Une bien belle pour les amateurs de ternaires (1e825)

Bonjour à tous


030 090 000
020 060 000
004 100 007

007 200 008
500 001 000
000 000 430

000 000 690
008 700 004
100 005 000

N°MC A127554317673034003132-1e825
21 cases Nishio(3x) Essais de possibilités((4x)

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X(1)
1 | 67a8__ 3_____ 1l56__ | 458__ 9_____ 247A8 | 1258_ 124n568 1256____ |
2 | 7A89__ 2_____ 1L59__ | 3458_ 6_____ 347a8 | 13589 14N58__ 13p59___ |
3 | 689___ 5g68q9 4_____ | 1____ 2o35m8 238__ | 23589 2568___ 7_______ |

4 | 3b4j69 1C469_ 7_____ | 2____ 3m5M__ 34r69 | 159__ 156____ 8_______ |
5 | 5_____ 4r689_ 2h3B69 | 34689 348___ 1____ | 27I9_ 267i___ 269_____ |
6 | 268q9_ 1c689_ 269___ | 5m689 7_____ 689__ | 4____ 3______ 1C2h5M69 |

7 | 234J__ 7_____ 235g__ | 348__ 1f2348 2o348 | 6____ 9______ 1F235G__ |
8 | 2369__ 5G69__ 8_____ | 7____ 1F23__ 6k9K_ | 123p5 125____ 4_______ |
9 | 1_____ 4j69__ 2369__ | 6K9k_ 234J__ 5____ | 7i8I_ 7I8i___ 2d3D____ |

GM mg fusion G=m=====
hM mb Bh h faux

X(2)
1 | 67a8__ 3_____ 1l56 | 458__ 9_____ 247A8 | 1258_ 124n568 126___ |
2 | 7A89__ 2_____ 1L59 | 3458_ 6_____ 347a8 | 13589 14N58__ 13p9__ |
3 | 689___ 5M68q9 4___ | 1____ 2o35m8 238__ | 2389_ 268____ 7_____ |

4 | 3b4j69 1C469_ 7___ | 2____ 3m5M__ 34r69 | 159__ 156____ 8_____ |
5 | 5_____ 4r689_ 3B69 | 34689 348___ 1____ | 27I9_ 267i___ 269___ |
6 | 2h68q9 1c689_ 2H69 | 5m689 7_____ 689__ | 4____ 3______ 1C5M69 |

7 | 234J__ 7_____ 235M | 348__ 1f2348 2o348 | 6____ 9______ 1F235m |
8 | 2369__ 5m69__ 8___ | 7____ 1F23__ 6k9K_ | 123p5 125____ 4_____ |
9 | 1_____ 4j69__ 2369 | 6K9k_ 234J__ 5____ | 7i8I_ 7I8i___ 2d3D__ |

OU(BM)=>-3c7

X(3)
1 | 67a8__ 3_____ 1l56_ | 458__ 9_____ 247A8 | 1258_ 124n568 126___ |
2 | 7A89__ 2_____ 1L59_ | 3458_ 6_____ 347a8 | 13589 14N58__ 13p9__ |
3 | 689___ 5M68q9 4____ | 1____ 2o35m8 238__ | 2389_ 268____ 7_____ |

4 | 3b4j69 1C469_ 7____ | 2____ 3m5M__ 34r69 | 159__ 156____ 8_____ |
5 | 5_____ 4r689_ 3B69_ | 34689 348___ 1____ | 27I9_ 267i___ 269___ |
6 | 2h68q9 1c689_ 2H69_ | 5m689 7_____ 689__ | 4____ 3______ 1C5M69 |

7 | 234J__ 7_____ 2m5M_ | 348__ 1f2348 2o348 | 6____ 9______ 1F235m |
8 | 2369__ 5m69__ 8____ | 7____ 1F23__ 6k9K_ | 123p5 125____ 4_____ |
9 | 1_____ 4j69__ 23b69 | 6K9k_ 234J__ 5____ | 7i8I_ 7I8i___ 2d3D__ |

qh Hm Mq q faux

X(4)
1 | 67a8__ 3_____ 1l56_ | 458__ 9_____ 247A8 | 1258_ 124n568 126___ |
2 | 7A89__ 2_____ 1L59_ | 3458_ 6_____ 347a8 | 13589 14N58__ 13p9__ |
3 | 689___ 5M69__ 4____ | 1____ 2o35m8 238__ | 2389_ 268____ 7_____ |

