The Knight Challenge

Edward Winter

(1998, with updates)

knight

Illustration from Das leidenschaftliche Spiel by Gustav Schenk (Bremen, 1936)



How does the knight move? Or, rather, how can the knight’s move be described succinctly? Innumerable formulations have been proposed, but where is the ‘perfect’ definition? Readers are invited to try their hand, and for general guidance a sample of some of the old-timers’ efforts is offered.



C.N. 4693 mentioned that page 3 of Across the Board: The Mathematics of Chessboard Problems by John J. Watkins (Princeton and Oxford, 2004) offered a simple wording which may be better than any of those quoted above:



In C.N. 5096 Jon Crumiller (Princeton, NJ, USA) gave the following pre-nineteenth-century examples:

Our correspondent mentioned too that the description quoted above from Stratagems of Chess (1817) is a word-for-word copy from page 117 of Hoyle’s Games Improved (1800) and that a very similar text occurs on page 88 of R. Lambe’s The History of Chess (1764):

‘The Knights move obliquely, stepping upon every third square, including that which they quit; from black to white, and from white to black, over the heads of men, which none else do.’

We note a similar wording on page 20 of Chess Made Easy by J.A. Guthrie (London, 1922):

‘The Knights move obliquely upon every third square, Black to White and White to Black.’



In C.N. 5132 Pablo S. Domínguez (Madrid) pointed out Emanuel Lasker’s unusual explanation which appeared on pages 5-6 of Lasker’s Manual of Chess (New York, 1927), as well as in later editions of the book:

‘... the knight jumps in making the shortest move that is not a straight one.’

The corresponding text in the earlier German edition, Lehrbuch des Schachspiels, reads:

‘... der Springer macht einen Sprung, nämlich den kürzesten auf dem Schachbrett möglichen Zug, der nicht gerade ist.’

The English volume (page 10) also had this description of the knight’s move:

‘The shortest jump on the chess board is, namely, to take two squares (in the air) in a line or row and one square perpendicularly thereto.’



Another curiosity, on pages 25-26 of Learn Chess Fast! by S. Reshevsky and F. Reinfeld (various editions), is the presentation of the knight’s move in the captions to diagrams 50-53:

reshevsky reinfeld

reshevsky reinfeld

Have many other instructional works explained the knight’s move in this way, i.e. by reference to squares inaccessible to the queen?

(8431)

C.N. 8431 asked whether many instructional works had explained the knight’s move by reference to squares inaccessible to the queen, as did Learn Chess Fast! by S. Reshevsky and F. Reinfeld.

Trevor Moore (Baughurst, England) draws attention to Chess by C.H.O’D. Alexander (London, 1937), as well as the expanded, updated edition, Alexander on Chess (London, 1974). From pages 4-5 of both books:

‘Like the other pieces it [the knight] moves in a straight line, but one less clearly indicated on the board than those of the rook and bishop. The rook moves parallel to the edges of the board, the bishops diagonally and the knight in a direction bisecting the angle between the rook’s and bishop’s move. ... The knight’s move is complementary to that of the queen, as we may easily see in the following way. Place the queen on one of the 16 central squares of the board – it controls 16 of the 24 squares surrounding it. Now place a knight on the square instead – it controls precisely those eight squares not attacked by the queen. ... It is often inaccurately said that the knight “jumps” other pieces – actually, it simply moves between them.’

(8465)

A similar point about the knight was made on page 4 of Learn Chess: A New Way for All by C.H.O’D. Alexander and T.J. Beach (Oxford, 1963):

‘It is not obstructed by pieces of either colour, since moving across the two by three box it passes between them.’

(8502)



A further citation is FIDE’s definition of the knight’s move, which Sven Mühlenhaus (Düsseldorf, Germany) appreciates for its concision:

‘The knight may move to one of the squares nearest to that on which it stands but not on the same rank, file or diagonal.’

(8454)



‘The knights move in a letter L one square orthogonally in one direction and then two squares orthogonally at right angles to the first move, or two squares orthogonally in one direction and then one square at right angles to it.’

Source: Page 11 of the original (Aylesbury, 1976) edition of Discovering Chess by R.C. Bell (‘R.C. Bell MB FRCS’).

