XYwing/XYChain/XY-Loop
定义1 XYwing
XYwing是一个基于双候选数单元格之间的技巧。三个单元格XY,XZ,YZ被链连结,如(Z==X)--(X==Y)--(Y==Z),则XZ与YZ共同影响到的单元格删除Z。
XYwing is a technique with 2-candidate cells. Three cells XZ, XY, YZ, they are linked by chains (Z==X)--(X==Y)--(Y==Z), the candidate Z of cells affected by XZ and YZ will be deleted.
一共有两类XYwing,一种是直角型,只能删除一个Z(例题1);另一种会删除两个方向上的多个Z(例题2)。我将它们称为直角型XYwing和斜角型XYwing。
Two kinds of XYwing, one is as a right angle, only one Z will be deleted (The example 1); In the other situation, several Z will be deleted on two directions (The example 2). I called them Right-Angle XYwing and Bevel-Angle XYwing.
◆当目标格位于显性数对中时,XYwing可能是孪生的。
XYwing may be Siamese when the goal cell is in a Naked Pair.
◆XYwing也可能通过相等的单元格进行传递。
XYwing may transmit by equal cells.
定义2 XY链 XYchain
XY链是XYwing的延申。XYChain is the extend of XYwing.
定义3 XY环 XY-Loop
XY环是XY链的特殊情况,可以导致一大片区域的删减。
XY-Loop is a special case of XYChain, it can cause a large area deletings.
◆衍生技巧Extends
蓝色格不能构成XYwing,因为没有被单链连结。但观察第四行,3只能在黄色格里。这时E1(3)和F4(3)不能同时为真,XYwing因此而成立。
Blue cells cannot form XYwing, for (2==3)-X-(3==5)--(2==5). But in Row 4, number 3 can only be in yellow cells. Now E1(3) and F4(3) cannot be all true, so the XYwing can be formed.
*例题来源:独数之道.
练习 Practice
① 在标记了候选数的格子里寻找XYwing。
Find XYwing in cells with candidates.
答案 Answer
① Like this.