boards for odd numbers, and are believed to be impossible for the 8x8 chessboard. The "most magic'' knight tour known on the board is the Semimagic Square illustrated in the above left figure having main diagonal sums of 348 and 168. Combining two half-knights' tours one above the other as in the above right figure does, however, give a full Magic Square, in which the diagonals add up to 260 – but the steps 32 and 33 are not linked by a knight's jump.
All known magic knight's tours of the normal chessboard are listedhere. There are 131 different geometrical forms.
Practising the knight's tour
In the 19th century H. C. Warnsdorff presented a practical method of constructing knight's tours ("Des Rösselsprungs einfachste und allgemeinste Lösung", Schmalkalden, 1823). The aim is simply to avoid creating dead ends – squares from which the knight cannot get further without getting to an already visited square. For that reason the possible squares to be chosen next are examined before every move. One counts the number of free new choices – entrances – every one of them has, and then moves to the square with the lowest number of new choices.
Another largerDelphi program (executable 434 KB) allows you to practise and solve the problem, including closed tours. In case you become seriously interested the author has supplied the full source on his knight's tour page.
How difficult is the knight's tour?
Let us return to our nine-year-old boy on the TV show. As mentioned in the introduction to this article Xaver Neuhäusler was able to complete a knight's tour blindfolded and from a starting square given to him by the host of the show. Exactly how prodigious was this feat? How deeply must we be impressed?
In order to test the effort involved in learning a knight's tour we asked a guest who was visiting over the weekend of the TV show whether she could do it.Elizabeth Pähtz is the current women's under 18 world champion, and she was in Hamburg to play in the first German Internet championship. "I used to be able to do the knight's tour when I was a child," Elli told us, "but now I have forgotten how it went."
So we asked her to try to learn it again. Using a knight's tour of her choice Elli started learning it by heart. It's not as easy as it looks! With some effort Elli was able to master a tour in 40 minutes. It must be mentioned that the poor thing was in some pain, having had two wisdom teeth extracted a few day previously. So there was some problem with motivation.
How about someone who is not a very strong chess player. Thomas Friedel, 20, gave up competitive chess when he was 14 and is now a full-blood programmer. How would an algorithmic mind fare with the task?
After 12 minutes studying the diagram Tommy announced that he could do it. And indeed, with Elli checking the moves he completed a knight's tour flawlessly on an empty chessboard.
With some effort Tommy was able to dictate the squares without looking at the chessboard. He could only do the tour starting from one starting square, but wagered that with half an hour of practice he could pick it up at any point in the closed circuit. Maybe an hour to do it reliably, dictating the squares with a blindfold covering his eyes.
Sorry, Xaver, for demystifying your great performance. And sorry everybody for being such spoilsports. We can only close by giving you the following advice: pick a knight's tour above, invest an hour or two learning it, use one of the gorgeous little programs to practise it and be prepared for your moment of glory. If you don't make it to a big TV show it at least makes for a great party trick.
The knight's tours of George Koltanowski
The second point was brought to my attention by an old friend whom I hadn't seen in years. After reading my article he wrote to me reminding me of the most remarkable knight's tour we – both of us together – had ever witnessed. I shamefully admit that it had completely slipped my mind while I was dealing with the young German TV star.
It happened many years ago, at a US chess club, where a blindfold master was giving a demonstration of his extraordinary abilities. At one stage he asked for a helper from the audience, and I was pushed and poked by my friends to take the stage. There the master gave me block of sticky notes and asked me to write down names, words and numbers dictated at random by the audience. Each was stuck on a big demo chessboard, starting from the square a8 and working sequentially to h1.
The audience call out a variety of words: names of cities, family members, phone numbers, abstract expressions. It went something like: Dayton, Margaret-Lee Farrow, pride before a fall, 212-783-4529, my dad's dog Skippy. While this was going on the master sat on his chair, listening to the audience, chatting with them. He was completely relaxed and not making any visible effort to memorise the notes.
After all the squares had been covered the master was blindfolded. He then asked someone in the audience to name a square on the chessboard. Starting from that square he started repeating words and numbers, while I removed the corresponding sticky notes from the demo board. The order of the words resulted in a perfect knight's tour. I believe he got one or two words slightly wrong, on the lines of Margaret-Mae Farrow instead of Margaret-Lee. All the numbers were perfect.
