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Carrés magiques

 

Débutants

Carrés

magiques

Carré magique 4 x 4

 

Glossaire

Carrés

magiques

 

 

INDEX

 

Carrés magiques

   Ordres

   Constructions

 

Magie

Jeux de grilles

Jeux et énigmes

Carré 4 x 4

Décompte

Formules

Propriétés

Dürer – Mélancolie 

Subirach – Sagrada Familia

Autres

Romain LV

 

Sommaire de cette page

>>> Caractéristiques du carré pseudo-magique

>>> Le carré magique

>>> Configurations basiques et autres

>>> 101 configurations magiques

 

 

 

Sagrada Familia – BARCELONE

Carré pseudo-magique 4 x 4

  

La façade de la basilique de Barcelone – La Sagrada Familia d'Antoni Gaudi – a été décorée par Josep Maria Subirachs (1987).

Elle présente douze groupes de sculptures dont le baiser de Judas (ou la trahison de Judas) flanqué d'un carré magique.

Subirachs avait demandé qu'il puisse utiliser son style personnel, afin de ne pas créer de confusion avec l'œuvre originale de Gaudí.

 

 

Caractéristiques du carré pseudo-magique

 

Contrairement à un carré magique conventionnel, les nombres utilisés ne sont pas les nombres de 1 à 16, mais les nombres 10 et 14 sont doublés et les nombres 12 et 16 sont absents.

Ce carré est cependant très intéressant: il contient 101 combinaisons de somme magique.

 

La somme (lignes, colonnes et diagonales) est 33 et non 34.

Ce nombre représente l'âge du Christ à sa mort (fait non-scientifiquement confirmé).

Il est formé de "3", symbole de la trinité divine dans le Christianisme.

 

Le carré magique

 

Ce carré est bien magique de par ses sommes: 33

Il n'est pas orthodoxe quant aux nombres utilisés: {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 10, 11, 13, 14, 14, 15}

 

Il existe 1 680 manières de choisir quatre nombres parmi cette liste; il y en a 88 avec la somme 33 dont 53 sans redondance.

 

 

 

Configurations

 

Huit carrés réguliers

Quelques carrés présentant des configurations remarquables:

*      H et V pour sommes horizontales et verticales;

*      CS: Carrés des sommets

*      D: Diagonales;

*      CC: Avec carré au centre;

*      D2: Diagonales espacées de 2;

*      C2: Carrés avec espace de 2; et

*      B2: Bandes de deux.

 

 

Sommes 33

Les 30 sommes utilisées sont présentées dans le tableau du dessous à gauche avec repère du type de configuration.

Les autres sommes égales à 33 sont listées dans le tableau de droite.

 

 

 

Liste des 88 sommes avec les redondances (du fait des double 10 et double 14)

[1, 3, 14, 15], [1, 3, 14, 15], [1, 4, 13, 15], [1, 4, 14, 14], [1, 5, 13, 14], [1, 5, 13, 14], [1, 6, 11, 15], [1, 7, 10, 15], [1, 7, 10, 15], [1, 7, 11, 14], [1, 7, 11, 14], [1, 8, 9, 15], [1, 8, 10, 14], [1, 8, 10, 14], [1, 8, 10, 14], [1, 8, 10, 14], [1, 8, 11, 13], [1, 9, 10, 13], [1, 9, 10, 13], [2, 3, 13, 15], [2, 3, 14, 14], [2, 4, 13, 14], [2, 4, 13, 14], [2, 5, 11, 15], [2, 6, 10, 15], [2, 6, 10, 15], [2, 6, 11, 14], [2, 6, 11, 14], [2, 7, 9, 15], [2, 7, 10, 14], [2, 7, 10, 14], [2, 7, 10, 14], [2, 7, 10, 14], [2, 7, 11, 13], [2, 8, 9, 14], [2, 8, 9, 14], [2, 8, 10, 13], [2, 8, 10, 13], [2, 10, 10, 11], [3, 4, 11, 15], [3, 5, 10, 15], [3, 5, 10, 15], [3, 5, 11, 14], [3, 5, 11, 14], [3, 6, 9, 15], [3, 6, 10, 14], [3, 6, 10, 14], [3, 6, 10, 14], [3, 6, 10, 14], [3, 6, 11, 13], [3, 7, 8, 15], [3, 7, 9, 14], [3, 7, 9, 14], [3, 7, 10, 13], [3, 7, 10, 13], [3, 8, 9, 13], [3, 9, 10, 11], [3, 9, 10, 11], [4, 5, 9, 15], [4, 5, 10, 14], [4, 5, 10, 14], [4, 5, 10, 14], [4, 5, 10, 14], [4, 5, 11, 13], [4, 6, 8, 15], [4, 6, 9, 14], [4, 6, 9, 14], [4, 6, 10, 13], [4, 6, 10, 13], [4, 7, 8, 14], [4, 7, 8, 14], [4, 7, 9, 13], [4, 8, 10, 11], [4, 8, 10, 11], [4, 9, 10, 10], [5, 6, 7, 15], [5, 6, 8, 14], [5, 6, 8, 14], [5, 6, 9, 13], [5, 7, 8, 13], [5, 7, 10, 11], [5, 7, 10, 11], [5, 8, 9, 11], [5, 8, 10, 10], [6, 7, 9, 11], [6, 7, 10, 10], [6, 8, 9, 10], [6, 8, 9, 10]

