SOLO-020 · Futoshiki
EXTREMEColumns Under Tension
Complete square 8 × 8 with figures from 1 to 8.
This page contains the solution.
The answer
Grid, line by line:
4 8 6 3 5 2 1 7
7 1 2 5 8 4 6 3
6 3 8 4 7 1 5 2
2 5 1 7 3 6 8 4
8 4 3 6 2 5 7 1
5 2 7 1 6 3 4 8
1 7 5 2 4 8 3 6
3 6 4 8 1 7 2 5
| L / C | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
|---|---|---|---|---|---|---|---|---|
| 1 | 4 | 8 | 6 | 3 | 5 | 2 | 1 | 7 |
| 2 | 7 | 1 | 2 | 5 | 8 | 4 | 6 | 3 |
| 3 | 6 | 3 | 8 | 4 | 7 | 1 | 5 | 2 |
| 4 | 2 | 5 | 1 | 7 | 3 | 6 | 8 | 4 |
| 5 | 8 | 4 | 3 | 6 | 2 | 5 | 7 | 1 |
| 6 | 5 | 2 | 7 | 1 | 6 | 3 | 4 | 8 |
| 7 | 1 | 7 | 5 | 2 | 4 | 8 | 3 | 6 |
| 8 | 3 | 6 | 4 | 8 | 1 | 7 | 2 | 5 |
The reasoning
- First enter the candidates from 1 to 8 in each empty box. Remove any numbers already fixed in its line or column. The rows and columns each require a complete permutation.
- Owns inequalities in both directions. If A < B, A can no longer take a value greater than or equal to the greatest candidate of B, and B can no longer take a value less than or equal to the smallest candidate of A.
- After each reduction, check the unique locations of each digit in each row and column. A growing chain of k boxes consumes at least k separate values; its ends also give bounds.
- The reference method combines these reductions and then controlled assumptions. On this problem, the exact search visits 55 knots, encounters 27 contradictions and reaches a depth of 9 nested choices. These numbers describe this solver and not a guaranteed human duration.
- A hypothesis is treated as a temporary branch: notes its box and its number, spreads all the constraints, then returns to the last choice if a box loses all its candidates or if a line can no longer contain a number. Do not erase a hypothesis without noting the contradiction.
- Here are the first assignments of the path that leads to the solution. "Assumption" means a choice to be confirmed in exploration, not a proven local deduction:
- L4C5 = 3 — inequality.
- L4C4 = 7 — inequality.
- L3C6 = 1 — inequality.
- L5C6 = 5 — inequality.
- L4C6 = 6 — row/column.
- L8C4 = 8 — single location.
- L1C4 = 3 — hypothesis.
- L3C5 = 7 — hypothesis.
- L2C5 = 8 — hypothesis.
- L7C6 = 8 — single location.
- L1C5 = 5 — hypothesis.
- L7C5 = 4 — row/column.
- L2C6 = 4 — hypothesis.
- L8C6 = 7 — row/column.
- L7C3 = 5 — single location.
- L6C1 = 5 — single location.
- L4C1 = 2 — hypothesis.
- L4C3 = 1 — row/column.
- L8C2 = 6 — inequality.
- L2C1 = 7 — hypothesis.
- L2C7 = 6 — single location.
- L2C3 = 2 — row/column.
- L8C3 = 4 — row/column.
- L2C2 = 1 — inequality.
- L2C8 = 3 — row/column.
- L8C1 = 3 — row/column.
- L8C7 = 2 — single location.
- L3C1 = 6 — row/column.
- L7C1 = 1 — row/column.
- L1C1 = 4 — single location.
- Example of a rebutted branch: supposes L1C4 = 1. The propagation results in: Two identical fixed digits in boxes L3C1, L3C2, L3C3, L3C4, L3C5, L3C6, L3C7, L3C8 The certificate of exploration gives all branches, with indices of squares counted from zero.
- Example of a rebutted branch: supposes L1C4 = 3, then L3C5 = 7, then L2C5 = 4, then L1C8 = 1. The propagation results in: L-inequality L8C3 < L7C3 no longer has compatible torque values. The exploration certificate gives all branches, with indices of squares counted from zero.
