连续Consecutive

来源:本站 作者:Halcyon 发布时间:2023-03-21 19:47:57

连续数独 Consecutive

 

标准数独基础上,挡板两侧数字连续,相邻两格之间如果没有挡板,则这两格一定不连续。

Classic rules applied. Additionally, the 2 numbers adjacent to the bar is consecutive, 2 adjacent cells with no bar cannot be consecutive.

在一些描述里,规则是:标准数独基础上,挡板两侧数字连续,符合条件的情况被全部标记。这种描述被称为全标,意味着没有标记的任何地方都不符合标记的要求。

In some description, the rule is: Additionally, the 2 numbers adjacent to the bar is consecutive, all conditions are marked. This is called full-marked, it means anywhere no mark must do not obey the rules.

 

在连续数独中,至少应该有1个已知数。如果N阶题目中,N是奇数,那么这个给定的已知数不是(N-1)/2。

There should be at least one number in Consecutive. If N is odd in NxN puzzles, the unique given number cannot be (N-1)/2.

 

在接下来的例子中,灰色区域内的挡板被全部标记,其他挡板可能没有给出。

In next examples, bars in grey zones are all given. Other bars may not given in white zones.

 

连续对 Consecutive Pairs

一个挡板两侧的数字构成一个连续对。如果一个连续对的一个数字已知,我们应当试图寻找另一个数字,也就是它的配偶。

Two numbers adjacent to one Bar is a Consecutive Pair.If a number in Consecutive Pair is known, we should try to find the other one, we called it as Couple.

① 如果一个连续对里有1,则它一定有2。同理N和N-1。

If a Consecutive Pair contains 1, it must contain 2 either. And also N with N-1.

② 如果某格的配偶不是2,则该格不是1。同理N-1和N。

1 cannot be in one cell when it's Couple is not 2. And also N with N-1.

③ 如果某格的配偶不是X+1和X-1,则该格不是X。

X cannot be in one cell when it's Couple is not X+1 and X-1. 

 

长连续 Long Consecutives

至少三个不同的格子,被挡板连起来,构成长连续。

At least 3 different cells conbined by bars form a long consecutives.

① 长连续有方向 Long consecutive has directions.

② 六阶数独中,四格的长连续必须有3和4。

4-cell long consecutive in 1~6 must contain 3 and 4.

③ 如果长连续里没有2,则1不能在长连续内。

1 cannot be in long consecutives without 2.

④ 长连续分组 Groups of long consecutive

下图中,已知数3将1~6分成了1+2以及4~6两组。The given 3 seperate 1~6 into 1+2 and 4~6.

 

奇偶性 Parity

挡板两侧的数字必定是一个奇数和一个偶数。我们可以对奇偶单元格进行计数,尤其是在长连续的分析里。

Adjacent cells with a bar must be one odd and one even. We can count odd and even cells, especailly in long consecutives.

 

六阶同区三组 3 groups a region in 6x6

一个区域内有三组不同的连续对,必定是12/34/56组合。

Three groups of different Consecutive Pairs in one region, they must be 12+34+56.

 

无挡板结构Structure without bars

① 两个相邻格有A Two adjacent cells with A

It cannot contain A+1 or A-1.

② 三个不同的相邻格有A Three adjacent different cells with A

The center cannot contain A+1 or A-1.

 

以下这些技巧在不连续数独中更为常见。

These next ways are more often seen in Non-consecutive.

 

有挡板结构 Structure with bars

① A1≠2. ② C2≠2.

③ 无论3在哪里,都有B2=4。Wherever 3 is, B2=4.

④ EF5=[5,6].

 

2x2不连续方 Non-consecutive in 2x2 squares

2x2不连续方是2x2的区域,其内部没有任何挡板。

Non-consecutive in 2x2 squares is a 2x2 square with no bars inside.

① 这种区域不包含三连数(如234或者678)。

3-combined consecutives (such like 234 or 678) cannot be in.

② 四连数(1234或6789)不能同时在0个或2个挡板的2x2区域之中。

4-combined consecutives (such like 1234 or 6789) cannot be all in a 2x2 square with 0 or 2 bars. 

 

练习 Practice A

① 第一宫有一个长连续占据了四个单元格。它们都不能是6,那么它们之中一定有______。

A long consecutives in Box 1 occupies 4 cells. All of them cannot be 6, they must contain ______.

② 四阶连续数独中是否能有一个宫没有挡板?

In 4x4 Consecutive, can there be a box without bars?

③ 填完灰色区域 Fill the grey cells.

 

答案 Answer A

① 2~4 ② No As the picture.

练习 Practice B

① 寻找灰色区域内的下一步 Find the next step in grey zones.

② 在这道连续中,第八宫的1应该在______,G5=______。

In this Consecutive, Hidden Single 1 in Box 8 should be in ______, G5=______.

③ 解答问号格 Find the ?cells.

答案 Answer B

① H5≠6, G5=6; H9=8, I9=9. ② H4; 8. 

③ A3=5; C4=9;

C6=2 (C5≠2, otherwise no number in B5);

B5=1(Hidden Single in Row B), C4=2, D4=3.