Solver App for Android and iPhone
Strategies for Number Puzzles of all kinds

Page Index
Basic Strategies
Tough Strategies
Diabolical Strategies
Extreme Strategies
Deprecated Strategies
Order Str8ts Book 1
Order Now! Order Str8ts Book 2
Order Now!


XY-Chain example 1
XY-Chain example 1 : Load Example or : From the Start
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.

XY-Chain example 2
XY-Chain example 2 : Load Example or : From the Start

This next Sudoku puzzle contains an entertaining series of XY-Chains, starting with this rectangular one. It proves that 8 must be in either B3 or B8 and therefore we can remove the other three 8s in row B. Starting on B3 if that cell is either 8 or 6. If it is 6 then D3 must be 4 which pushes 2 into D8 which in turn makes B8 8. You can trace this from B8 back round for the same effect. A nice short XY-Chain, but as the next example shows, these four cells are a rich seam.
Same cells - different XY-Chain
Same cells - different XY-Chain : Load Example or : From the Start

Looking at exactly the same starting cell it appears we can make further eliminations, this time 6s in column 3. We go clock-wise, this time, round the rectangle. It proves 6 will either be on B3 or D3.

If you want to finish the puzzle by yourself, look out for a third elimination with those same four cells using 2s on column 8, or step through with the solver.

XY-Chains Exemplars

These puzzles require the XY-Chains strategy at some point but are otherwise trivial.
They also require one Naked Pair (except for #5).
They make good practice puzzles. Thanks to Klaus Brenner for number 5

Go back to Y-Wing ChainsContinue to 3D Medusa


Your Name/Handle

Email Address - required for confirmation (it will not be displayed here)

Your comment or question

Please enter the
letters you see:
Enter these letters Remember me

Please keep your comments relevant to this article.
Email addresses are never displayed, but they are required to confirm your comments. When you enter your name and email address, you'll be sent a link to confirm your comment. Line breaks and paragraphs are automatically converted - no need to use <p> or <br> tags.
Talk Subject Comments
Comments here pertain to corrections to the text, not the subject itself
Article created on 11-April-2008. Views: 231418
This page was last modified on 27-December-2014.
All text is copyright and for personal use only but may be reproduced with the permission of the author.
Copyright Andrew Stuart @ Syndicated Puzzles Inc, 2014