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[]
[null,null,null,"Solutions pour la 2ème question du problème 611.13 de la pesée de 12 billes "]
[]
["Les billes et la balance."]
[]
[null,"On dispose de 12 billes indiscernables à l’œil (c’est-à-dire de même apparence) dont une est un tout petit peu plus légère que les autres."]
[null,"On dispose aussi d’une balance de précision, juste et fidèle, suffisamment sensible pour accuser la différence de masse de la bille la plus légère."]
[null,"Comment feriez-vous pour déterminer (en trois pesées seulement) la bille qui est la plus légère ?"]
[null,"Même problème, mais on ne sait pas si la bille différente des onze autres est plus lourde ou plus légère. (il est possible de déterminer les trois pesées sans connaitre les résultats de ces pesées) "]
[]
["La première question "]
[]
[null,"La première question est relativement simple. Il s'agit d'une dichotomie. (4 billes par plateau pour la 1ère pesée, puis 2 billes pour la 2ème pesée et 1 bille pour la dernière pesée)"]
[]
["La deuxième question "]
[]
[null,"La deuxième question est soluble par le fait qu'on a 3 états de balance et 3 pesées ; 33 =27, pour résoudre 24 possibilités (12 billes, dont l'une est soit légère, soit lourde)."]
[null,"On fera donc 3 pesées de 4 billes par plateau. Le problème est de savoir répartir les billes pour bien isoler chacune des 24 possibilités."]
[]
[null,"Afin de limiter les solutions doubles, la première pesée est fixée à :",null,null,null,null,null,null,null,null,"abcd","sur le plateau de gauche, et,",null,null,null,"efgh","sur le plateau de droite"]
[]
["La feuille \"Anal\", analyse des solutions"]
[]
[null,"Cette feuille permet de vérifier la validité d'une solution et de voir les interactions entre les pesées de 4 billes par plateau."]
[null,"Ne pas hésiter à consulter les commentaires signalés par le fond rose clair, et visible par un simple survol de la souris."]
[]
[null,"Procédure de vérification de la validité"]
[null,null,"On passe en revue, l'effet sur l'indication de la balance pour chacune des trois pesées, suivant chacune des 24 hypothèses : bille a légère, bille a lourde, bille b légère … bille l lourde."]
[null,null,"Cet effet est codé en colonne AG. Le code est l'expression décimale de la réponse ternaire des trois pesées."]
[null,null,"Le but est de vérifier que chacun des codes n'est utilisé qu'une fois."]
[]
[null,"Analyse des interactions",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Cod",null,"p1","p2","p3",null,"1G","1D","2G","2D","3G","3D"]
[null,null,"Le code est le résultat de l'effet sur les trois pesées de la présence de 4 + 4 billes."]
[null,null,"Prenons l'exemple précis de la solution :",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,1,null,0,0,1,null,"","","","","","l"]
[null,null,"1G","abcd","1D","efgh","2G","ahid","2D","jkfc","3G","jbgh","3D","ldfk",null,null,null,null,2,null,0,1,-1,null,"","","","j","j",""]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,3,null,0,1,0,null,"","","i","","",""]
[null,null,"Si on choisit d'affecter la bille h au code 5, il faut que, du fait du code 1, -1, -1,",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,4,null,0,1,1,null,"","","","k","","k"]
[null,null,null,"cette bille g soit présente à chacune des trois pesées,",null,null,null,null,null,null,null,null,null,null,null,null,null,null,5,null,1,-1,-1,null,"","h","h","","h",""]
[null,null,null,"et, de plus, sur le même plateau des pesées 2 et 3, par exemple G, tandis qu'elle sera à droite pour la pesée 1.",null,null,null,null,null,null,null,null,null,null,null,null,null,null,6,null,1,-1,0,null,"c","","","c","",""]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,7,null,1,-1,1,null,"","","","","",""]
[null,null,"Il s'agit donc bien d'agencer, de répartir les codes entre les six plateaux de manière à avoir 4 codes par plateau.",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,8,null,1,0,-1,null,"","g","","","g",""]
[null,null,null,"C'est seulement après qu'on donnera un nom aux billes utilisées pour chaque code.",null,null,null,null,null,null,null,null,null,null,null,null,null,null,9,null,1,0,0,null,"","e","","","",""]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,10,null,1,0,1,null,"b","","","","b",""]
[null,null,"On voit déjà très bien que le nombre de possibilités d'arrangements des billes pour une configuration des codes est énorme.",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,11,null,1,1,-1,null,"d","","d","","","d"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,12,null,1,1,0,null,"a","","a","","",""]
[null,null,"C'est simplement factorielle de 12.",null,null,null,null,null,null,null,null,null,null,null,{"$f":"FACT(12)","v":479001600},null,null,null,13,null,1,1,1,null,"","f","","f","","f"]
[null,null,"Et si on fixe la 1ère pesée à \"abcd efgh\", les arrangements pour ijkl sont au nombre de ",null,null,null,null,null,null,null,null,null,null,null,{"$f":"FACT(4)","v":24}]
[]
["La feuille \"AffectCod\", affectation des codes aux plateaux"]
[]
[null,"Plutôt que codes on dira classes de répartitions des billes entre les trois pesées"]
[null,"Cette feuille permet deux choses :"]
[]
[null,null,1,"Rechercher une solution manuellement"]
[null,null,2,"Rechercher toutes les solutions"]
[null,"Le tableau de répartition des classes sur les 6 plateaux se remplit automatiquement en fonction des impératifs de la classe (connus en colonnes F à H) et de la version (-1 ou +1) choisie pour chaque classe."]