- Example of a rebutted branch: supposes L1C4 = 3, then L3C5 = 7, then L2C5 = 4, then L1C8 = 7. Propagation results in: The number 4 can no longer be placed in the group L7C1, L7C2, L7C3, L7C4, L7C5, L7C6, L7C7, L7C8 The certificate of exploration gives all branches, with indices of boxes counted from zero.
- The final grid allows line-by-line and column-by-column control: each one contains once all the numbers. Then check the inequalities one by one:
- L4C5 < L4C4 : 3 < 7.
- L8C6 < L7C6 : 7 < 8.
- L1C4 < L1C3 : 3 < 6.
- L2C3 < L1C3 : 2 < 6.
- L2C2 < L2C3 : 1 < 2.
- L3C6 < L3C7 : 1 < 5.
- L1C7 < L2C7 : 1 < 6.
- L6C6 < L6C7 : 3 < 4.
- L6C6 < L5C6 : 3 < 5.
- L8C1 < L8C2 : 3 < 6.
- L8C3 < L7C3 : 4 < 5.
- L7C4 < L7C5 : 2 < 4.
- L3C1 < L2C1 : 6 < 7.
- L6C2 < L5C2 : 2 < 4.
- L6C4 < L6C5 : 1 < 6.
- L5C6 < L4C6 : 5 < 6.
- L6C2 < L7C2 : 2 < 7.
- L7C1 < L8C1 : 1 < 3.
- L7C5 < L7C6 : 4 < 8.
- The exact counting continued after finding this grid to look for a second solution. All other branches fail: the solution is unique.
Common mistakes and false leads
- Add the Sudoku regions: they are not part of Futoshiki.
- Forget that inequality forces its two ends.
- Take a search hypothesis for a figure deducted unconditionally.
Show the full search proof
Each branch is independent. The tree records the deductions and contradictions found with the method used here.
{
"indexing": "Case i = ligne i//n+1, colonne i%n+1. Les indices bruts commencent à zéro.",
"events": [
{
"event": "branch",
"assumptions": [],
"cell": 3,
"values": [
1,
3
]
},
{
"event": "contradiction",
"assumptions": [
{
"cell": 3,
"value": 1
}
],
"reason": "Deux chiffres fixés identiques dans les cases L3C1, L3C2, L3C3, L3C4, L3C5, L3C6, L3C7, L3C8"
},
{
"event": "branch",
"assumptions": [
{
"cell": 3,
"value": 3
}
],
"cell": 20,
"values": [
7,
8
]
},
{
"event": "branch",
"assumptions": [
{
"cell": 3,
"value": 3
},
{
"cell": 20,
"value": 7
}
],
"cell": 12,
"values": [
4,
8
]
},
{
"event": "branch",
"assumptions": [
{
"cell": 3,
"value": 3
},
{
"cell": 20,
"value": 7
},
{
"cell": 12,
"value": 4
}
],
"cell": 7,
"values": [
1,
7
]
},
{
"event": "contradiction",
"assumptions": [
{
"cell": 3,
"value": 3
},
{
"cell": 20,
"value": 7
},
{
"cell": 12,
"value": 4
},
{
"cell": 7,
"value": 1
}
],
"reason": "L’inégalité L8C3 < L7C3 ne possède plus de couple de valeurs compatible."
