by **_m_k** » Tue Mar 20, 2007 3:13 am

sirdave, sorry for not being precise. Here is what I was trying to say.

1. Do as much as you can using (a) basic eliminations, (b) hidden singles, and (c) some other techniques of your choice except for (contradiction) chains.

2. When no more progress can be made, pick any cell of your choice, and assume that this cell has a value chosen from possible candidates for this cell. Then, proceed again as in step 1. However, I prefer to use only (a) and (b) for this step.

3. One of the three things will happen:

(i) The puzzle is solved. Of course, whether you are satisfied or not is another matter.

(ii) You get a contradiction. Then, you can eliminate the value used in step 2 from the cell. Again, whether you accept this method or not is another matter.

(iii) No more progress can be made.

4. If you come to 3(iii), use recursion to do steps 2 and 3 above. Again, I prefer to use only (a) and (b) for these step.

It is true that all puzzles can be solved using the steps 1, 2, 3, and 4. However, practically speaking, the level of recursion becomes an important issue, and to a lesser degree, length of step 2. If you use in step 1 only (a) and (b) but no other techniques, then the level of recursion easily becomes 10 or more for very difficult puzzles.

On the other hand, if you include in (c) naked/hidden pairs, triples, quad, and locked candidates (but these are not included in step 2), then most puzzles can be solved by steps 1 and 2 only because you don’t get 3(iii), and even for difficult puzzles, one level of recursion is usually enough to solve them, and seldom two or more levels.

Remember that I am using only (a) and (b) for step 2 (contradiction) chains and step 3 recursion.

M.K.