[]
[null,"Qu'est-ce que la version ?"]
[null,null,"Pour chaque code on a deux possibilités."]
[null,null,"Par exemple pour la classe 2 qui est \"0, 1, -1\", le plateau 1 n'est pas utilisé, tandis que pour les pesées 2 et 3 on utilise 2 plateaux différents."]
[null,null,"Le +1 de la pesée 2 ira sur le plateau de droite et le -1 de la pesée 3 ira sur le palteau gauche (ou vice versa)."]
[null,"Donc on a deux versions pour chaque classe."]
[null,null,"La deuxième version qui consisterait à mettre -1 en B10 va inverser les positions (G à D et D à G)."]
[null,"De plus on dispose de 13 classes pour 12 billes. Une des classes ne sera pas utilisée."]
[]
[null,"Recherche manuelle d'une solution"]
[null,null,"Garder à l'esprit qu'une des classes ne doit pas être utilisée. On mettra 0 (ou vide) en colonne B, ligne correspondant à la classe."]
[null,null,"Ensuite il faut tatonner entre les -1 et +1 de la colonne B de manière à arriver à avoir 4 classes pour chaque plateau. Le nom de la classe non utilisée fait aussi partie du choix."]
[null,null,null,"Il y a d'ailleurs certaines classes dont la présence est obligatoire. On ne trouvera pas de solutions si on ne l'utilise pas."]
[null,null,"Lorsque J25 indique la valeur 0, c'est qu'il n'y a plus aucun plateau dont le nombre de classes affectés est différent de quatre. Cela veut dire qu'on a trouvé une solution."]
[]
[null,"Recherche automatique de toutes les solutions"]
[null,null,"La macro \"Affect\" fait la même chose d'une manière systématique"]
[null,null,null,1,"Elle examine toutes les classes exprimées en décimal de 0 à 4095 qu'elle transforme en binaire -1 et +1 dans la colonne B (212 = 4096)."]
[null,null,null,2,"Elle choisit successivement une des 13 classes comme non utilisée"]
[null,null,"A chaque fois elle regarde le contenu de la cellule J25"]
[null,null,"Si J25 est égal à zéro, c'est une solution qu'elle enregitre dans les colonnes S à AH"]
[null,null,"Elle trouve 304 solutions, qui sont en fait symétriques deux à deux (plateaux G mis à D et vice versa). Donc il y a 152 solutions."]
[]
["Interprétation d'une des solutions"]
[]
[null,null,"Il n'y a pas de signification absolue des -1 ou +1 de la version de la classe ou de la réponse de la balance."]
[null,null,"Il faut interpréter au cas pas cas."]
[null,null,"Je prends par exemple une réponse égale à la classe \"x\". C’est-à-dire que les pesées 1 et 3 donnent l'équilibre. Il n'y a que la pesée 2 qui montre un déséquilibre."]
[null,null,null,"Si la bille qui correspond à cette classe est à gauche et que la balance penche à gauche, c'est qu'il s'agit d'une bille lourde."]
[null,null,null,"Bille à gauche et balance penche à droite, c'est une bille légère."]
[null,null,null,"Bille à droite et balance à gauche, c'est une bille légère."]
[null,null,null,"Bille à droite et penche à droite = bille lourde."]
[null,null,"S'il s'agit de la bille de la classe \"s\" seule la pesée 1 est en équilibre. Les pesées 2 et 3 vont dans le même sens. Les conclusions sont les mêmes."]
[null,null,"Exemple de la bille de la classe \"t\", c'est la pesée 3 qui est en équilibre et les pesées 1 et 2 sont en opposition. Je m'attache à une des pesées et je tire les mêmes conclusions."]