},
{
"event": "contradiction",
"assumptions": [
{
"cell": 3,
"value": 3
},
{
"cell": 20,
"value": 7
},
{
"cell": 12,
"value": 4
},
{
"cell": 7,
"value": 7
}
],
"reason": "Le chiffre 4 ne peut plus se placer dans le groupe L7C1, L7C2, L7C3, L7C4, L7C5, L7C6, L7C7, L7C8"
},
{
"event": "branch",
"assumptions": [
{
"cell": 3,
"value": 3
},
{
"cell": 20,
"value": 7
},
{
"cell": 12,
"value": 8
}
],
"cell": 4,
"values": [
4,
5
]
},
{
"event": "branch",
"assumptions": [
{
"cell": 3,
"value": 3
},
{
"cell": 20,
"value": 7
},
{
"cell": 12,
"value": 8
},
{
"cell": 4,
"value": 4
}
],
"cell": 6,
"values": [
1,
6
]
},
{
"event": "branch",
"assumptions": [
{
"cell": 3,
"value": 3
},
{
"cell": 20,
"value": 7
},
{
"cell": 12,
"value": 8
},
{
"cell": 4,
"value": 4
},
{
"cell": 6,
"value": 1
}
],
"cell": 7,
"values": [
7,
8
]
},
{
"event": "branch",
"assumptions": [
{
"cell": 3,
"value": 3
},
{
"cell": 20,
"value": 7
},
{
"cell": 12,
"value": 8
},
{
"cell": 4,
"value": 4
},
{
"cell": 6,
"value": 1
},
{
"cell": 7,
"value": 7
}
],
"cell": 1,
"values": [
6,
8
]
},
{
"event": "branch",
"assumptions": [
{
"cell": 3,
"value": 3
},
{
"cell": 20,
"value": 7
},
{
"cell": 12,
"value": 8
},
{
"cell": 4,
"value": 4
},
{
"cell": 6,
"value": 1
},
{
"cell": 7,
"value": 7
},
{
"cell": 1,
"value": 6
}
],
"cell": 0,
"values": [
5,
8
]
},
{
"event": "contradiction",
"assumptions": [
{
"cell": 3,
"value": 3
},
{
"cell": 20,
"value": 7
},
{
"cell": 12,
"value": 8
},
{
"cell": 4,
"value": 4
},
{
"cell": 6,
"value": 1
},
{
"cell": 7,
"value": 7
},
{
"cell": 1,
"value": 6
},
{
"cell": 0,
"value": 5
}
],
"reason": "Deux chiffres fixés identiques dans les cases L1C2, L2C2, L3C2, L4C2, L5C2, L6C2, L7C2, L8C2"
},
{
"event": "contradiction",
"assumptions": [
{
"cell": 3,
"value": 3
},
{
"cell": 20,
"value": 7
},
{
"cell": 12,
"value": 8
},
{
"cell": 4,
"value": 4
},
{
"cell": 6,
"value": 1
},
{
"cell": 7,
"value": 7
},
{
"cell": 1,
"value": 6
},
{
"cell": 0,
"value": 8
}
],
"reason": "Le chiffre 7 ne peut plus se placer dans le groupe L6C1, L6C2, L6C3, L6C4, L6C5, L6C6, L6C7, L6C8"
},
{
"event": "branch",
"assumptions": [
{
"cell": 3,
"value": 3
},
{
"cell": 20,
"value": 7
},
{
"cell": 12,
"value": 8
},
{
"cell": 4,
"value": 4
},
{
"cell": 6,
"value": 1
},
{
"cell": 7,
"value": 7
},
{
"cell": 1,
"value": 8
}
],
"cell": 0,
"values": [
5,
6
]
},
{
"event": "contradiction",
"assumptions": [
{
"cell": 3,
"value": 3
},
{
"cell": 20,
"value": 7
},
{
"cell": 12,
"value": 8
},
{
"cell": 4,
"value": 4
},
{
"cell": 6,
"value": 1
},
{
"cell": 7,
"value": 7
},
{
"cell": 1,
"value": 8
},
{
"cell": 0,
"value": 5
}
],
"reason": "Le chiffre 1 ne peut plus se placer dans le groupe L1C1, L2C1, L3C1, L4C1, L5C1, L6C1, L7C1, L8C1"
},
{
"event": "contradiction",
"assumptions": [
{
"cell": 3,
"value": 3
},
{
"cell": 20,
"value": 7
},
{
"cell": 12,
"value": 8
},
{
"cell": 4,
"value": 4
},
{
"cell": 6,
"value": 1
