How do I know how many cells are between 1 and 9?

The clue limits the possible sandwich lengths. One cell between 1 and 9 allows sums 2-8; two cells allow 5-15; three allow 9-21; four allow 14-26; five allow 20-30; six allow 27-33; seven is exactly 35. Compare the clue against these ranges to find the possible gaps, then use Sudoku logic to pick the actual positions.

如何知道1和9之间有多少个单元格？

最后更新 2026年6月11日

线索本身很少告诉你确切的三明治长度——但它总是缩小范围。因为填充使用2到8的不同数字，每个长度有固定的最小和最大和，任何超出长度范围的线索都会排除该长度。

每个长度的最小和最大和

The smallest digits available are 2, 3, 4, … and the largest are 8, 7, 6, … - So each sandwich length has a hard range:

0 cells: sum 0 (the 0 clue)
1 cell: 2 to 8
2 cells: 5 (2+3) to 15 (7+8)
3 cells: 9 (2+3+4) to 21 (6+7+8)
4 cells: 14 to 26
5 cells: 20 to 30
6 cells: 27 to 33
7 cells: exactly 35

Notice that 1 and 34 are impossible clue values, and a clue of 2, 3, or 4 can only be a single cell.

从长度到位置

每个允许的长度转化为1和9的允许位置对。长度为2的三明治意味着1和9恰好相隔三个单元格，在九单元格行中给出六种可能放置；长度为6的三明治只允许两种。列出幸存的对，并删除任何与已放置数字、宫限制或交叉行自身三明治约束冲突的对。在大多数谜题中，两行或三行迅速坍缩为单一排列，这些放置级联到它们的交叉行中。

示例解析 - 8的线索

Suppose a row's clue is 8. Three or more cells is impossible (minimum 9), so the sandwich is one or two cells long. One cell: that cell holds exactly the digit 8. Two cells: the only distinct pairs from 2-8 summing to 8 are {2,6} and {3,5} - Never {4,4}, since repeats are banned. So the 1 and 9 are either two or three cells apart, and the cells between them are limited to three small candidate sets. That is an enormous restriction from a single outside number.