4 | 3b4j69 1C469_ 7____ | 2____ 3m5M__ 34r69 | 159__ 156____ 8_____ |
5 | 5_____ 4r68q9 3B69_ | 34689 348___ 1____ | 27I9_ 267i___ 269___ |
6 | 2h69__ 1c68Q9 2H69_ | 5m689 7_____ 689__ | 4____ 3______ 1C5M69 |

7 | 234J__ 7_____ 2m5M_ | 348__ 1f2348 2o348 | 6____ 9______ 1F235m |
8 | 2369__ 5m69__ 8____ | 7____ 1F23__ 6k9K_ | 123p5 125____ 4_____ |
9 | 1_____ 4j69__ 23b69 | 6K9k_ 234J__ 5____ | 7i8I_ 7I8i___ 2d3D__ |

Fusion ö=C {8ü 8ö 8â}
üC(üm MC)
öc( öq Qc)
âC( âf FC)

Fusion ö=m {8ü 8ö 8â}
üm()
öM( öq Qc CM)
âm( âf Fm)

Fusion ö=Q {8ü 8ö 8â}
üQ(üm MC cQ)
öq()
âQ( âf FC cQ)

ó faux {3ú 4ù 8ö}
úó()
ùó( ùJ jb Bó)
öó( óm MC cQ qö)

Ternaire 3b 4ù 8C=Ternaire 3b 3C 3ò
ù=ò

X(7)
1 | 67a8__ 3_____ 1l56__ | 458___ 9_______ 2s47A8__ | 1258___ 124n568 126q___ |
2 | 7A89__ 2_____ 1L59__ | 3e458_ 6_______ 347a8___ | 13ì589_ 14N58__ 13p9m__ |
3 | 689ñ__ 5c6ç9û 4_____ | 1_____ 2o3ê5C8ü 2t3î8ô__ | 2ó3à89ã 268____ 7______ |

4 | 3b4j69 1C4w69 7_____ | 2_____ 3C5c____ 3ò4r6ë9y | 159____ 156____ 8______ |
5 | 5_____ 4r68c9 3B69__ | 4ä69__ 3b4ò8C__ 1_______ | 27I9___ 267i___ 26Q9M__ |
6 | 2h69__ 1c8C__ 2H69__ | 5C68í9 7_______ 6á8é9z__ | 4______ 3______ 1C5c___ |

7 | 23è4J_ 7_____ 2C5c__ | 3E48__ 1f234ù8â 2o348___ | 6______ 9______ 1F23v5C |
8 | 23ú69_ 5C69__ 8_____ | 7_____ 1F2ö3õ__ 6k9K____ | 123p5__ 125____ 4______ |
9 | 1_____ 4j69__ 2u3b69 | 6K9k__ 2g3x4J__ 5_______ | 7i8I___ 7I8i___ 2d3D___ |

ù faux (-4e7) {3C 3ò 3b}
Cù( CF fù)
òù()
bù( bj Jù)

X(8)
1 | 67a8__ 3_____ 1l56__ | 458___ 9_______ 2s47A8__ | 1258___ 124n568 126q___ |
2 | 7A89__ 2_____ 1L59__ | 3e458_ 6_______ 3ò47a8__ | 13ì589_ 14N58__ 13p9m__ |
3 | 689ñ__ 5c6ç9û 4_____ | 1_____ 2o3ê5C8ü 2t3î8ô__ | 2ó3à89ã 268____ 7______ |

4 | 3b4j69 1C4w69 7_____ | 2_____ 3C5c____ 3j4r6ë9y | 159____ 156____ 8______ |
5 | 5_____ 4r68c9 3B69__ | 4ä69__ 3b4j8C__ 1_______ | 27I9___ 267i___ 26Q9M__ |
6 | 2h69__ 1c8C__ 2H69__ | 5C68í9 7_______ 6á8é9z__ | 4______ 3______ 1C5c___ |

7 | 23è4J_ 7_____ 2C5c__ | 3E48__ 1f238â__ 2o348___ | 6______ 9______ 1F23v5C |
8 | 23ú69_ 5C69__ 8_____ | 7_____ 1F2ö3õ__ 6k9K____ | 123p5__ 125____ 4______ |
9 | 1_____ 4j69__ 2u3b69 | 6K9k__ 2g3x4J__ 5_______ | 7i8I___ 7I8i___ 2d3D___ |

Ternaire 4j 4w 4C=Ternaire 4ä 4j 4C=Ternaire 3b4j 4C=Ternaire 4r 4ä 4j
ä=b w=b r=C