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[]
[null,null,"Exercice 611.13  -  Pesée de 12 billes  -  Vérif d'une solution",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"bille","qualité","Pesée 1","Pesée 2","Pesée 3",null,"Code",null,"Code","Nombre","C non ut",null,"bille","Code"]
[]
[null,"2G","adhi",null,"2D","cbjk",null,"3G","bghj",null,"3D","dfkl",null,null,null,"Nombre maxi même code",null,null,null,null,null,null,{"$f":"MAX(AJ5:AJ31)","v":1},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"2G","ahid",null,"2D","jkfc",null,"3G","jbgh",null,"3D","ldfk"]
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[null,"Pes n° 1 , gauche",null,null,null,"Pes n° 1 , droite",null,null,null,"Pes n° 2 , gauche",null,null,null,"Pes n° 2 , droite",null,null,null,"Pes n° 3 , gauche",null,null,null,"Pes n° 3 , droite",null,null,null,null,"a","+",{"$f":"IF(COUNTIF($B$7:$E$7,AA6)>0,-1,IF(COUNTIF($F$7:$I$7,AA6)>0,1,0))","v":-1},{"$f":"IF(COUNTIF($J$7:$M$7,AA6)>0,-1,IF(COUNTIF($N$7:$Q$7,AA6)>0,1,0))","v":-1},{"$f":"IF(COUNTIF($R$7:$U$7,AA6)>0,-1,IF(COUNTIF($V$7:$Y$7,AA6)>0,1,0))","v":0},null,{"$f":"9*AC6+3*AD6+AE6","v":-12},null,-12,{"$f":"COUNTIF($AG$5:$AG$28,AI6)","v":1},{"$f":"IF(AJ6=0,AI6,\"\")","v":""},null,"b",{"$f":"MAX(INDIRECT(CONCATENATE(\"AG\",2*ROW()-5,\":AG\",2*ROW()-4)))","v":7}]
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[null,"Code affecté à la bille",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"c","-",{"$f":"IF(COUNTIF($B$7:$E$7,AA9)>0,1,IF(COUNTIF($F$7:$I$7,AA9)>0,-1,0))","v":1},{"$f":"IF(COUNTIF($J$7:$M$7,AA9)>0,1,IF(COUNTIF($N$7:$Q$7,AA9)>0,-1,0))","v":-1},{"$f":"IF(COUNTIF($R$7:$U$7,AA9)>0,1,IF(COUNTIF($V$7:$Y$7,AA9)>0,-1,0))","v":0},null,6,null,-9,1,"",null,"e",9]
[null,{"$f":"INDIRECT(CONCATENATE(\"AN\",CODE(B7)-92))","v":12},{"$f":"INDIRECT(CONCATENATE(\"AN\",CODE(C7)-92))","v":7},6,11,9,10,8,5,12,11,5,3,6,7,2,4,7,8,5,2,11,10,4,1,null,"c","+",{"$f":"IF(COUNTIF($B$7:$E$7,AA10)>0,-1,IF(COUNTIF($F$7:$I$7,AA10)>0,1,0))","v":-1},{"$f":"IF(COUNTIF($J$7:$M$7,AA10)>0,-1,IF(COUNTIF($N$7:$Q$7,AA10)>0,1,0))","v":1},{"$f":"IF(COUNTIF($R$7:$U$7,AA10)>0,-1,IF(COUNTIF($V$7:$Y$7,AA10)>0,1,0))","v":0},null,-6,null,-8,1,"",null,"f",10]
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[null,null,null,"Les interactions dues à la présence de 4 billes par plateau",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"d","+",{"$f":"IF(COUNTIF($B$7:$E$7,AA12)>0,-1,IF(COUNTIF($F$7:$I$7,AA12)>0,1,0))","v":-1},{"$f":"IF(COUNTIF($J$7:$M$7,AA12)>0,-1,IF(COUNTIF($N$7:$Q$7,AA12)>0,1,0))","v":-1},{"$f":"IF(COUNTIF($R$7:$U$7,AA12)>0,-1,IF(COUNTIF($V$7:$Y$7,AA12)>0,1,0))","v":1},null,-11,null,-6,1,"",null,"h",5]
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[null,null,null,"Code",null,"Pesée 1","Pesée 2","Pesée 3",null,null,null,"Code",null,"Pesée 1","Pesée 2","Pesée 3",null,"Affectations pour",null,null,null,null,null,null,null,null,"e","+",{"$f":"IF(COUNTIF($B$7:$E$7,AA14)>0,-1,IF(COUNTIF($F$7:$I$7,AA14)>0,1,0))","v":1},{"$f":"IF(COUNTIF($J$7:$M$7,AA14)>0,-1,IF(COUNTIF($N$7:$Q$7,AA14)>0,1,0))","v":0},{"$f":"IF(COUNTIF($R$7:$U$7,AA14)>0,-1,IF(COUNTIF($V$7:$Y$7,AA14)>0,1,0))","v":0},null,9,null,-4,1,"",null,"j",2]
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[null,null,null,0,null,null,null,null,null,null,null,0,null,"Le code 0 ne peut être utilisé",null,null,null,null,null,null,null,null,null,null,null,null,"g","-",{"$f":"IF(COUNTIF($B$7:$E$7,AA17)>0,1,IF(COUNTIF($F$7:$I$7,AA17)>0,-1,0))","v":-1},{"$f":"IF(COUNTIF($J$7:$M$7,AA17)>0,1,IF(COUNTIF($N$7:$Q$7,AA17)>0,-1,0))","v":0},{"$f":"IF(COUNTIF($R$7:$U$7,AA17)>0,1,IF(COUNTIF($V$7:$Y$7,AA17)>0,-1,0))","v":1},null,-8,null,-1,1,""]
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[]
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[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,131,1857,"p","mrtu","noqy","movx","nqst","mnrw","osuv",null,"ABCD","EFGH","AFIJ","EGKC","AEBL","FKDI","x"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,132,1873,"n","mprt","oquy","movx","pqst","mruw","opsv",null,"ABCD","EFGH","AEIJ","BFKD","ACGL","EBKI"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,133,1876,"p","mrty","noqu","movx","nqst","mnru","osvw",null,"ABCD","EFGH","AFIJ","EGKC","AEBH","FKIL"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,134,1889,"o","mpru","nqty","mtvx","npqs","mnrw","psuv",null,"ABCD","EFGH","AGIJ","EBFK","AECL","BKDI"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,135,1890,"p","mruy","noqt","motv","nqsx","mnrw","osuv",null,"ABCD","EFGH","AFHI","EGJK","AEBL","FJCI"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,136,1897,"n","mpru","oqty","motx","pqsv","mrvw","opsu",null,"ABCD","EFGH","AEGI","BFJK","ACKL","EBJD"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,137,1900,"p","mruy","noqt","motx","nqsv","mnrv","osuw",null,"ABCD","EFGH","AFHI","EGJK","AEBK","FJCL"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,138,1906,"n","mpry","oqtu","motv","pqsx","mruw","opsv",null,"ABCD","EFGH","AEGI","BFJK","ACHL","EBJI"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,139,1908,"o","mpry","nqtu","mtvx","npqs","mnru","psvw",null,"ABCD","EFGH","AGIJ","EBFK","AECH","BKIL"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,140,1912,"m","npry","oqtu","notx","pqsv","ruvw","nops",null,"ABCD","EFGH","AEGI","BFJK","CHKL","AEBJ"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,141,1916,"n","mpry","oqtu","motx","pqsv","mruv","opsw",null,"ABCD","EFGH","AEGI","BFJK","ACHK","EBJL"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,142,1921,"o","mptu","nqry","msvx","npqt","mnsw","pruv",null,"ABCD","EFGH","AIJK","EBFC","AEIL","BGDJ"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,143,1922,"p","mtuy","noqr","mosv","nqtx","mnsw","oruv",null,"ABCD","EFGH","AFIJ","EGBK","AEIL","FHCJ"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,144,1929,"n","mptu","oqry","mosx","pqtv","msvw","opru",null,"ABCD","EFGH","AEIJ","BFCK","AIKL","EBGD"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,145,1932,"p","mtuy","noqr","mosx","nqtv","mnsv","oruw",null,"ABCD","EFGH","AFIJ","EGBK","AEIK","FHCL"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,146,1938,"n","mpty","oqru","mosv","pqtx","msuw","oprv",null,"ABCD","EFGH","AEIJ","BFCK","AIHL","EBGJ"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,147,1940,"o","mpty","nqru","msvx","npqt","mnsu","prvw",null,"ABCD","EFGH","AIJK","EBFC","AEIH","BGJL"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,148,1944,"m","npty","oqru","nosx","pqtv","suvw","nopr",null,"ABCD","EFGH","AEIJ","BFCK","IHKL","AEBG"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,149,1948,"n","mpty","oqru","mosx","pqtv","msuv","oprw",null,"ABCD","EFGH","AEIJ","BFCK","AIHK","EBGL"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,150,1954,"o","mpuy","nqrt","mstv","npqx","mnsw","pruv",null,"ABCD","EFGH","AIHJ","EBFK","AEIL","BGCJ"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,151,1962,"n","mpuy","oqrt","most","pqvx","msvw","opru",null,"ABCD","EFGH","AEIH","BFJK","AIJL","EBGC"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,152,1964,"o","mpuy","nqrt","mstx","npqv","mnsv","pruw",null,"ABCD","EFGH","AIHJ","EBFK","AEIK","BGCL"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,153,2131,"o","nqrt","mpuy","npqv","mstx","pruw","mnsv",null,"Solution symétrique de celle de la ligne : 160"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,154,2133,"n","oqrt","mpuy","pqvx","most","opru","msvw",null,"Solution symétrique de celle de la ligne : 159"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,155,2141,"o","nqrt","mpuy","npqx","mstv","pruv","mnsw",null,"Solution symétrique de celle de la ligne : 158"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,156,2147,"n","oqru","mpty","pqtv","mosx","oprw","msuv",null,"Solution symétrique de celle de la ligne : 157"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,157,2151,"m","oqru","npty","pqtv","nosx","nopr","suvw",null,"Solution symétrique de celle de la ligne : 156"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,158,2155,"o","nqru","mpty","npqt","msvx","prvw","mnsu",null,"Solution symétrique de celle de la ligne : 155"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,159,2157,"n","oqru","mpty","pqtx","mosv","oprv","msuw",null,"Solution symétrique de celle de la ligne : 154"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,160,2163,"p","noqr","mtuy","nqtv","mosx","oruw","mnsv",null,"Solution symétrique de celle de la ligne : 153"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,161,2166,"n","oqry","mptu","pqtv","mosx","opru","msvw",null,"Solution symétrique de celle de la ligne : 152"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,162,2173,"p","noqr","mtuy","nqtx","mosv","oruv","mnsw",null,"Solution symétrique de celle de la ligne : 151"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,163,2174,"o","nqry","mptu","npqt","msvx","pruv","mnsw",null,"Solution symétrique de celle de la ligne : 150"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,164,2179,"n","oqtu","mpry","pqsv","motx","opsw","mruv",null,"Solution symétrique de celle de la ligne : 149"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,165,2183,"m","oqtu","npry","pqsv","notx","nops","ruvw",null,"Solution symétrique de celle de la ligne : 148"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,166,2187,"o","nqtu","mpry","npqs","mtvx","psvw","mnru",null,"Solution symétrique de celle de la ligne : 147"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,167,2189,"n","oqtu","mpry","pqsx","motv","opsv","mruw",null,"Solution symétrique de celle de la ligne : 146"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,168,2195,"p","noqt","mruy","nqsv","motx","osuw","mnrv",null,"Solution symétrique de celle de la ligne : 145"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,169,2198,"n","oqty","mpru","pqsv","motx","opsu","mrvw",null,"Solution symétrique de celle de la ligne : 144"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,170,2205,"p","noqt","mruy","nqsx","motv","osuv","mnrw",null,"Solution symétrique de celle de la ligne : 143"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,171,2206,"o","nqty","mpru","npqs","mtvx","psuv","mnrw",null,"Solution symétrique de celle de la ligne : 142"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,172,2219,"p","noqu","mrty","nqst","movx","osvw","mnru",null,"Solution symétrique de celle de la ligne : 141"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,173,2222,"n","oquy","mprt","pqst","movx","opsv","mruw",null,"Solution symétrique