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[Advanced Techniques Of Sudoku] Odd-Chain And Its Extended Application [数独高级技巧]单数链及其延伸的运用 ?

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? 关于强弱链的定义请先参考。 About weak definitions please refer to the chain of logic. 本帖将讨论单一数字利用强弱链关系所形成的一些技巧，有X-Wing、Skyscraper、Turbot Fish等等不同的结构，但是他们的本质都是相同的。

? This post will discuss the number formed by using strength of chain a few techniques, X-Wing, Skyscraper, Turbot Fish and so on different structures, but they are all essentially the same.

? 构成矩形摒除（X-Wing）需要四个节点（节点指需要观察的数字个数），要直接观察到并不容易。

? Constitute a rectangle to exclude (X-Wing) requires a

four-node (node refers to the need to observe the number of digits), direct observation is not easy.

? 箭鱼摒除（）有 6～9 个节点，观察极度困难，即使懂得这种方法，也很难运用在解题过程中。

? Swordfish exclusion (Swordfish) 6~9 node to observe

extremely difficult, even if understood this way, it is difficult to use in problem-solving.

? 有一种解法叫做简易分色法（Simple Coloring）是利用单数的

? There is a method called simple separation method (Simple

Coloring) is to use the singular for strong export chain

? 简易分色法是解析出一条色链之后，可同时得到多个格位的解，

? Simple method of separation is to parse a color chain after,

but with multiple cells for solutions, while working in the candidate, is very good observations, but too much to

observe cells, therefore does not apply to straightforward. ? 有一种解法称做多宝鱼（Turbotfish）解法，它是由五个节点所

? There is a solution for that long on fish (Turbotfish) method, it

is formed by five nodes, observation and comparison easier. ? 多宝鱼解法与简易分色法不同之处是简易分色法全部由强链构

? How precious fish and simple solution for simple separation

method of different colour separation method is entirely by a strong chain, whereas the solution of how precious fish from weak and strong chain chain, they formed a good chance. ? 多宝鱼解法虽然只有 5 个格位，但要观察也是不容易的，因此

? Turbot solution although there are only 5 cells, but to observe

is not easy, so we will be deconstructed to strong double chain (Two Strong Link), observe two strong chain is much easier.

? 双强链的按其强链所在区域及组成可分为三种。

Two strong chains, according to their strong chain area and composition can be divided into three types.

1. 摩天楼（Skyscraper）

2. 鱼（Fish）

3. 双线风筝（Two Strings Kite） ?

we talk about the skyscrapers, the structures of the most vulnerable.

1. 上左图，两条强链都是在「行」，其中一端点（底端）在同一列上，另一端点（顶端）在同一大列区块上（row chute）称为行摩天楼。

1.on the left, two strong chains are in "line", one end point (bottom) on the same column, the other end point (top) on the blocks in the same column (row chute) is called a row of skyscrapers.

2. 上右图，两条强链都是在「列」，其中一端点（底端）在同一行上，另一端点（顶端）在同一大行区块上（column chute）称为列摩天楼。

2. on the right, two strong chains are in "column", one end point (bottom) on the same line and the other end (top) on the block on the same line (column chute) known as the skyscraper.

3. 图中红色「X」处就是不能有构成强链数字之处。

3. the Red "x" is cannot constitute a strong chain at digital point. 底下是一种特殊情况，底端在同一行，顶端也在同一行。

Below is a special case, on the same line at the bottom, on the same line at the top. This structure is called "rectangle"

(internationally known as X-Wing-cross wing, Japan called the diagonal of the square principle).

1. 上左图，黄色端点是底端，红色端点是顶端，可删减两顶端共同作用格，如红色「X」处。

1. on the left, a yellow endpoint is at the bottom, red endpoint is the top, subtract two top interaction, such as a red "x".

2. 上右图，黄色端点是底端，红色端点是顶端，可删减两顶端共同作用格，如红色「X」处。

2. right on, yellow ends was the bottom, red endpoint is the top, subtract two top interaction, such as a red "x".

● 综合前面两图，图中红色「X」处就是 X-Wing 可删减的所有格位。 Integrated front two, a red "x" is the genitive case of X-Wing to derogation.

·以下是双线风筝（Two Strings Kite）、鱼（Fish）的结构及其删减情形。

· The following is a dual line kite (Two Strings Kite), fish (Fish) of the structure and its deletion.

1. 上左图，两条强链一条在「行」另一条在「列」，红色顶端之共同作用格（红色「X」）就是不能有构成强链数字之处，这个结构称为双线风筝。 1.on the left, two strong chains in "line" another "column",

interaction of red-top (red "x") is not to constitute a strong chain of digital, this structure is called a dual-line kite.

2. 上右图，两条强链一条在「宫」另一条在「列」，红色顶端之共同作用格（红色「X」）就是不能有构成强链数字之处，这个结构称为鱼。

2. on the right, two strong links in the "Palace" another "column", interaction of red-top (red "x") is not to constitute a strong chain of digital, this structure is called fish.

·以下是一个双强链的实例，也是大家耳熟能详的 X-Wing。 · The following is an instance of a pair of strong chain, is also called the X-Wing.

1. 上左图，数字 4 在 C4,C8 形成 X-Wing

1.on the left, the number 4 in C4,C8 form X-Wing.

2. 上右图，R2,R4 除了形成 X-Wing 的四格之外，其它格位不能存在数字 4，因此画 X 处就是可以删减候选数 4 的格位。

2. the figure on the right, beyond forming X-Wing four R2,R4, other cells do not exist the number 4, painted x's is to cut down the candidate 4.

·若仔细观察前一帖的盘势可以发现还有一个 X-Wing 的结构。 · Should look closely at the potential of the previous posts can be found a X-Wing structure.