 

 

 

101 configurations magiques

 

Il existe 101 configurations magiques comme les huit exposées ci-dessus.

La liste complète est donnée ci-dessous.

Les 18 premiers (bleu sur la liste) sont illustrés en carré colorés.

 

Les 18 configurations avec [1, 3, 14, 15] en jaune

 

 

Liste des 101 configurations magiques

 

[1, 3, 14, 15], [2, 4, 13, 14], [5, 7, 10, 11], [6, 8, 9, 10]

[1, 3, 14, 15], [2, 4, 13, 14], [5, 8, 9, 11], [6, 7, 10, 10]

[1, 3, 14, 15], [2, 4, 13, 14], [5, 8, 10, 10], [6, 7, 9, 11]

[1, 3, 14, 15], [2, 6, 11, 14], [4, 7, 9, 13], [5, 8, 10, 10]

[1, 3, 14, 15], [2, 6, 11, 14], [4, 9, 10, 10], [5, 7, 8, 13]

[1, 3, 14, 15], [2, 7, 10, 14], [4, 5, 11, 13], [6, 8, 9, 10]

[1, 3, 14, 15], [2, 7, 10, 14], [4, 6, 10, 13], [5, 8, 9, 11]

[1, 3, 14, 15], [2, 7, 10, 14], [4, 8, 10, 11], [5, 6, 9, 13]

[1, 3, 14, 15], [2, 7, 11, 13], [4, 5, 10, 14], [6, 8, 9, 10]

[1, 3, 14, 15], [2, 7, 11, 13], [4, 6, 9, 14], [5, 8, 10, 10]

[1, 3, 14, 15], [2, 7, 11, 13], [4, 9, 10, 10], [5, 6, 8, 14]

[1, 3, 14, 15], [2, 8, 9, 14], [4, 5, 11, 13], [6, 7, 10, 10]

[1, 3, 14, 15], [2, 8, 9, 14], [4, 6, 10, 13], [5, 7, 10, 11]

[1, 3, 14, 15], [2, 8, 10, 13], [4, 5, 10, 14], [6, 7, 9, 11]

[1, 3, 14, 15], [2, 8, 10, 13], [4, 6, 9, 14], [5, 7, 10, 11]

[1, 3, 14, 15], [2, 10, 10, 11], [4, 6, 9, 14], [5, 7, 8, 13]

[1, 3, 14, 15], [2, 10, 10, 11], [4, 7, 8, 14], [5, 6, 9, 13]

[1, 3, 14, 15], [2, 10, 10, 11], [4, 7, 9, 13], [5, 6, 8, 14]

[1, 4, 13, 15], [2, 3, 14, 14], [5, 7, 10, 11], [6, 8, 9, 10]

[1, 4, 13, 15], [2, 3, 14, 14], [5, 8, 9, 11], [6, 7, 10, 10]

[1, 4, 13, 15], [2, 3, 14, 14], [5, 8, 10, 10], [6, 7, 9, 11]

[1, 4, 13, 15], [2, 6, 11, 14], [3, 7, 9, 14], [5, 8, 10, 10]

[1, 4, 13, 15], [2, 7, 10, 14], [3, 5, 11, 14], [6, 8, 9, 10]

[1, 4, 13, 15], [2, 7, 10, 14], [3, 6, 10, 14], [5, 8, 9, 11]

[1, 4, 13, 15], [2, 7, 10, 14], [3, 9, 10, 11], [5, 6, 8, 14]

[1, 4, 13, 15], [2, 8, 9, 14], [3, 5, 11, 14], [6, 7, 10, 10]

[1, 4, 13, 15], [2, 8, 9, 14], [3, 6, 10, 14], [5, 7, 10, 11]

[1, 4, 13, 15], [2, 10, 10, 11], [3, 7, 9, 14], [5, 6, 8, 14]

[1, 4, 14, 14], [2, 3, 13, 15], [5, 7, 10, 11], [6, 8, 9, 10]

[1, 4, 14, 14], [2, 3, 13, 15], [5, 8, 9, 11], [6, 7, 10, 10]

[1, 4, 14, 14], [2, 3, 13, 15], [5, 8, 10, 10], [6, 7, 9, 11]

