锯齿/不规则 Jigsaw/Irregular
锯齿数独，又名不规则数独/混沌数独，是一种更改宫的形状的变型数独。关于它的规则，有以下两种描述：
Jigsaw, or Irregular / Chaos, is a kind of variant which change the Boxes' shapes. There are different descriptions about the rules:
① 标准数独基础上，宫可能变成不规则的（由粗线围成的算作宫）。
Classic rules applied, but the Boxes may change to irregular ones. (The boxes are distinguished by thick lines).
② 填入1~N使得行列内数字不重复，每个由粗线围成的区域内包含了1~N的所有数字。
Write 1~N to make numbers no repeated in each Row and Column. Each box surrounded by thick lines should contain all kind of numbers from 1~N.
我们的网站上默认使用规则②。
We use Rule② in our web.
例1，从两个规则解释没有区别；
Example 1, Jigsaw 4x4, no difference from Rule ① and ②.
例2，规则②内的五阶锯齿数独，明显的差异。
Example 2, Jigsaw 5x5 in Rule ②, obvious difference from different rules.
◆隐性唯一（尤其是宫内隐性唯一）会与在标准之中有很大区别，而显性唯一会更加隐蔽。
Hidden Singles (especially in Box) will be obviously different with in Classic. Naked Singles may be more covert.
定义1 LoL
LoL是一种非常重要的技巧。
LoL(Law of Leftovers) is the most important technique in Jigsaw.
◆一些例子 Some examples
① A=B, C和D等于E和F，但是顺序不确定 (C,D)=(E,F) without order .
② 第一至第三行有三组1~6，三个给出的宫内也有三组1~6. 凸出部分B必定等于凹陷部分A。
Row A~C contain 3 groups of 1~6, 3 given Boxes are 3 groups of 1~6 too. The bulge B must be same to the concavity A.
③ 凸出的B和D部分，和A、C部分等价，顺序未知。
Bulge (B,D) must be same to the concavity (A,C) without order.
④ 四个宫占了三行+一个凸出部分，凸出部分是一个额外宫。
4 given Boxes occupy 3 Rows, and a grey bulge. So the grey cells are an extra box.
◆实践 Example in practice
① 蓝色=橙色，橙色有1，结合另一个1区块，在左下角的宫内得到1的隐性唯一。
Blue = Orange, so the orange contains 1. With another block with 1, we will get the Hidden Single of 1 in the left-lower Box.
② 另外两个解法 Another 2 ways
(a) 带有区块的单链，F6≠1，删除D3的1，D3=5.
Chains with Clocks, F6≠1, Blocks in Row 6 of 1 deletes 1 from D3, D3=5.
(b) F3=D2，设它们都是A，A只可能是1或4，第二列得到2的隐性唯一。
F3=D2, set them as A, A can only be 1 or 4, Hidden Singles of 2 in Column 2.
练习 Practice A
① 在六阶锯齿数独中，A1和B6能在一个宫内吗？
In Jigsaw 6x6, can A1 and B6 be in the same Box?
② 填满图1里的灰色的宫。
Fill the grey Box in Practice-1.
③ 证明图2中E1≠C5.
Prove E1≠C5 in Practice-2.
Practice-1 and Practice-2
Answer A
① 只在规则②内可以 Only Yes in Rule②
② 如下图所示↓
③ LoL, C5=B6, E1=F6; ∵B6≠F6, ∴E1≠C5.
练习 Practice B
① 寻找下一步 Find the next hint.
练习 Answer B
① 如图所示 As the picture.