Now that is a truly remarkable feat. We were all deeply impressed, not the least because the master was approaching ninety years in age! He was George Koltanowski, one of the greatest mental acrobats the world has ever seen. George Koltanowski, 1903-2000, copyright (C)
George Koltanowski was born in Antwerp on Sept. 17, 1903. He developed his prodigious memory skills by studying memory games while he was very ill as a child and confined to bed for a couple of years. When he was 14 he started playing chess, and at the age of 21 when he played and drew Siegbert Tarrasch at the 1924 Meran tournament. In the early thirties he was the top Belgian player, beating Akiba Rubinstein in Antwerp 1931 and drawing Alekhine at Hastings 1936/37. He was awarded the title of IM in 1950 and in 1988 he was given an honorary GM title by FIDE.
Koltanowsky held a number of records in another area of chess. For centuries, the greatest masters in the world tested their mettle by playing blindfolded. It was long believed that three blindfolded games at once marked the limit of human capacity. Then, in 1933, Alexander Alekhine successfully played 32 simultaneous blindfolded games. Later, other grandmasters left Alekhine's record in the dust. Koltanowski set the current record, playing 56 blindfolded games San Francisco in 1960. He played the games sequentially at 10 seconds a move in 9 hours, scoring +50 =6. He also gave huge simultaneous displays with sight of the board, playing 271 games in 1949 and 110 in 1955.
(Some of this is described in an article entitled "The Einstein Factor", a very readable article which explains in general terms why everyone should play chess).
When the Nazis overran Belgium during World War II, several of his family members perished in the Holocaust. Koltanowski was on a chess tour of Central America and was allowed to immigrate to the United States, mainly because a chess-playing consul in Cuba had been amazed by one of his demonstrations. He started writing a column for the San Francisco Chronicle. He had completed over 19,000 instalments when he died of complications resulting from congestive heart failure in February 2000, at the age of 96.
A full obituary is still available in the archives of the San Francisco Chronicle:Grandmaster Of Chess, George Koltanowski.
It was the 1998 Mass Open where my opponent arrived in full camo uniform, cap, fortunately sans gun or hunting knife. Like a character in the movie Deliverance, this should have been a tip off that our game was about to take us on a journey through the chessic twilight zone.
Move after move my opponent placed his pieces more and more off center until it was a little painful to look at the position. On my move, stating "J'adoube" I went to adjust a pawn of my opponent's color that was nestled in a corner of a square when my opponent stopped the clock and stated that I could not adjust any of his pieces. I could adjust only my own pieces.
His claim was that the 4th edition /1993 section A10 rule in the USCF book was: "Adjustment of the pieces. a player who is on the move and first expresses intention to adjust (e.g. by saying j'aboube or I adjust) may adjust one or more pieces on his or her squares."
I told him that I didn't think that was a correct interpretation of the rule and said I would like a ruling from the TD Steve Frymer. We led a parade of about 1/2 dozen players, who thought this conflict quite entertaining, and we marched into the TD's office.
My opponent cited page and paragraph to argue his point that only he had the right to adjust his pieces. I asked that Steve look at our board and I made the claim that I had the right to adjust the pieces, any piece, that was not in the approximate middle of a square and in fact felt that this consistent eccentric placement of the pieces was a type of harassment.
TD Steve Frymer looked at the position, and then us, and ruled that according to rule 10A I had the right to adjust any piece on my move and that he was going to watch us.
BTW the following Edition 5 says "on their squares" no "his or her". Fortunately I defeated my opponent once the J'adoube Gambit had been dealt with.
Upon telling this to my kids they offered to purchase for me a camo hunting uniform, including a camo mad bomber hat, and camo full rifle bag in order to hold my set and clock. Building 19 apparently was having a sale. I don't think Boston is ready to see me rolling on the Red Line to Davis Square in this getup no matter how stylin' it would be considered at the BCF.
What do you feel the perfect chess uniform should be? Should there be a dress code? Have you experienced some odd behavior at a chess tournament or have a story that you could please make comment about?
Cheating chess player loses mobile phone gambit
By K.R. Nayar, Senior Reporter
Dubai: A chess player from Iran, who cheated using his mobile phone to try and win a game, was chucked out of the Dubai Open Chess tournament.
