sudoku 数独 XY-Chains

XY-Chains

The Y-Wing Chains are infact part of a more encompassing strategy called XY-Chains. The commonality is the same pincer-like attack on candidates that both ends can see and that the chain is made of bi-value cells. With Y-Chains the hinge was expanded to a chain of identical bi-value cells but in an XY-Chain these can be different - as long as there is one candidate to make all the links. The "X" and the "Y" in the name represent these two values in each chain link.

The example here is a very simple XY-Chain of length 4 which removed all 5's highlighted in yellow. The chain ends are 5 A7 and C2 - so all cells that can see both of these are under fire. It's possible to start at either end but lets follow the example from A7. We can reason as follows

• If A7 is 5 then A3/C7/C9 cannot be.
• if A7 is NOT 5 then it's 9, so A5 must be 2, which forces A1 to be 6. If A1 is 6 then C2 is 5.

Which ever choice in A7 the 5's in A3/C7/C9 cannot be 5. The same logic can be traced from C2 to A7 so the strategy is bi-directional, in the jargon.

https://www.sudokuwiki.org/sudoku.htm?bd=080103070090506000001408020578241639143659782926837451037905200000304097419782060

C2的candidates是56

A1的candidate是26

A5的candidates是29

A7的candidates是59

XY-Chain
length=4, chain ends: A7 and C2
This proves 5 is the solution at one end of the chain or the other
-5[A7]+9[A7]-9[A5]+2[A5]-2[A1]+6[A1]-6[C2]+5[C2]
5 taken off A3
5 taken off C7
5 taken off C9

 

 

 

 

 

 

 

作者:Chuck Lu    GitHub