[1, 4, 14, 14], [2, 5, 11, 15], [3, 7, 10, 13], [6, 8, 9, 10]

[1, 4, 14, 14], [2, 5, 11, 15], [3, 8, 9, 13], [6, 7, 10, 10]

[1, 4, 14, 14], [2, 6, 10, 15], [3, 7, 10, 13], [5, 8, 9, 11]

[1, 4, 14, 14], [2, 6, 10, 15], [3, 8, 9, 13], [5, 7, 10, 11]

[1, 4, 14, 14], [2, 6, 10, 15], [3, 9, 10, 11], [5, 7, 8, 13]

[1, 4, 14, 14], [2, 7, 9, 15], [3, 6, 11, 13], [5, 8, 10, 10]

[1, 4, 14, 14], [2, 7, 11, 13], [3, 5, 10, 15], [6, 8, 9, 10]

[1, 4, 14, 14], [2, 7, 11, 13], [3, 6, 9, 15], [5, 8, 10, 10]

[1, 4, 14, 14], [2, 8, 10, 13], [3, 5, 10, 15], [6, 7, 9, 11]

[1, 4, 14, 14], [2, 8, 10, 13], [3, 6, 9, 15], [5, 7, 10, 11]

[1, 4, 14, 14], [2, 8, 10, 13], [3, 9, 10, 11], [5, 6, 7, 15]

[1, 4, 14, 14], [2, 10, 10, 11], [3, 6, 9, 15], [5, 7, 8, 13]

[1, 4, 14, 14], [2, 10, 10, 11], [3, 7, 8, 15], [5, 6, 9, 13]

[1, 4, 14, 14], [2, 10, 10, 11], [3, 8, 9, 13], [5, 6, 7, 15]

[1, 5, 13, 14], [2, 6, 10, 15], [3, 7, 9, 14], [4, 8, 10, 11]

[1, 5, 13, 14], [2, 6, 10, 15], [3, 9, 10, 11], [4, 7, 8, 14]

[1, 5, 13, 14], [2, 6, 11, 14], [3, 7, 8, 15], [4, 9, 10, 10]

[1, 5, 13, 14], [2, 7, 9, 15], [3, 6, 10, 14], [4, 8, 10, 11]

 

[1, 5, 13, 14], [2, 7, 10, 14], [3, 4, 11, 15], [6, 8, 9, 10]

[1, 5, 13, 14], [2, 7, 10, 14], [3, 6, 9, 15], [4, 8, 10, 11]

[1, 5, 13, 14], [2, 7, 10, 14], [3, 9, 10, 11], [4, 6, 8, 15]

[1, 5, 13, 14], [2, 8, 9, 14], [3, 4, 11, 15], [6, 7, 10, 10]

[1, 5, 13, 14], [2, 10, 10, 11], [3, 6, 9, 15], [4, 7, 8, 14]

[1, 5, 13, 14], [2, 10, 10, 11], [3, 7, 8, 15], [4, 6, 9, 14]

[1, 5, 13, 14], [2, 10, 10, 11], [3, 7, 9, 14], [4, 6, 8, 15]

[1, 6, 11, 15], [2, 3, 14, 14], [4, 7, 9, 13], [5, 8, 10, 10]

[1, 6, 11, 15], [2, 3, 14, 14], [4, 9, 10, 10], [5, 7, 8, 13]

[1, 6, 11, 15], [2, 4, 13, 14], [3, 7, 9, 14], [5, 8, 10, 10]

[1, 6, 11, 15], [2, 7, 10, 14], [3, 8, 9, 13], [4, 5, 10, 14]

[1, 6, 11, 15], [2, 8, 9, 14], [3, 7, 10, 13], [4, 5, 10, 14]

[1, 6, 11, 15], [2, 8, 10, 13], [3, 7, 9, 14], [4, 5, 10, 14]

[1, 7, 10, 15], [2, 3, 14, 14], [4, 5, 11, 13], [6, 8, 9, 10]

[1, 7, 10, 15], [2, 3, 14, 14], [4, 6, 10, 13], [5, 8, 9, 11]

[1, 7, 10, 15], [2, 3, 14, 14], [4, 8, 10, 11], [5, 6, 9, 13]

[1, 7, 10, 15], [2, 4, 13, 14], [3, 5, 11, 14], [6, 8, 9, 10]

[1, 7, 10, 15], [2, 4, 13, 14], [3, 6, 10, 14], [5, 8, 9, 11]

[1, 7, 10, 15], [2, 4, 13, 14], [3, 9, 10, 11], [5, 6, 8, 14]

[1, 7, 10, 15], [2, 6, 11, 14], [3, 8, 9, 13], [4, 5, 10, 14]

[1, 7, 10, 15], [2, 8, 9, 14], [3, 5, 11, 14], [4, 6, 10, 13]

