Birthday Magic Square
How to Construct a Forcing Matrix History: The forcing matrix concept was first given magical application by Walter Gibson in 1938 in a strictly informational description. The actual forcing modification was put into print by Maurice Kraitchik in 1942. Other notables who subsequently worked with it include Mel Stover, Stewart James, Martin Gardner, Howard Lyons, Leslie May, Sam Dalal, Paul Hallas, Max Maven, and Richard Busch. The forcing matrix does not have to be a grid of numbers (check out the elegant Quintasense in T.A. Waters’ Mind, Myth and Magick, p. 279), but that is perhaps the most “open” way of doing it. To try it out, circle any number, and then cross out the remaining numbers in the same row (horizontally) and column (vertically). Then circle another number (one not already eliminated), and again strike out the numbers above, below, to the left, and to the right of same. Repeat until all numbers are either circled (there will eventually be five) or crossed out. Add the chosen (circled) numbers together. Now concentrate ... I sense that the total will be ... wait a second ... fifty-seven! There are more deceptive approaches than the above method of choosing the numbers. Max Maven suggested the use of coloured pencils (for a 5x5 square, five colours are needed; draw a differently-coloured line through each column; repeat for the rows; add the numbers where like colours intersect). I have often used the following presentation: pick an interesting word with the same number of (different) letters as the rank of the matrix (say “MAGIC” for the above); write this word across the top, a letter over each column; have the participant rearrange the letters in any order desired, and write them down the left side, a letter beside each row; circle the numbers at the intersection points of matching letters. These alternative presentations avoid the appearance of a diminishing (and thus limited) choice of numbers, suggesting a force. Which, in fact, it is. It’s best if you actually take the trouble to try this for yourself, before reading on to learn how it works. The result is quite elegant and surprising, even to those with some mathematical sophistication.
Grogono Magic Squares
Magic square links
This illustrated treatise on Magic Squares covers the history of Magic Squares, information about the general classes of Magic Squares, various formulae for creating Magic Squares, detailed analyses of 3 x 3, 4 x 4 and 5 x 5 Magic Squares, variations on Magic Squares, Magic Square routines, puzzles and presentations, including \"one novel contribution by the author which combines origami (the Crossed Box Pleat) with a Magic Square, The Origami Magic Square\" (Eddie Dawes, M.I.M.C., in The Magic Circular), as well as references to approximately 40 other works on Magic Squares and mnemonics and over 40 pages of detailed Appendices. Note that many of the magical routines are not explained, since the secrets are not mine to reveal, although the book does cross-reference all of the necessary sources. Comments from reviews by other magicians and mathematicians include: \"... the definitive work on Magic Squares for years to come\" (Joe Riding, M.I.M.C.) \"... a significant addition to the literature of magic squares\" (Eddie Dawes, M.I.M.C., in The Magic Circular) \"... a splendid piece of work\" (Alan Shaxon, M.I.M.C.) \"I wish a book like this would have been available to me a long time ago\" (Jules Lenier) \"... an excellent reference book ...\" (Michael Close in Magic) \"... I can honestly say that I have never seen such a thorough treatise on magic squares anywhere ...\" (Andrew Jeffrey, Head of Maths, St Aubyns School, Rottingdean)