X(9)
1 | 67a8__ 3_____ 1l56__ | 458___ 9_______ 2s47A8__ | 1258___ 124n568 126q___ |
2 | 7A89__ 2_____ 1L59__ | 3e458_ 6_______ 3ò47a8__ | 13ì589_ 14N58__ 1r3p9m_ |
3 | 689ñ__ 5c6ç9û 4_____ | 1_____ 2o3ê5C8ü 2t3î8ô__ | 2ó3à89ã 268____ 7______ |

4 | 3b4j69 1C4b69 7_____ | 2_____ 3C5c____ 3j4C6ë9y | 159____ 156____ 8______ |
5 | 5_____ 4C8c__ 3B69__ | 4b69__ 3b4j8C__ 1_______ | 27I9___ 267i___ 26Q9M__ |
6 | 2h69__ 1c8C__ 2H69__ | 5C68í9 7_______ 6á8é9z__ | 4______ 3______ 1C5c___ |

7 | 2w3è4J 7_____ 2C5c__ | 3E48__ 1f238â__ 2o348___ | 6______ 9______ 1F23v5C |
8 | 2ä3ú69 5C69__ 8_____ | 7_____ 1F2ö3õ__ 6k9K____ | 123p5__ 125____ 4______ |
9 | 1_____ 4j69__ 2u3b69 | 6K9k__ 2g3x4J__ 5_______ | 7i8I___ 7I8i___ 2d3D___ |

C faux {2u 2g 2d}
uC()
gC( Cj Jg)
dC()=>{3b 3x 3D}+bC()+xC()


u faux (-2c9) {2g 3x 4J}
gu()
xu( ud Dx)
Ju()=>{4b 4C 4j}+bu()+Cu()

Fusion p=b {3ú 3õ 3p}
úb()
õb()
pB()=>{3è 3ú 3b}+èp()+úp()

Fusion õ=è {3ú 3õ 3p}
úè()
õÈ()=> {3è 3ú 3b}+úõ()+bõ()
pè( èE ep)

Ternaire{3b 3è 3ú}=Teranire{3ú 3è 3p}
b=p

X(10)
1 | 67a8__ 3___ 1l5z6 | 45s8__ 9_____ 247A8_ | 1258___ 124n568 126q__ |
2 | 7A89__ 2___ 1L5Z9 | 3e45S8 6_____ 3ò47a8 | 13ì589_ 14N58__ 1r3b9m |
3 | 6c89g_ 5___ 4____ | 1_____ 2o38v_ 2t3î8ô | 2ó3à89G 26C8___ 7_____ |

4 | 3b4B__ 4b69 7____ | 2_____ 5_____ 3B6ë9_ | 1h9H___ 1H6h___ 8_____ |
5 | 5_____ 8___ 3B69_ | 4b69__ 3b4B__ 1_____ | 27I9___ 267i___ 26Q9M_ |
6 | 6x9X__ 1___ 2____ | 68j9__ 7_____ 6á8J9_ | 4______ 3______ 5_____ |

7 | 2w3è4b 7___ 5____ | 3E48__ 1f238V 2o348_ | 6______ 9______ 1F23__ |
8 | 2W3ú69 6y9Y 8____ | 7_____ 1F2ö3è 6k9K__ | 123b5o_ 125O___ 4_____ |
9 | 1_____ 4B69 3b69_ | 6K9k__ 2D34b_ 5_____ | 7i8I___ 7I8i___ 2d3D__ |

gX xc Ch HG fusion g=x=C=H===
Gm MH hC cg fusion G=M=h=c===
hQ qC cg GH fusion h=q=c=G===
ëB bm MH hë ë faux (-6f4)

X(11)
Deus fois 6C en région 4 =>C faux
FIN

Bonjour André, bonjour à tous,

Sur cette grille, je commencerais par quelques éliminations en marquage simple :

_ | a_____ b_____ c_____ | d____ e_____ f_____ | g______ h______ i_______ |
1 | 67q8__ ______ 1d56__ | 458__ ______ 2g47Q8 | 1258___ 124k568 1256w___ |
2 | 7Q89__ ______ 1D59__ | 3458_ ______ 347q8_ | 13589__ 14K58__ 13v59y__ |
3 | 689___ 5o68x9 ______ | _____ 2u35N8 238___ | 23i589s 256p8__ ________ |

4 | 3j4M69 1e469_ ______ | _____ 345n__ 3469__ | 159____ 156____ ________ |
5 | ______ 4l68r9 2h3J69 | 34689 348___ ______ | 27B9___ 267b___ 269_____ |
6 | 2t68x9 1E689_ 269___ | 5N689 ______ 689___ | _______ _______ 1e2h5n69 |

