VIII.

MAGIC SQUARES THAT INVOLVE THE MOVE OF THE CHESS-KNIGHT.

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.