1. 上左图，数字 4 在 R1,R5 形成 X-Wing。

on the left, the number 4 in R1,R5 form X-Wing.

2. 上右图，C2,C7 除了形成 X-Wing 的四格之外，其它格位不能存在数字 4，因此画 X 处就是可以删减候选数 4 的格位。

2. the figure on the right, beyond forming X-Wing four C2,C7, other cells do not exist the number 4, painted x's is to cut down the candidate 4.

·以下是另一个双强链的实例，是两个不同的观点去处理删减的问题。

· the following is another example of a pair of strong chains, are two different points of view to deal with deletion issues.

1. 上左图，数字 6 在 R6,R8 形成 Skyscraper。

1. on the left, number 6 in R6,R8 form the Skyscraper

2. 上右图，r4c3（画 X 之红色格位）可以删减候选数 6。

. 2. right on, r4c3 (draw x red cells) can cut down the candidate 6.

3. 上左图，数字 6 在 C3,C7 形成Skyscraper。

3. on the left, the number 6 in the C3,C7 formation Skyscraper.

4. 上右图，r6c1（画 X 之红色格位）可以删减候选数 6。

4. right on, r6c1 (draw x red cells) can cut down the candidate 6. ·经两次删减后，得到第 6 宫的宫摒余解 r5c1 = 6。

·以这个盘势而言，经第一次删减就可以得到 r8c3 = 6，本例主要的目的是在说明双强链的多面向删减功能。

·这个盘势还有其它地方有双强链的结构，网友们可自行找找看。 （· After two deletions, r5c1=6 solutions over Palace left behind by the 6th House. · in terms of potential, deletion will be r8c3=6

for the first time, in this case mainly aims to describe a pair of strong chain-oriented deletion function. · this potential is there anywhere else has a dual structure of strong chains, netizens can find out on their own.）

● 上图，数字 5 在 R1,C1 形成双线风筝（黄色是强链起点，红色是强链终点）。

The diagram above, the numbers 5 formed in R1,C1 dual line kites (yellow is starting a strong chain, red is the end strong chain). ● 两红色终点共同作用格不得为数字5。

Two red-end interaction must not be a number 5.

Here is another example of a pair of strong chains, known as fish (Fish).

●上左图，数字 4 在 C5,C7 形成摩天楼（黄色是强链起点，红色是强链终点）。

On the left, number 4 C5,C7 to form skyscraper (yellow is starting a strong chain, red is the end strong chain).

● 上右图，数字 4 在 R4,B3 形成鱼（黄色是强链起点，红色是强链终点）。

On the figure on the right, the number 4 form in R4,B3 fish (yellow is starting a strong chain, red is the end strong chain).

● 两红色终点共同作用格不得为数字4。

Two red-end interaction must not be number 4.

Strong double-strong chain of problem-solving ability, mathematicians properly using double-strong chain, we can avoid the entanglement of many annoying structure.

? I designed some of the following pair of strong potential for netizens in a chain of exercise observed, every potential has many solutions of double-strong chain, try to find all sorts of structures.

? Pair of strong chains can often be over XY-Wing, XYZ-Wing, UR, ... ... Such difficulties, reduction in solving many

problems.

Can replace most of the Turbotfish pair of strong chains, netizens are to learn problem-solving skills.

Following I filter a few puzzles, as long as you use the Palace left behind reach double-strong chain of potential solutions,

practice more observation is familiar with the way to the solution of this. 双强链的解法往往发生在多处，因此有许多不同的解法，欢迎网友们提出您的解法。

Solution of a pair of strong chains tended to occur in more than one place, so there are many different solutions, welcome your solutions by netizens.

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Following I filter a few puzzles, and exclude to reach the basis through double-strong chain, and for netizens to practice. 从第一题开始，谜题双强链盘势的观察会越来越困难。

Starting from the first question, puzzle pair of strong chain potentials of observations will be more difficult. 欢迎网友们提出您的解法。

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1. 上左图，数字 8 对第 3,9 行进行摒除，得到第 3,9 行构成的双强链。

1.on the left, the number 8 on the 3rd, 9 rows are excluded, 3rd, double-strong chain of 9 lines.

2. 上中图，红色顶点的交集不能有数字 8，如图中蓝色 X。

2. map, red vertex of intersection cannot have the number 8, as the blue x.

3. 上图，数字 8 对第 4 列进行摒除，得到列摒余解 r9c4 = 8。

3. on the map, the number 8 to exclude the 4th column, be denied the solution r9c4=8.

In front after a pair of strong chains cut potential, and all other kinds of solutions.

● 上图，数字 8 对第 8 行进行摒除，得到第 8 行的区块 {8}。

On the map, the number 8 to exclude the 8th row, 8th block {8}.

● 上左图，数字 8 及区块 {8} 对第 9 行进行摒除，得到行摒余解 r9c4 = 8。

On the left, the number 8 and 9th row block {8} to be excluded, r9c4=8 get left behind more than solutions.

● 上右图，数字 8 及区块 {8} 对第 8 宫进行摒除，得到宫摒余解 r9c4 = 8。

On the figure on the right, the number 8 blocks {8} to exclude the 8th House, r9c4=8 get left behind more than solutions.

This potential is the potential of advanced dual-line kite, before reaching the potential, one must have after X-Wing of exclusion.

1. on the left, 2nd, 8 rows form candidate 8 X-Wing,r1c5 <> 8.

2. 上右图，候选数 8 形成双线风筝 r9c7 <> 8。

2. right on, candidate 8 form a dual line kite r9c7 <> 8.

3. 第 9 宫

r8c9 = 8（宫摒余解）。

3. r8c9=8 Palace (Palace left behind more than solutions[数独高级技巧]单数链及其延伸的运用