de celle de la ligne : 140"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,174,2238,"p","noqy","mrtu","nqst","movx","osuv","mnrw",null,"Solution symétrique de celle de la ligne : 139"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,175,2241,"m","oqtu","npry","pqvx","nost","nopw","rsuv",null,"Solution symétrique de celle de la ligne : 138"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,176,2256,"n","oqty","mpru","pqvx","most","opuw","mrsv",null,"Solution symétrique de celle de la ligne : 137"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,177,2260,"m","oqty","npru","pqvx","nost","nopu","rsvw",null,"Solution symétrique de celle de la ligne : 136"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,178,2264,"o","nqty","mpru","npqx","mstv","puvw","mnrs",null,"Solution symétrique de celle de la ligne : 135"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,179,2274,"m","oquy","nprt","pqtv","nosx","nopw","rsuv",null,"Solution symétrique de celle de la ligne : 134"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,180,2280,"n","oquy","mprt","pqtx","mosv","opvw","mrsu",null,"Solution symétrique de celle de la ligne : 133"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,181,2284,"m","oquy","nprt","pqtx","nosv","nopv","rsuw",null,"Solution symétrique de celle de la ligne : 132"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,182,2296,"p","noqy","mrtu","nqtx","mosv","ouvw","mnrs",null,"Solution symétrique de celle de la ligne : 131"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,183,2307,"o","nrtu","mpqy","npsv","mqtx","prsw","mnuv",null,"Solution symétrique de celle de la ligne : 130"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,184,2309,"n","ortu","mpqy","psvx","moqt","oprs","muvw",null,"Solution symétrique de celle de la ligne : 129"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,185,2317,"o","nrtu","mpqy","npsx","mqtv","prsv","mnuw",null,"Solution symétrique de celle de la ligne : 128"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,186,2325,"p","nort","mquy","nsvx","moqt","orsu","mnvw",null,"Solution symétrique de celle de la ligne : 127"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,187,2326,"o","nrty","mpqu","npsv","mqtx","prsu","mnvw",null,"Solution symétrique de celle de la ligne : 126"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,188,2339,"p","noru","mqty","nstv","moqx","orsw","mnuv",null,"Solution symétrique de celle de la ligne : 125"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,189,2342,"n","oruy","mpqt","pstv","moqx","oprs","muvw",null,"Solution symétrique de celle de la ligne : 124"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,190,2349,"p","noru","mqty","nstx","moqv","orsv","mnuw",null,"Solution symétrique de celle de la ligne : 123"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,191,2350,"o","nruy","mpqt","npst","mqvx","prsv","mnuw",null,"Solution symétrique de celle de la ligne : 122"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,192,2358,"p","nory","mqtu","nstv","moqx","orsu","mnvw",null,"Solution symétrique de celle de la ligne : 121"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,193,2384,"o","nrty","mpqu","npvx","mqst","pruw","mnsv",null,"Solution symétrique de celle de la ligne : 120"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,194,2400,"n","oruy","mpqt","ptvx","moqs","oprw","msuv",null,"Solution symétrique de celle de la ligne : 119"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,195,2404,"m","oruy","npqt","ptvx","noqs","nopr","suvw",null,"Solution symétrique de celle de la ligne : 118"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,196,2408,"o","nruy","mpqt","nptx","mqsv","prvw","mnsu",null,"Solution symétrique de celle de la ligne : 117"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,197,2416,"p","nory","mqtu","ntvx","moqs","oruw","mnsv",null,"Solution symétrique de celle de la ligne : 116"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,198,2432,"n","otuy","mpqr","psvx","moqt","opsw","mruv",null,"Solution symétrique de celle de la ligne : 115"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,199,2436,"m","otuy","npqr","psvx","noqt","nops","ruvw",null,"Solution symétrique de celle de la ligne : 114"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,200,2440,"o","ntuy","mpqr","npsx","mqtv","psvw","mnru",null,"Solution symétrique de celle de la ligne : 113"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,201,2448,"p","noty","mqru","nsvx","moqt","osuw","mnrv",null,"Solution symétrique de celle de la ligne : 112"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,202,2472,"p","nouy","mqrt","nstx","moqv","osvw","mnru",null,"Solution symétrique de celle de la ligne : 111"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,203,2591,"p","nqrt","mouy","noqs","mtvx","rsuv","mnow",null,"Solution symétrique de celle de la ligne : 110"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,204,2615,"n","opqr","mtuy","qstv","mopx","orsu","mpvw",null,"Solution symétrique de celle de la ligne : 109"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,205,2623,"o","npqr","mtuy","nqst","mpvx","rsuv","mnpw",null,"Solution symétrique de celle de la ligne : 108"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,206,2649,"p","nqrt","mouy","noqx","mstv","ruvw","mnos",null,"Solution