An illustrated introduction to Caïssan squares: the magic of chess

  • George P. H. Styan McGill University, Department of Mathematics and Statistics, Burnside Hall 1005, 805 ouest rue Sherbrooke, Montréal (Québec), Canada H3A 0B9
Keywords: alternate-couplets property, Pavle Bidev, Caïssan beauties, Caïssan magic squares, Cavendish, CSP2-magic, CSP3-magic, EP magic matrices, Equal Projectors, 4-pac magic squares, 4-ply magic squares, Andrew Hollingworth Frost, involution-associated, involutory matrix, Henry Jones, William Jones, Henry James Kesson, keyed magic matrices, knight-Nasik, magic key, most-perfect magic squares, Nasik squares, pandiagonal magic square, philatelic items, Charles Planck, postage stamps, Ursus

Abstract

We study various properties of n × n Caïssan magic squares. Following the seminal 1881 article by "Ursus" [Henry James Kesson (b. c. 1844)] in The Queen, we define a magic square to be Caïssan whenever it is pandiagonal and knight-Nasik so that all paths of length n by a chess bishop are magic (pandiagonal, Nasik, CSP1-magic) and by a (regular) chess knight are magic (CSP2-magic). We also study Caïssan beauties, which are pandiagonal and both CSP2- and CSP3-magic; a CSP3-path is by a special knight that leaps over 3 instead of 2 squares. Our paper ends with a bibliography of over 100 items (many with hyperlinks) listed chronologically from the 14th century onwards. We give special attention to items by (or connected with) "Ursus": Henry James Kesson (b. c. 1844), Andrew Hollingworth Frost (1819–1907), Charles Planck (1856–1935), and Pavle Bidev (1912–1988). We have tried to illustrate our findings as much as possible, and whenever feasible, with images of postage stamps or other philatelic items.

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Published
2020-09-25
Section
Articles