XY-Chain is another colouring method. If you have understood the principles of colouring,
this method should not be too difficult to spot and apply in-game.
Chains are formed by only using bi-value cells, i.e. cells containing two candidates.
There are two types of links: within a cell and outside of a cell. If, within a cell, only one
candidate has been coloured, then the other must be coloured with the opposite colour. If two candidates are in different cells,
see each other and are the only two candidates within a row, column or a square, we can colour them with different colours.
Please note, that we use a dashed line here purely for better user interface. All links are strong and the dashed line
has nothing to do with the weak links in X-Cycles.
Let us consider the first chain: (2, C1) ⇔ (9, C1) ⇔ (9, D1)
⇔ (1, D1) ⇔ (1, D8) ⇔ (9, D8) ⇔
(9, E8) ⇔ (2, E8) ⇔ (2, E7) ⇔ (1, E7)
⇔ (1, I7) ⇔ (2, I7). As with previous colouring strategies,
we do not know which colour is ON and which colour is OFF.
What we do know is that if (2, C1) is OFF and (2, I7) is ON,
then I1 cannot be 2. Conversely,
if (2, C1) is ON and (2, I7) is OFF then I1 still cannot be 2.
In both cases we can eliminate the candidate 2 from I1.
The elimination rule for XY-Chains is similar to Rule 1 in X-Cycles. The difference is that we are only allowed to eliminate
candidates from the end-points of the chain, where as in X-Cycles, we can consider any two candidates in the loop.
In the second example there are two eliminations. Looking at the endpoints of the chain, we see that (4, A9) and (4, D7) have different colours. We know that there will be a 4 in one of these two cells, but we do not in know which one. However both cells (4, A7) and (4, D9) see the endpoints of the chain and they cannot have a value of 4.
Hey there and welcome to our Learn Section!
If you are new to our website, please check out the How To Play section. It will introduce you to
the various tools and options used in our Web Platform. The section also contains interesting articles on
grading and generating our sudoku boards.
We are ordering our boards into the following difficulties - Very Easy, Easy, Medium, Hard,
Extreme and Impossible. The first three include the most basic strategies, which are a good point
for Sudoku Beginners to start at.
The last three include, among others, various Wings, Colourings and -Fish strategies which are often used by
advanced Sudoku players.
One great feature in our website is our Solver which can be used to Learn Sudoku on the go.
If you are stuck on a Hard Sudoku board, you can use the solver to grade it and show
you a step-by-step solution. The "Load in Solver" option is very useful and available for every example in our
Learn section.
For any questions, requests or recommendations, feel free to use the online contact form at the top of each page.
Happy learning! :)