symétrique de celle de la ligne : 107"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,207,2673,"n","opqr","mtuy","qtvx","mops","oruw","mpsv",null,"Solution symétrique de celle de la ligne : 106"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,208,2677,"m","opqr","ntuy","qtvx","nops","noru","psvw",null,"Solution symétrique de celle de la ligne : 105"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,209,2681,"o","npqr","mtuy","nqtx","mpsv","ruvw","mnps",null,"Solution symétrique de celle de la ligne : 104"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,210,2682,"p","nqry","motu","noqt","msvx","ruvw","mnos",null,"Solution symétrique de celle de la ligne : 103"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,211,2705,"n","opqt","mruy","qsvx","mopt","osuw","mprv",null,"Solution symétrique de celle de la ligne : 102"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,212,2709,"m","opqt","nruy","qsvx","nopt","nosu","prvw",null,"Solution symétrique de celle de la ligne : 101"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,213,2713,"o","npqt","mruy","nqsx","mptv","suvw","mnpr",null,"Solution symétrique de celle de la ligne : 100"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,214,2714,"p","nqty","moru","noqs","mtvx","suvw","mnor",null,"Solution symétrique de celle de la ligne : 99"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,215,2723,"m","opqu","nrty","qstv","nopx","nosw","pruv",null,"Solution symétrique de celle de la ligne : 98"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,216,2729,"n","opqu","mrty","qstx","mopv","osvw","mpru",null,"Solution symétrique de celle de la ligne : 97"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,217,2733,"m","opqu","nrty","qstx","nopv","nosv","pruw",null,"Solution symétrique de celle de la ligne : 96"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,218,2738,"n","opqy","mrtu","qstv","mopx","osuw","mprv",null,"Solution symétrique de celle de la ligne : 95"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,219,2742,"m","opqy","nrtu","qstv","nopx","nosu","prvw",null,"Solution symétrique de celle de la ligne : 94"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,220,2746,"o","npqy","mrtu","nqst","mpvx","suvw","mnpr",null,"Solution symétrique de celle de la ligne : 93"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,221,2748,"n","opqy","mrtu","qstx","mopv","osuv","mprw",null,"Solution symétrique de celle de la ligne : 92"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,222,2800,"m","opqy","nrtu","qtvx","nops","nouw","prsv",null,"Solution symétrique de celle de la ligne : 91"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,223,2825,"p","nrtu","moqy","nosx","mqtv","rsvw","mnou",null,"Solution symétrique de celle de la ligne : 90"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,224,2833,"o","nprt","mquy","nsvx","mpqt","rsuw","mnpv",null,"Solution symétrique de celle de la ligne : 89"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,225,2834,"p","nrty","moqu","nosv","mqtx","rsuw","mnov",null,"Solution symétrique de celle de la ligne : 88"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,226,2844,"p","nrty","moqu","nosx","mqtv","rsuv","mnow",null,"Solution symétrique de celle de la ligne : 87"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,227,2849,"n","opru","mqty","stvx","mopq","orsw","mpuv",null,"Solution symétrique de celle de la ligne : 86"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,228,2853,"m","opru","nqty","stvx","nopq","nors","puvw",null,"Solution symétrique de celle de la ligne : 85"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,229,2857,"o","npru","mqty","nstx","mpqv","rsvw","mnpu",null,"Solution symétrique de celle de la ligne : 84"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,230,2858,"p","nruy","moqt","nost","mqvx","rsvw","mnou",null,"Solution symétrique de celle de la ligne : 83"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,231,2866,"o","npry","mqtu","nstv","mpqx","rsuw","mnpv",null,"Solution symétrique de celle de la ligne : 82"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,232,2868,"n","opry","mqtu","stvx","mopq","orsu","mpvw",null,"Solution symétrique de celle de la ligne : 81"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,233,2876,"o","npry","mqtu","nstx","mpqv","rsuv","mnpw",null,"Solution symétrique de celle de la ligne : 80"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,234,2976,"m","opuy","nqrt","stvx","nopq","nosw","pruv",null,"Solution symétrique de celle de la ligne : 79"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,235,3079,"o","qrtu","mnpy","pqsv","mntx","nprs","muvw",null,"Solution symétrique de celle de la ligne : 78"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,236,3087,"n","qrtu","mopy","opqs","mtvx","prsv","mouw",null,"Solution symétrique de celle de la ligne : 77"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,237,3111,"p","oqru","mnty","qstv","mnox","nors","muvw",null,"Solution symétrique de celle de la ligne : 76"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,238,3137,"o","qrtu","mnpy","pqvx","mnst","nprw","msuv",null,"Solution symétrique de celle de la ligne : 