},
{
"cell": 7,
"value": 7
},
{
"cell": 1,
"value": 8
},
{
"cell": 0,
"value": 6
}
],
"reason": "Deux chiffres fixés identiques dans les cases L1C2, L2C2, L3C2, L4C2, L5C2, L6C2, L7C2, L8C2"
},
{
"event": "contradiction",
"assumptions": [
{
"cell": 3,
"value": 3
},
{
"cell": 20,
"value": 7
},
{
"cell": 12,
"value": 8
},
{
"cell": 4,
"value": 4
},
{
"cell": 6,
"value": 1
},
{
"cell": 7,
"value": 8
}
],
"reason": "Le chiffre 1 ne peut plus se placer dans le groupe L1C1, L2C1, L3C1, L4C1, L5C1, L6C1, L7C1, L8C1"
},
{
"event": "contradiction",
"assumptions": [
{
"cell": 3,
"value": 3
},
{
"cell": 20,
"value": 7
},
{
"cell": 12,
"value": 8
},
{
"cell": 4,
"value": 4
},
{
"cell": 6,
"value": 6
}
],
"reason": "Deux chiffres fixés identiques dans les cases L1C3, L2C3, L3C3, L4C3, L5C3, L6C3, L7C3, L8C3"
},
{
"event": "branch",
"assumptions": [
{
"cell": 3,
"value": 3
},
{
"cell": 20,
"value": 7
},
{
"cell": 12,
"value": 8
},
{
"cell": 4,
"value": 5
}
],
"cell": 13,
"values": [
4,
7
]
},
{
"event": "branch",
"assumptions": [
{
"cell": 3,
"value": 3
},
{
"cell": 20,
"value": 7
},
{
"cell": 12,
"value": 8
},
{
"cell": 4,
"value": 5
},
{
"cell": 13,
"value": 4
}
],
"cell": 24,
"values": [
1,
2
]
},
{
"event": "contradiction",
"assumptions": [
{
"cell": 3,
"value": 3
},
{
"cell": 20,
"value": 7
},
{
"cell": 12,
"value": 8
},
{
"cell": 4,
"value": 5
},
{
"cell": 13,
"value": 4
},
{
"cell": 24,
"value": 1
}
],
"reason": "Le chiffre 8 ne peut plus se placer dans le groupe L6C1, L6C2, L6C3, L6C4, L6C5, L6C6, L6C7, L6C8"
},
{
"event": "branch",
"assumptions": [
{
"cell": 3,
"value": 3
},
{
"cell": 20,
"value": 7
},
{
"cell": 12,
"value": 8
},
{
"cell": 4,
"value": 5
},
{
"cell": 13,
"value": 4
},
{
"cell": 24,
"value": 2
}
],
"cell": 8,
"values": [
6,
7
]
},
{
"event": "contradiction",
"assumptions": [
{
"cell": 3,
"value": 3
},
{
"cell": 20,
"value": 7
},
{
"cell": 12,
"value": 8
},
{
"cell": 4,
"value": 5
},
{
"cell": 13,
"value": 4
},
{
"cell": 24,
"value": 2
},
{
"cell": 8,
"value": 6
}
],
"reason": "Deux chiffres fixés identiques dans les cases L8C1, L8C2, L8C3, L8C4, L8C5, L8C6, L8C7, L8C8"
},
{
"event": "solution",
"assumptions": [
{
"cell": 3,
"value": 3
},
{
"cell": 20,
"value": 7
},
{
"cell": 12,
"value": 8
},
{
"cell": 4,
"value": 5
},
{
"cell": 13,
"value": 4
},
{
"cell": 24,
"value": 2
},
{
"cell": 8,
"value": 7
}
]
},
{
"event": "branch",
"assumptions": [
{
"cell": 3,
"value": 3
},
{
"cell": 20,
"value": 7
},
{
"cell": 12,
"value": 8
},
{
"cell": 4,
"value": 5
},
{
"cell": 13,
"value": 7
}
],
"cell": 6,
"values": [
1,
4
]
},
{
"event": "contradiction",
"assumptions": [
{
"cell": 3,
"value": 3
},
{
"cell": 20,
"value": 7
},
{
"cell": 12,
"value": 8
},
{
"cell": 4,
"value": 5
},
{
"cell": 13,
"value": 7
},
{
"cell": 6,
"value": 1
}
],
"reason": "La case L2C3 ne possède plus aucun candidat après exclusion des chiffres fixés dans sa ligne/colonne."