M. Sadatnajafi, with an Elo rating of 2301, while playing against Chinese Grandmaster Li Chao, made his moves based on the text messages he received on his mobile phone.
Chief arbiter Casto Abundo, confirming the incident, said: "As per the International Chess Federation (FIDE) laws, no player is supposed to use the mobile phone while playing. The matter is still being investigated and a report is being forwarded to the FIDE for further action," said Abundo.
Sadatnajafi is alleged to have followed instructions from some top player in Iran while playing against Chao. This match was relayed live on the internet and his friend, closely following his moves on the web, guided Sadatnajafi accordingly.
Sadatnajafi had made only 10 moves when he was caught looking into his mobile handset. When confronted, he immediately dropped his cellphone.
On examining the handset, it was found that he had received SMS instructions in Farsi. The identity of the friend who had sent the text messages is still to be known.
Losing the title
Chao went on to tie for the top position, but lost the title owing to Wesley So's better technical count.
In December 2006, Indian chess player Umakant Sharma was banned for 10 years by the All Indian Chess Federation for using a bluetooth headset sewn into a cap to get help from a computer.
Sharma's friends relayed moves made by a computer programme to him through the bluetooth set.
Sadatnajafi may also face a ban or may even lose his rating.
In the former Soviet Union the Botvinnik chess school had a very effective way of educating players that was unsurpassed anywhere else in the world. The distribution of grandmasters in each country 20 years ago had the Soviet Union leading with 100'ds of GM's. As players started to leave the Soviet Union, many coming to the USA, they spread their good chess coaching techniques to other parts of the world. The reason why there are so many good very very young players in the US today relates in most part to these émigrés’ great coaching. Germany has the most chessplayers in the world but only 1/3 of the grandmasters that Russia has.
One émigré and coach, Master Jacob Rasin,says that style accounts for 5% to 10% of a differentiator between one individual and another because in order to be a good chess player tactics and positional understanding must be mastered and those two elements constitute most of a person's chess knowledge.
Over the course of the 2007-2008 school year, the Boylston Chess Foundation is planning to hold a series of chess camps December, February, and April school recesses, as well as one just as school gets out in June.
December recess: 26th, 27th, 28th 9:00 a.m. to 12:30 p.m. each day
February recess: 19th, 20th, 21st, and 22nd 9:00 a.m. to 12:30 p.m. each day
April recess: 22nd, 23rd, 24th, and 25th 9:00 a.m. to 12:30 p.m. each day
June (school’s out): 23rd, 24th, 25th, and 26th 9:00 a.m. to 12:30 p.m. each day
These chess camps invite young chess players who already have a complete understanding of the rules of chess to come and develop their abilities. With a combination of lecture, question/answer, and hands-on techniques, the instructor(s) will cover:
Students will develop their memory, critical thinking skills, sense of fairness, attention span, and have fun in the process.
Instructor: The head instructor will be Chess Master Jacob Rasin, an experienced coach who has been the coach of many of New England’s best young players and has inspired them to many championships.
Who can join?:
School-age children, K to 12, interested in getting better at chess from motivated beginner to intermediate.
How much does it cost?:
Each camp is $60 for Boylston Chess Club members. Non-members who have never been members before will need to pay to join the club for one year in which case the camp fee is waived. (Parents with more than one child in the camp can get a discount—only $35 per child.)
|BCC Junior Membership - $100||BCC Family Membership - $125|
Reserve your place in one or more camps by contacting Paul MacIntyre, President of the Boylston Chess Foundation at (781) 322-7936 or email@example.com
Mikhail Derazhne, Tony Scali and Rachel Dillon, Dave Vigorito and Greg Kaden, Kent Leung, Tony Cortizas, Stuart Finney, Katherine Gasser, Alexander Ivanov, Ruben Portugues, Griffin Price, Mike Griffin, Bob Oresick, Vikas Shiva, not to mention the powerhouse Lung and Wang families.
Boris you blew this one(???).
Is there any way US chess should prepare for the future change in demographics? Do you have any stories or comments about bigotry in chess? Please Comment.
Mike Griffin 04/08/2008
Pew Hispanic Center