75"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,239,3139,"m","qrtu","nopy","opqv","nstx","nprw","osuv",null,"Solution symétrique de celle de la ligne : 74"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,240,3145,"n","qrtu","mopy","opqx","mstv","prvw","mosu",null,"Solution symétrique de celle de la ligne : 73"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,241,3149,"m","qrtu","nopy","opqx","nstv","nprv","osuw",null,"Solution symétrique de celle de la ligne : 72"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,242,3154,"n","qrty","mopu","opqv","mstx","pruw","mosv",null,"Solution symétrique de celle de la ligne : 71"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,243,3156,"o","qrty","mnpu","pqvx","mnst","npru","msvw",null,"Solution symétrique de celle de la ligne : 70"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,244,3158,"m","qrty","nopu","opqv","nstx","npru","osvw",null,"Solution symétrique de celle de la ligne : 69"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,245,3164,"n","qrty","mopu","opqx","mstv","pruv","mosw",null,"Solution symétrique de celle de la ligne : 68"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,246,3169,"p","oqru","mnty","qtvx","mnos","norw","msuv",null,"Solution symétrique de celle de la ligne : 67"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,247,3170,"o","qruy","mnpt","pqtv","mnsx","nprw","msuv",null,"Solution symétrique de celle de la ligne : 66"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,248,3178,"n","qruy","mopt","opqt","msvx","prvw","mosu",null,"Solution symétrique de celle de la ligne : 65"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,249,3180,"o","qruy","mnpt","pqtx","mnsv","nprv","msuw",null,"Solution symétrique de celle de la ligne : 64"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,250,3182,"m","qruy","nopt","opqt","nsvx","nprv","osuw",null,"Solution symétrique de celle de la ligne : 63"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,251,3188,"p","oqry","mntu","qtvx","mnos","noru","msvw",null,"Solution symétrique de celle de la ligne : 62"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,252,3201,"p","oqtu","mnry","qsvx","mnot","nosw","mruv",null,"Solution symétrique de celle de la ligne : 61"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,253,3202,"o","qtuy","mnpr","pqsv","mntx","npsw","mruv",null,"Solution symétrique de celle de la ligne : 60"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,254,3210,"n","qtuy","mopr","opqs","mtvx","psvw","moru",null,"Solution symétrique de celle de la ligne : 59"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,255,3212,"o","qtuy","mnpr","pqsx","mntv","npsv","mruw",null,"Solution symétrique de celle de la ligne : 58"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,256,3214,"m","qtuy","nopr","opqs","ntvx","npsv","oruw",null,"Solution symétrique de celle de la ligne : 57"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,257,3220,"p","oqty","mnru","qsvx","mnot","nosu","mrvw",null,"Solution symétrique de celle de la ligne : 56"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,258,3234,"p","oquy","mnrt","qstv","mnox","nosw","mruv",null,"Solution symétrique de celle de la ligne : 55"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,259,3244,"p","oquy","mnrt","qstx","mnov","nosv","mruw",null,"Solution symétrique de celle de la ligne : 54"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,260,3272,"m","qtuy","nopr","opqx","nstv","npvw","orsu",null,"Solution symétrique de celle de la ligne : 53"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,261,3330,"n","rtuy","mopq","opsv","mqtx","prsw","mouv",null,"Solution symétrique de celle de la ligne : 52"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,262,3332,"o","rtuy","mnpq","psvx","mnqt","nprs","muvw",null,"Solution symétrique de celle de la ligne : 51"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,263,3334,"m","rtuy","nopq","opsv","nqtx","nprs","ouvw",null,"Solution symétrique de celle de la ligne : 50"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,264,3340,"n","rtuy","mopq","opsx","mqtv","prsv","mouw",null,"Solution symétrique de celle de la ligne : 49"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,265,3364,"p","oruy","mnqt","stvx","mnoq","nors","muvw",null,"Solution symétrique de celle de la ligne : 48"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,266,3392,"m","rtuy","nopq","opvx","nqst","nprw","osuv",null,"Solution symétrique de celle de la ligne : 47"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,267,3587,"p","qrtu","mnoy","oqsv","mntx","nrsw","mouv",null,"Solution symétrique de celle de la ligne : 46"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,268,3597,"p","qrtu","mnoy","oqsx","mntv","nrsv","mouw",null,"Solution symétrique de celle de la ligne : 45"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,269,3603,"n","pqrt","mouy","oqsv","mptx","rsuw","mopv",null,"Solution symétrique de celle de la ligne : 44"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,270,3605,"o","pqrt","mnuy","qsvx","mnpt","nrsu","mpvw",null,"Solution symétrique de celle de la ligne : 43"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,271,3606,"p","qrty","mnou","oqsv","mntx","nrsu","movw",null,"Solution symétrique de celle de la ligne : 