},
{
"event": "contradiction",
"assumptions": [
{
"cell": 3,
"value": 3
},
{
"cell": 20,
"value": 7
},
{
"cell": 12,
"value": 8
},
{
"cell": 4,
"value": 5
},
{
"cell": 13,
"value": 7
},
{
"cell": 6,
"value": 4
}
],
"reason": "Deux chiffres fixés identiques dans les cases L1C1, L2C1, L3C1, L4C1, L5C1, L6C1, L7C1, L8C1"
},
{
"event": "branch",
"assumptions": [
{
"cell": 3,
"value": 3
},
{
"cell": 20,
"value": 8
}
],
"cell": 12,
"values": [
4,
7
]
},
{
"event": "branch",
"assumptions": [
{
"cell": 3,
"value": 3
},
{
"cell": 20,
"value": 8
},
{
"cell": 12,
"value": 4
}
],
"cell": 4,
"values": [
5,
7
]
},
{
"event": "contradiction",
"assumptions": [
{
"cell": 3,
"value": 3
},
{
"cell": 20,
"value": 8
},
{
"cell": 12,
"value": 4
},
{
"cell": 4,
"value": 5
}
],
"reason": "La case L3C3 ne possède plus aucun candidat après exclusion des chiffres fixés dans sa ligne/colonne."
},
{
"event": "branch",
"assumptions": [
{
"cell": 3,
"value": 3
},
{
"cell": 20,
"value": 8
},
{
"cell": 12,
"value": 4
},
{
"cell": 4,
"value": 7
}
],
"cell": 7,
"values": [
1,
8
]
},
{
"event": "contradiction",
"assumptions": [
{
"cell": 3,
"value": 3
},
{
"cell": 20,
"value": 8
},
{
"cell": 12,
"value": 4
},
{
"cell": 4,
"value": 7
},
{
"cell": 7,
"value": 1
}
],
"reason": "L’inégalité L8C3 < L7C3 ne possède plus de couple de valeurs compatible."
},
{
"event": "contradiction",
"assumptions": [
{
"cell": 3,
"value": 3
},
{
"cell": 20,
"value": 8
},
{
"cell": 12,
"value": 4
},
{
"cell": 4,
"value": 7
},
{
"cell": 7,
"value": 8
}
],
"reason": "Deux chiffres fixés identiques dans les cases L7C1, L7C2, L7C3, L7C4, L7C5, L7C6, L7C7, L7C8"
},
{
"event": "branch",
"assumptions": [
{
"cell": 3,
"value": 3
},
{
"cell": 20,
"value": 8
},
{
"cell": 12,
"value": 7
}
],
"cell": 4,
"values": [
4,
5
]
},
{
"event": "branch",
"assumptions": [
{
"cell": 3,
"value": 3
},
{
"cell": 20,
"value": 8
},
{
"cell": 12,
"value": 7
},
{
"cell": 4,
"value": 4
}
],
"cell": 7,
"values": [
7,
8
]
},
{
"event": "branch",
"assumptions": [
{
"cell": 3,
"value": 3
},
{
"cell": 20,
"value": 8
},
{
"cell": 12,
"value": 7
},
{
"cell": 4,
"value": 4
},
{
"cell": 7,
"value": 7
}
],
"cell": 1,
"values": [
6,
8
]
},
{
"event": "contradiction",
"assumptions": [
{
"cell": 3,
"value": 3
},
{
"cell": 20,
"value": 8
},
{
"cell": 12,
"value": 7
},
{
"cell": 4,
"value": 4
},
{
"cell": 7,
"value": 7
},
{
"cell": 1,
"value": 6
}
],
"reason": "Le chiffre 7 ne peut plus se placer dans le groupe L3C1, L3C2, L3C3, L3C4, L3C5, L3C6, L3C7, L3C8"
},
{
"event": "branch",
"assumptions": [
{
"cell": 3,
"value": 3
},
{
"cell": 20,
"value": 8
},
{
"cell": 12,
"value": 7
},
{
"cell": 4,
"value": 4
},
{
"cell": 7,
"value": 7
},
{
"cell": 1,
"value": 8
}
],
"cell": 0,
"values": [
5,
6
]
},
{
