What one of our readers does not know the problems contained in the
recreation columns of our magazines, the requirements of which are to
compose into a verse 8 times 8 quadratically arranged syllables, of
which every two successive syllables stand on spots so situated with
respect to each other that a chess-knight can move from the one to the
other? If we replace in such an arrangement the 64 successive syllables
by the 64 numbers from 1 to 64, we shall obtain a knight-problem made
up of numbers. Methods also exist indeed for the construction of
such dispositions of numbers, which then form the foundation of the
construction of the problems in the newspapers. But the majority of
knight-problems of this class are the outcome of experiment rather than
the product of methodical creation. If however it is a severe test of
patience to form a knight-problem by experiment, it stands to reason that
it is a still severer trial to effect at the same time the additional
result that the 64 numbers which form the knight-problem shall also form
a magic square.
This trial of endurance was undertaken several decades ago, by a
pensioned Moravian officer named Wenzelides, who was spending the last
days of his life in the country. After a series of trials which lasted
years he finally succeeded in so inscribing in the 64 squares of the
chess-board the numbers from 1 to 64 that successive numbers, as well
also as the numbers 64 and 1, were always removed from one another in
distance and direction by the move of a knight, and that in addition
thereto the summation of the horizontal and the vertical rows always
gave the same sum 260. Ultimately he discovered several squares of this
description, which were published in the _Berlin Chess Journal_. One of
these is here appended:
[Illustration: Fig. 30.
+--+--+--+--+--+--+--+--+
|47|10|23|64|49| 2|59| 6|
+--+--+--+--+--+--+--+--+
|22|63|48| 9|60| 5|50| 3|
+--+--+--+--+--+--+--+--+
|11|46|61|24| 1|52| 7|58|
+--+--+--+--+--+--+--+--+
|62|21|12|45| 8|57| 4|51|
+--+--+--+--+--+--+--+--+
|19|36|25|40|13|44|53|30|
+--+--+--+--+--+--+--+--+
|26|39|20|33|56|29|14|43|
+--+--+--+--+--+--+--+--+
|35|18|37|28|41|16|31|54|
+--+--+--+--+--+--+--+--+
|38|27|34|17|32|55|42|15|
+--+--+--+--+--+--+--+--+
]
The move of the knight and the equality of the summation of the
horizontal and vertical rows, therefore, are the facts to be noted here.
The diagonal rows do _not_ give the sum 260. Perhaps some one among our
readers who possesses the time and patience will be tempted to outdo
Wenzelides, and to devise a numeral knight-problem of this kind which
will give 260 not only in the horizontal and vertical but also in the two
diagonal rows.