[1, 7, 10, 15], [2, 8, 9, 14], [3, 6, 10, 14], [4, 5, 11, 13]

[1, 7, 10, 15], [2, 8, 9, 14], [3, 6, 11, 13], [4, 5, 10, 14]

[1, 7, 10, 15], [2, 8, 10, 13], [3, 5, 11, 14], [4, 6, 9, 14]

[1, 7, 11, 14], [2, 3, 13, 15], [4, 5, 10, 14], [6, 8, 9, 10]

[1, 7, 11, 14], [2, 3, 13, 15], [4, 6, 9, 14], [5, 8, 10, 10]

[1, 7, 11, 14], [2, 3, 13, 15], [4, 9, 10, 10], [5, 6, 8, 14]

[1, 7, 11, 14], [2, 4, 13, 14], [3, 5, 10, 15], [6, 8, 9, 10]

[1, 7, 11, 14], [2, 4, 13, 14], [3, 6, 9, 15], [5, 8, 10, 10]

[1, 7, 11, 14], [2, 6, 10, 15], [3, 8, 9, 13], [4, 5, 10, 14]

[1, 7, 11, 14], [2, 8, 9, 14], [3, 5, 10, 15], [4, 6, 10, 13]

[1, 7, 11, 14], [2, 8, 10, 13], [3, 5, 10, 15], [4, 6, 9, 14]

[1, 7, 11, 14], [2, 8, 10, 13], [3, 6, 9, 15], [4, 5, 10, 14]

[1, 7, 11, 14], [2, 8, 10, 13], [3, 6, 10, 14], [4, 5, 9, 15]

[1, 8, 9, 15], [2, 3, 14, 14], [4, 5, 11, 13], [6, 7, 10, 10]

[1, 8, 9, 15], [2, 3, 14, 14], [4, 6, 10, 13], [5, 7, 10, 11]

[1, 8, 9, 15], [2, 4, 13, 14], [3, 5, 11, 14], [6, 7, 10, 10]

[1, 8, 9, 15], [2, 4, 13, 14], [3, 6, 10, 14], [5, 7, 10, 11]

[1, 8, 9, 15], [2, 6, 11, 14], [3, 7, 10, 13], [4, 5, 10, 14]

[1, 8, 9, 15], [2, 7, 10, 14], [3, 5, 11, 14], [4, 6, 10, 13]

[1, 8, 9, 15], [2, 7, 10, 14], [3, 6, 10, 14], [4, 5, 11, 13]

[1, 8, 9, 15], [2, 7, 10, 14], [3, 6, 11, 13], [4, 5, 10, 14]

[1, 8, 9, 15], [2, 7, 11, 13], [3, 6, 10, 14], [4, 5, 10, 14]

[1, 8, 10, 14], [2, 3, 13, 15], [4, 5, 10, 14], [6, 7, 9, 11]

[1, 8, 10, 14], [2, 3, 13, 15], [4, 6, 9, 14], [5, 7, 10, 11]

[1, 8, 10, 14], [2, 4, 13, 14], [3, 5, 10, 15], [6, 7, 9, 11]

[1, 8, 10, 14], [2, 4, 13, 14], [3, 6, 9, 15], [5, 7, 10, 11]

[1, 8, 10, 14], [2, 4, 13, 14], [3, 9, 10, 11], [5, 6, 7, 15]

[1, 8, 10, 14], [2, 5, 11, 15], [3, 6, 10, 14], [4, 7, 9, 13]

[1, 8, 10, 14], [2, 5, 11, 15], [3, 7, 9, 14], [4, 6, 10, 13]

[1, 8, 10, 14], [2, 5, 11, 15], [3, 7, 10, 13], [4, 6, 9, 14]

[1, 8, 10, 14], [2, 6, 10, 15], [3, 5, 11, 14], [4, 7, 9, 13]

 

Les deux dernières configurations

 

 

 

Suite

*    Carré diabolique de Dürer

*    Carré de la Sainte Famille

*    Exemple de calcul sur un carré 4 x 4

*    Carré 4 x 4  en cercles

*    Carré 5 x 5

*    Carrés magiquesIndex

Voir

*      Carrés – les nombres

*      Carrés en géométrie

*      Carrés mystérieux

*      Dominos magiques

*      Géométrie

*      Humour

*      Jeux

*      Jeux  de  chiffres

*      Nombres consécutifs

*      Nombres magiques - Index

*      Pannumérique

*      Rubriques débutants

*      Sudoku

*    Propriétés du carré magique

Diconombre

*    Nombre 3 / Nombre 15 / Nombre 34

Sites

*      Liens vers les sites carrés magiques

*    Order 4 Magic Squares – Harvey Heinz – Plus que complet, y compris la liste des 880 carrés magiques.

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