42"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,272,3607,"m","pqrt","nouy","oqsv","nptx","nrsu","opvw",null,"Solution symétrique de celle de la ligne : 41"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,273,3613,"n","pqrt","mouy","oqsx","mptv","rsuv","mopw",null,"Solution symétrique de celle de la ligne : 40"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,274,3619,"o","pqru","mnty","qstv","mnpx","nrsw","mpuv",null,"Solution symétrique de celle de la ligne : 39"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,275,3627,"n","pqru","moty","oqst","mpvx","rsvw","mopu",null,"Solution symétrique de celle de la ligne : 38"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,276,3629,"o","pqru","mnty","qstx","mnpv","nrsv","mpuw",null,"Solution symétrique de celle de la ligne : 37"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,277,3630,"p","qruy","mnot","oqst","mnvx","nrsv","mouw",null,"Solution symétrique de celle de la ligne : 36"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,278,3631,"m","pqru","noty","oqst","npvx","nrsv","opuw",null,"Solution symétrique de celle de la ligne : 35"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,279,3638,"o","pqry","mntu","qstv","mnpx","nrsu","mpvw",null,"Solution symétrique de celle de la ligne : 34"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,280,3646,"n","pqry","motu","oqst","mpvx","rsuv","mopw",null,"Solution symétrique de celle de la ligne : 33"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,281,3664,"p","qrty","mnou","oqvx","mnst","nruw","mosv",null,"Solution symétrique de celle de la ligne : 32"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,282,3665,"m","pqrt","nouy","oqvx","npst","nruw","opsv",null,"Solution symétrique de celle de la ligne : 31"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,283,3688,"p","qruy","mnot","oqtx","mnsv","nrvw","mosu",null,"Solution symétrique de celle de la ligne : 30"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,284,3689,"m","pqru","noty","oqtx","npsv","nrvw","opsu",null,"Solution symétrique de celle de la ligne : 29"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,285,3696,"o","pqry","mntu","qtvx","mnps","nruw","mpsv",null,"Solution symétrique de celle de la ligne : 28"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,286,3698,"m","pqry","notu","oqtv","npsx","nruw","opsv",null,"Solution symétrique de celle de la ligne : 27"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,287,3704,"n","pqry","motu","oqtx","mpsv","ruvw","mops",null,"Solution symétrique de celle de la ligne : 26"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,288,3708,"m","pqry","notu","oqtx","npsv","nruv","opsw",null,"Solution symétrique de celle de la ligne : 25"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,289,3720,"p","qtuy","mnor","oqsx","mntv","nsvw","moru",null,"Solution symétrique de celle de la ligne : 24"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,290,3721,"m","pqtu","nory","oqsx","nptv","nsvw","opru",null,"Solution symétrique de celle de la ligne : 23"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,291,3728,"o","pqty","mnru","qsvx","mnpt","nsuw","mprv",null,"Solution symétrique de celle de la ligne : 22"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,292,3730,"m","pqty","noru","oqsv","nptx","nsuw","oprv",null,"Solution symétrique de celle de la ligne : 21"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,293,3736,"n","pqty","moru","oqsx","mptv","suvw","mopr",null,"Solution symétrique de celle de la ligne : 20"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,294,3740,"m","pqty","noru","oqsx","nptv","nsuv","oprw",null,"Solution symétrique de celle de la ligne : 19"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,295,3752,"o","pquy","mnrt","qstx","mnpv","nsvw","mpru",null,"Solution symétrique de celle de la ligne : 18"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,296,3754,"m","pquy","nort","oqst","npvx","nsvw","opru",null,"Solution symétrique de celle de la ligne : 17"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,297,3840,"p","rtuy","mnoq","osvx","mnqt","nrsw","mouv",null,"Solution symétrique de celle de la ligne : 16"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,298,3841,"m","prtu","noqy","osvx","npqt","nrsw","opuv",null,"Solution symétrique de celle de la ligne : 15"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,299,3856,"n","prty","moqu","osvx","mpqt","rsuw","mopv",null,"Solution symétrique de celle de la ligne : 14"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,300,3860,"m","prty","noqu","osvx","npqt","nrsu","opvw",null,"Solution symétrique de celle de la ligne : 13"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,301,3872,"o","pruy","mnqt","stvx","mnpq","nrsw","mpuv",null,"Solution symétrique de celle de la ligne : 12"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,302,3874,"m","pruy","noqt","ostv","npqx","nrsw","opuv",null,"Solution symétrique de celle de la ligne : 11"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,303,3880,"n","pruy","moqt","ostx","mpqv","rsvw","mopu",null,"Solution symétrique de celle de la ligne : 10"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,304,3884,"m","pruy","noqt","ostx","npqv","nrsv","opuw",null,"Solution symétrique de celle de la ligne : 9"]