(8460)



From Robert John McCrary (Columbia, SC, USA):

‘The “American Chess Code”, published in 1897 and the same as the “British Chess Code” published shortly beforehand, contains on page 24 the earliest official definition of a knight’s move in a Code that I have seen. It states that a square is commanded by a knight ...

“... when that square and the square on which the knight stands are as near to each other as, without being of the same rank or file or diagonal, it is possible for two squares to be ...”

This appears to be an official definition that is essentially the same as saying that the knight moves to the nearest square that cannot be commanded by a queen.’

We add another explanation of the knight’s move, from page 19 of First Book of Chess by I.A. Horowitz and Fred Reinfeld (New York, 1952):

‘“The old one-two” is the phrase that aptly describes the knight’s move. Each knight move is a combination of one square and two squares:

(a) one square “North” or “South”; then two squares “East” or “West”.

(b) one square “East” or “West”; then two squares “North” or “South”.’

(8532)

From page 14 of An Invitation to Chess by Irving Chernev and Kenneth Harkness (New York, 1945):

‘The knight jumps over friendly or enemy pieces. It leaps one square (to the North, South, East or West) and lands to the right or to the left on a square of the opposite color to the one from which it started.’

The explanation on page 8 of Chess Self-Teacher by Al Horowitz (New York, 1961):

‘The knight has a peculiar move, best described as “to the nearest square of opposite color that is not adjacent”. He moves in the shape of an inverted L.’



‘The simplest way to consider the knight’s move is to imagine a three-square L-shape. The basic L-shape is achieved by moving the knight two squares in any direction and then one square to either side.

This L-shape can also be achieved by imagining the short side of the “L” being played first. Move the knight one square in any direction, and then two squares to either side.’

Source: page 31 of Chess for Rookies by Craig Pritchett (London, 2009).



Above there is a line from page 154 of Amusements in Chess by Charles Tomlinson (London, 1845): ‘The move of the knight consists of the shortest rook’s move and the shortest bishop’s move, both at once.’

A similar remark was on page 47, alongside a more complex explanation:

‘Geometrically, the knight’s leap is always the hypothenuse of a right-angle triangle, of which the base equals twice the perpendicular, the latter being equal to the side of one square.’

tomlinson

Tomlinson’s text was originally published on page 191 of the Saturday Magazine, 13 November 1841.

From page 29 of Amusements in Chess:

knight

(9576)

knight

Bruce Monson (Colorado Springs, CO, USA) has pointed out an article, ‘The Mysterious Knight Move’, on pages 30-33 of the February 2015 Mensa Bulletin, and we are grateful to the writer, Frank Camaratta (Huntsville, AL, USA), for permission to reproduce extracts:

knight

Diagram 3 showed how the ‘primordial bishop, or al-fil, ... has the ability to jump one square diagonally in any direction. It does not control the intervening square, nor can it be obstructed’, and Mr Camaratta then commented, in connection with Diagram 4 (showing a rook): ‘Logically then, there must have been, at least in the embryonic forms of chess, a piece that “jumped” like the bishop but horizontally and vertically rather than diagonally.’

knight
knight

(9625)

Further to mention of the letter L in explanations of the knight’s move, it is worth adding that Russian-language sources often refer to the Г, as in the word Гамбит. A passage from page 7 of The Life and Games of Mikhail Tal (New York, 1976):

knight

The text is on page 17 of the London, 1997 edition.

(9631)

From page 27 of “Among These Mates” by Chielamangus (Sydney, 1939):

‘The knight’s move is very puzzling. It moves there and then there, or the same only backwards or sideways, and really all round.’

In the description of knights on page 11 of Easy Guide to the Game of Chess by Charles Check (London, 1818):

‘They move in a peculiar way in any direction; leaping from the square in which they stand, over either of the contiguous squares, into one of the two that have a corner in contact with one of the farther corners of the square over which they leap.’

From page 7 of Practical Chess Grammar by W.S. Kenny (London, 1817):

‘The knight has a peculiar way of moving, entirely different from any other piece on the board, in a direction partly diagonal and partly straight. His march is oblique, upon every third square, including that which he stood on, from black to white, and from white to black, over the heads of the men, which no other is allowed to do.’




knight

Source: Chess Amateur, July 1912, page 673.

(10216)



Latest update: 3 December 2016.

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