7 | 234m__ ______ 235o__ | 348__ 1f2348 2u348_ | _______ _______ 1F235O__ |
8 | 2369__ 5O69__ ______ | _____ 1F23__ 6a9A__ | 123v5__ 125____ ________ |
9 | ______ 4M69__ 2369__ | 6A9a_ 234m__ ______ | 7b8B___ 7B8b___ 2c3C____ |

1) D'abord un OU mixte :
l/M(4Kb) =>-4e4 (ni L=4de5, ni m=4e9) (->3e4=N)

2) Ensuite une fusion :
n/O(5Ki) et N/o(5L3) =fusion o=n =>-5gh3, -5i12 par saturation ligne 3 et colonne i

3) Encore un OU, consécutifs des éliminations précédentes :
j/N(3R5) =>-3c7 (ni J=3c5, ni n=5c7) (->2c7=N)

On peut alors passer à la recherche de ternaires qui font bien avancer vers la solution :

_ | a_____ b_____ c_____ | d____ e_____ f_____ | g_____ h______ i_______ |
1 | 67q8__ ______ 1d56__ | 458__ ______ 2g47Q8 | 1258__ 124k568 126w____ |
2 | 7Q89__ ______ 1D59__ | 3458_ ______ 347q8_ | 13589_ 14K58__ 13v9y___ |
3 | 689___ 5n68x9 ______ | _____ 2u35N8 238___ | 23i89s 26p8___ ________ |

4 | 3j4M69 1e469_ ______ | _____ 3N5n__ 34l69_ | 159___ 156____ ________ |
5 | ______ 4l68r9 2h3J69 | 34689 34z8__ ______ | 27B9__ 267b___ 269_____ |
6 | 2t68x9 1E689_ 269___ | 5N689 ______ 689___ | ______ _______ 1e2h5n69 |

7 | 234m__ ______ 2N5n__ | 348__ 1f2348 2u348_ | ______ _______ 1F235N__ |
8 | 2369__ 5N69__ ______ | _____ 1F23__ 6a9A__ | 123v5_ 125____ ________ |
9 | ______ 4M69__ 23j69_ | 6A9a_ 234m__ ______ | 7b8B__ 7B8b___ 2c3C____ |

4) Un interdit sur N, utilisant des dérivés ternaires débloque la grille :

DERIVE TERNAIRE (F-2e8-3e8)+F/N+3e8/N=>!2e8/N
F/N(i7)
3e8/N(3Ke)

DERIVE TERNAIRE (j-3e9-C)+j/N+3e9/N=>c/N
j/N(3L4)
3e9/N(3Ke)

INTERDIT TERNAIRE (2c9-2e9-c)/N=>-3e4
2c9/N(2Kc)
2e9/2e8(2Ke)-!2e8/N(DT)
c/N(DT)

En effet, la fin est obtenue par deux interdits sur 69c9 :

_ | a_____ b_____ c_______ | d____ e______ f_____ | g_____ h______ i____ |
1 | 67q8__ ______ 1d6D____ | 45Á8_ _______ 2g47Q8 | 1258__ 124k568 126w_ |
2 | 7Q89__ ______ 1D9d____ | 345á8 _______ 347q8_ | 13589_ 14K58__ 13v9y |
3 | 6P89S_ ______ ________ | _____ 2u38è__ 238___ | 23i89s 26p8___ _____ |

4 | 3j4M69 4m6ç9é ________ | _____ _______ 3J69__ | 1ã9Ã__ 1Ã6ã___ _____ |
5 | ______ ______ 3J69____ | 34Z69 3Z4z___ ______ | 27B9__ 267b___ 26W9Y |
6 | 2t69__ ______ 2T69____ | 68æ9_ _______ 68Æ9__ | ______ _______ _____ |

7 | 234m__ ______ ________ | 348__ 1f2348È 2u34à8 | ______ _______ 1F23_ |
8 | 2ä3Ä__ 6A9a__ ________ | _____ 1F23___ 6a9A__ | 123v5Â 125â___ _____ |
9 | ______ 4M69__ 2t3j6ç9é | 6A9a_ 234m___ ______ | 7b8B__ 7B8b___ 2c3C_ |

5) Pour finir, deux interdits en marquage simple :

ç/D(6Kc)-d/S(9R1)-s/Ã(9Kg)-ã/ç(6L4)

é/d(9Kc)-D/P(6R1)-p/ã(6Kh)-Ã/é(9L4). Fin

Cordialement.
Cenoman