三明治数独有哪些好的策略?

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三明治数独奖励有纪律的开局。与杀手数独不同,杀手数独中求和区域已经为你画出,而这里你必须首先发现每个三明治的起点和终点。这四个步骤让你在每个谜题中都有一个富有成效的开始。

步骤1 - 利用极端线索

Scan the outside of the grid for the most constrained clues before touching anything else. A clue of 0 means the 1 and 9 sit in adjacent cells - Only eight adjacent pairs exist in a nine-cell line, and box constraints usually eliminate several immediately. A clue of 35 forces the 1 and 9 to the two end cells of the line. Very small clues are nearly as good: a clue of 2, 3, or 4 means exactly one cell sits between the 1 and 9 (no two distinct digits from 2-8 sum below 5), and that cell holds the clue digit itself.

步骤2 - 映射1和9可能的位置

对于每条剩余的行,找出1和9的哪些位置与线索兼容。它们之间的间隔决定可能的和:一个单元格介于它们之间给出2-8,两个单元格给出5-15,三个给出9-21,四个给出14-26,五个给出20-30,六个给出27-33。例如,线索25需要1和9之间至少四个单元格——所以它们不能靠得很近,这直接排除了许多放置。交叉引用行和列:在某些行排列中必须持有1的单元格可能被其列线索禁止持有1。

步骤3 - 解码填充

Once a line's 1 and 9 are placed (or reduced to one arrangement), you know the exact length of the sandwich. Now list the sets of distinct digits from 2-8 of that length that sum to the clue. Three cells summing to 9 must be {2,3,4}; two cells summing to 15 must be {7,8}. These restricted candidate sets behave exactly like Killer Sudoku cages and combine with naked pairs and box eliminations.

步骤4 - 用标准技巧完成

在三明治约束播种候选数之后,终局是普通数独:裸单和隐单、数对和指向排除。每当你放置一个数字在夹心内部或紧邻外部时,重新检查线索——剩余总和不断缩小,通常直接迫使下一个单元格。

在实时谜题中尝试这个开局