"event": "contradiction",
"assumptions": [
{
"cell": 3,
"value": 3
},
{
"cell": 20,
"value": 8
},
{
"cell": 12,
"value": 7
},
{
"cell": 4,
"value": 4
},
{
"cell": 7,
"value": 7
},
{
"cell": 1,
"value": 8
},
{
"cell": 0,
"value": 5
}
],
"reason": "Le chiffre 1 ne peut plus se placer dans le groupe L1C1, L2C1, L3C1, L4C1, L5C1, L6C1, L7C1, L8C1"
},
{
"event": "contradiction",
"assumptions": [
{
"cell": 3,
"value": 3
},
{
"cell": 20,
"value": 8
},
{
"cell": 12,
"value": 7
},
{
"cell": 4,
"value": 4
},
{
"cell": 7,
"value": 7
},
{
"cell": 1,
"value": 8
},
{
"cell": 0,
"value": 6
}
],
"reason": "Le chiffre 8 ne peut plus se placer dans le groupe L1C3, L2C3, L3C3, L4C3, L5C3, L6C3, L7C3, L8C3"
},
{
"event": "contradiction",
"assumptions": [
{
"cell": 3,
"value": 3
},
{
"cell": 20,
"value": 8
},
{
"cell": 12,
"value": 7
},
{
"cell": 4,
"value": 4
},
{
"cell": 7,
"value": 8
}
],
"reason": "Le chiffre 6 ne peut plus se placer dans le groupe L3C1, L3C2, L3C3, L3C4, L3C5, L3C6, L3C7, L3C8"
},
{
"event": "branch",
"assumptions": [
{
"cell": 3,
"value": 3
},
{
"cell": 20,
"value": 8
},
{
"cell": 12,
"value": 7
},
{
"cell": 4,
"value": 5
}
],
"cell": 6,
"values": [
1,
4
]
},
{
"event": "branch",
"assumptions": [
{
"cell": 3,
"value": 3
},
{
"cell": 20,
"value": 8
},
{
"cell": 12,
"value": 7
},
{
"cell": 4,
"value": 5
},
{
"cell": 6,
"value": 1
}
],
"cell": 7,
"values": [
7,
8
]
},
{
"event": "branch",
"assumptions": [
{
"cell": 3,
"value": 3
},
{
"cell": 20,
"value": 8
},
{
"cell": 12,
"value": 7
},
{
"cell": 4,
"value": 5
},
{
"cell": 6,
"value": 1
},
{
"cell": 7,
"value": 7
}
],
"cell": 1,
"values": [
6,
8
]
},
{
"event": "contradiction",
"assumptions": [
{
"cell": 3,
"value": 3
},
{
"cell": 20,
"value": 8
},
{
"cell": 12,
"value": 7
},
{
"cell": 4,
"value": 5
},
{
"cell": 6,
"value": 1
},
{
"cell": 7,
"value": 7
},
{
"cell": 1,
"value": 6
}
],
"reason": "Le chiffre 7 ne peut plus se placer dans le groupe L3C1, L3C2, L3C3, L3C4, L3C5, L3C6, L3C7, L3C8"
},
{
"event": "branch",
"assumptions": [
{
"cell": 3,
"value": 3
},
{
"cell": 20,
"value": 8
},
{
"cell": 12,
"value": 7
},
{
"cell": 4,
"value": 5
},
{
"cell": 6,
"value": 1
},
{
"cell": 7,
"value": 7
},
{
"cell": 1,
"value": 8
}
],
"cell": 0,
"values": [
4,
6
]
},
{
"event": "branch",
"assumptions": [
{
"cell": 3,
"value": 3
},
{
"cell": 20,
"value": 8
},
{
"cell": 12,
"value": 7
},
{
"cell": 4,
"value": 5
},
{
"cell": 6,
"value": 1
},
{
"cell": 7,
"value": 7
},
{
"cell": 1,
"value": 8
},
{
"cell": 0,
"value": 4
}
],
"cell": 10,
"values": [
2,
4
]
},
{
"event": "contradiction",
"assumptions": [
{
"cell": 3,
"value": 3
},
{
"cell": 20,
"value": 8
},
{
"cell": 12,
"value": 7
},
{
"cell": 4,
"value": 5
},
{
"cell": 6,
"value": 1
},
{
"cell": 7,
"value": 7
},
{
