A) Though I don't have Friday's LA Times puzzle in front of me -- it's been tossed -- but I solved the puzzle without guessing.

B) The partially completed puzzle as posted here is rated by Pappocom's software as V.Hard, arguably unfair -- NOT invalid.

C) [ ...Edited by Pappocom: Comment C arose from a misunderstanding about the forum in which this topic was originally posted. The topic was moved to this forum ("Non-Pappocom") only when it was realized that the puzzle under discussion was a Non-Pappocom puzzle ...]

All the Los Angeles Times puzzles DO have a unique solution. So far, though I'm not averse to using it, I haven't required trial and error to solve any of them.

D) The partially completed puzzle as shown can be easily solved by a more than one method, for example:

- Code: Select all

8 2 4 | 7 6 9 | 5 1 3

9 . 6 | 1 2 . | 8 7 4

. . . | 8 4 . | . 2 .

-------------+---------------+-------------

. 8 9 | 3 5 . | . 4 .

6-7 4 5 | 2 9 1 | 3 6-8 .

. 1 . | 4 8 . | . 9 5

-------------+---------------+-------------

. . . | 6 1 4 | . . .

4 9 1-3 | 5 7 8 | . 3-6 2

1-7 6 8 | 9 3 2 | 4 5 .

Consider the cell at row 8, column 3 (r8c3) and it's relationship with r5c8.

1) r8c3 can only be 1 or 3

2) If r8c3 is 1, then r9c1 is 7, then r5c1 is 6, then r5c8 is 8.

3) If r8c3 is 3, then r8c8 is 6, then r5c8 is 8.

Since the only two possible results in r8c3 force an 8 in r5c8, we have proved that r5c8=8 and the rest falls easily.

I believe this method has been refered to as "forcing chains" or something like that. There is no guessing, no trial and error, no contradiction. I've found than many puzzles that Pappocom claims as "invalid" that supposedly require trial and error can be solved this way.

The chains can sometimes be very long, but as long as you're dealing with cells that have been narrowed down to two possibilities a piece, it's fairly simple to follow the connections by eye. If it gets too confusing, you can put a circle around pencil marks in a forcing sequence. I mean, if you are already placing marks in the cells other than the final answer numbers, there's no reason to limit the what other information keep track of in there.

Forcing chains can be similarly used to spot a contradiction. Using the same example above, if you start in r5c8, you can follow the forcing chain thusly:

If r5c8=6, then r5c1=7, then r9c1=1, then r8c3=3, then r8c8=6, then r5c8=8, a contradiction. This proves that r5c8 does NOT equal 6, so it must equal 8. This is just another way of looking at the same logic set. (In this case there is a contradiction, but to call this guessing is absurd.)

The argument over whether this is a fair way to solve the puzzle seems odd to me, since as far as I know, EVERYONE makes little pencil marks in the cells of the harder puzzles. If it's fair to write something other than the answer in the grid, any specific limitation is arbitrary. To me, this is the best part of solving the puzzle -- like the endgame in chess where you're looking for a forcing sequence so you can declare "mate in 5", humiliating your older brother, err. (Note to self: edit that bit out before posting.)

This method might be extended to include cells that still have 3 or more possibilities, but with current methods of using pencil marks, it usually beyond the capabilities of most humans. But that doesn't preclude the possibility of discovering a more efficient to handle the information and store it within the cells that might make possible what now appears not. For those that pooh-pooh this eventuallity -- or even the validity of using forcing chains -- why allow ANY pencil marks? If you can't solve it simply by using logic in your head and filling in the cells in big, fat, inked numbers, aren't you using a crutch anyway?

This is the loose, highly subjective rating scale I use for puzzles

Easy puzzles -- solved without pencil marks

Moderate puzzles -- require a few cells to have pencil marks, usually just two marks per cell.

Hard puzzles -- require many cells to have 2 or 3 pencil marks.

Very hard puzzles -- at some point, all empty cells will be filled with pencil marks.

Hardest -- as above, but pencil marks do not seem to help as most cells have 4 or more possibilites. Multiple trial and error required.