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# 15 Slide Puzzle • Le Taquin • Il Gioco del 15

 • 15 Puzzle • History • Il Gioco del 15 • Le Taquin

An Old Fashioned Game still in Vogue
15 Slide Puzzle: il gioco del 15 (it), taquin (fr), juego del 15 (sp), 14/15-Puzzle (ger), schuifpuzzel (du), 15パズル (jap), Пятнашки (ru), משחק ה-15 (he).

15 Puzzle
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 The History of 15 Puzzle
 It is not clear when the first slide puzzle was invented (or made). But it is a known fact that in 1878 Sam Loyd, America's puzzle-expert, "drove the whole world crazy" with his newly "discovered" 14-15 puzzle (though some accounts state that, other authorities dispute this fact). Sam Loyd claimed from 1891 until his death in 1911 that he invented the puzzle. Actually, he had nothing to do with the invention or popularity of the game... This was a variation on the "15 Puzzle" which was made and sold by the Embossing Company from New York about 10 years earlier!     The "15 Puzzle" consists of 15 squares numbered from 1 to 15 which are placed in a 4x4 box leaving one position out of the 16 empty. The goal is to reposition the squares from a given arbitrary starting arrangement by sliding them one at a time into the configuration shown above (for some initial arrangements, this rearrangement is possible, but for others, it is not).    It was not surprising that Sam Loyd drove the whole world crazy by his variation of the puzzle of 15. The problem that he formulated was impossible to solve. When you bought Loyd's 14-15 puzzle the empty square was positioned bottom right. The pieces were numbered in order from left to right and from top to bottom; only the pieces numbered 14 and 15 were reversed. You should re-order the pieces so all the pieces are in the correct position and the empty place should be positioned bottom right again. A slide puzzle with square pieces can only be solved when the number of exchanges necessary to solve the puzzle is even.    A nice variation of the basic slide puzzle is a slide puzzle with 15 pieces numbered form 0 (empty space) to 15 with the instruction to slide the pieces so that the sum of all rows and the sum of all columns and the sum of the diagonals equals 30. Such an ordering is called a magic square (see example opposite). Il gioco del 15 è un telaietto di 4 caselle x4 all'interno del quale si muovono tessere scorrevoli numerate. Lo scopo è quello di mettere in ordine crescente i numeri dall'1 al 15. Questo gioco, secondo Edouard Lucas, è stato inventato da un sordomuto nel 1870, e si è rapidamente diffuso negli Stati Uniti e nel mondo intero.    Le applicazioni concrete che risultano dall'abilità nel risolvere questi generi di puzzle sono: l'ottimizazione dei problemi di magazzinaggio, parcheggio, circolazione stradale, e così via... Le fameux jeu du 15 ou Taquin ou Pousse-Pousse, est une petite boîte ayant 4x4 cases occupées par 15 pièces carrées numérotées pouvant glisser et occuper un espace laissé vide. Le but du jeu étant de remettre en place les nombres de 1 à 15 en ordre croissant. Ce jeu a été inventé, selon Edouard Lucas, par un sourd-muet en 1870, et bénéficia d'une diffusion mondiale incroyable.    Les applications concretes de la maîtrise du Taquin sont l'optimisation des problèmes de magasinage, parking, circulation, etc...

ARCHIMEDES
 ARCHIMEDES is an interactive quarterly review devoted to entertaining and involving its readers with puzzles, recreational mathematics and visual creativity. ARCHIMEDES contains high-quality images for use as resource. Each issue offers original large illustrations or patterns the readers may reproduce or photocopy for classroom activities, workshops or just for fun...