"cell": 1,
"value": 8
},
{
"cell": 0,
"value": 4
},
{
"cell": 10,
"value": 2
}
],
"reason": "Le chiffre 5 ne peut plus se placer dans le groupe L6C1, L6C2, L6C3, L6C4, L6C5, L6C6, L6C7, L6C8"
},
{
"event": "contradiction",
"assumptions": [
{
"cell": 3,
"value": 3
},
{
"cell": 20,
"value": 8
},
{
"cell": 12,
"value": 7
},
{
"cell": 4,
"value": 5
},
{
"cell": 6,
"value": 1
},
{
"cell": 7,
"value": 7
},
{
"cell": 1,
"value": 8
},
{
"cell": 0,
"value": 4
},
{
"cell": 10,
"value": 4
}
],
"reason": "Le chiffre 1 ne peut plus se placer dans le groupe L1C1, L2C1, L3C1, L4C1, L5C1, L6C1, L7C1, L8C1"
},
{
"event": "contradiction",
"assumptions": [
{
"cell": 3,
"value": 3
},
{
"cell": 20,
"value": 8
},
{
"cell": 12,
"value": 7
},
{
"cell": 4,
"value": 5
},
{
"cell": 6,
"value": 1
},
{
"cell": 7,
"value": 7
},
{
"cell": 1,
"value": 8
},
{
"cell": 0,
"value": 6
}
],
"reason": "L’inégalité L8C3 < L7C3 ne possède plus de couple de valeurs compatible."
},
{
"event": "contradiction",
"assumptions": [
{
"cell": 3,
"value": 3
},
{
"cell": 20,
"value": 8
},
{
"cell": 12,
"value": 7
},
{
"cell": 4,
"value": 5
},
{
"cell": 6,
"value": 1
},
{
"cell": 7,
"value": 8
}
],
"reason": "Le chiffre 7 ne peut plus se placer dans le groupe L3C1, L3C2, L3C3, L3C4, L3C5, L3C6, L3C7, L3C8"
},
{
"event": "branch",
"assumptions": [
{
"cell": 3,
"value": 3
},
{
"cell": 20,
"value": 8
},
{
"cell": 12,
"value": 7
},
{
"cell": 4,
"value": 5
},
{
"cell": 6,
"value": 4
}
],
"cell": 10,
"values": [
2,
4
]
},
{
"event": "contradiction",
"assumptions": [
{
"cell": 3,
"value": 3
},
{
"cell": 20,
"value": 8
},
{
"cell": 12,
"value": 7
},
{
"cell": 4,
"value": 5
},
{
"cell": 6,
"value": 4
},
{
"cell": 10,
"value": 2
}
],
"reason": "Le chiffre 5 ne peut plus se placer dans le groupe L1C1, L2C1, L3C1, L4C1, L5C1, L6C1, L7C1, L8C1"
},
{
"event": "contradiction",
"assumptions": [
{
"cell": 3,
"value": 3
},
{
"cell": 20,
"value": 8
},
{
"cell": 12,
"value": 7
},
{
"cell": 4,
"value": 5
},
{
"cell": 6,
"value": 4
},
{
"cell": 10,
"value": 4
}
],
"reason": "Deux chiffres fixés identiques dans les cases L1C1, L2C1, L3C1, L4C1, L5C1, L6C1, L7C1, L8C1"
}
]
}How we verified this answer
Comprehensive research with different domains, constraints, unique locations and inequalities; independent control of the final grid.
{
"nodes": 55,
"branches": 27,
"contradictions": 27,
"max_depth": 9,
"forced": 493,
"solutions": 1,
"size": 8,
"givens": 16,
"inequalities": 19
}The crossover of single lines, single columns and inequities is not closed by propagation of the only forced numbers in the reference solver. Entwined hypotheses and non-local contradictions are necessary in its method; this motivates the Extreme level, without pretending to exclude a shorter human trick.