by tso » Thu Oct 27, 2005 9:34 pm
It's often a good idea to look for xy-wings before looking for longer chains -- though longer ones will sometimes become obvious during the process.
One simple systematic way to look for xy-wings:
Examine only 2-candidate cells. Look for the FIRST 2 cells that share EXACTLY one candidate in the same group (row, column or box).
In this case, that would be r2c29 -- [69][56].
Now look for a third cell containing the two candidates NOT in common in the first ([59] in this case) that is in the same group with exactly ONE of the first two cells. If one cannot be found (it cannot in this case), move on to the next pair of cells sharing one candidate.
In this example, eventually you will find the two cells r35c4 [59][15]. R4c6 [19] is in the same box as r5c4. Bingo! This is an xy-wing! Either r3c4 or r4c6 MUST be a 9 -- in either case, r4c4 and r3c6 must NOT be a 9.
[EDIT: The last sentence in this paragraph should be: "Either r3c4 or r4c6 MUST be a 9 -- in either case, r46c4 and r123c6 must NOT be a 9." Changes in bold.
This process will find all four cell xy-type forcing chains or show that none exist. It is only slightly more difficult than looking for triples -- maybe easier, as you can ignore cells with more than 2-candidates.
There are several ways to look for longer chains. Which method is best/easist depends on the puzzle.
Last edited by
tso on Fri Oct 28, 2005 11:13 am, edited 3 times in total.
