Setting aside the argument about whether a puzzle that requires T&E is invalid for the moment, I challenge anyone to point out where I guessed OR used trial-and-error? I’ve been solving these puzzles for years and though I shouldn’t, I take it personally when I’m told that I doesn’t really solves them like them smart peoples does, duh, I’m-a just guessing.
I entered the puzzle into a variety of Sudoku apps -- and they all got stuck at the same point, showing that certain logical steps have not (yet) been implemented. This does not change the fact that this IS simple logic, NOT guess work, NOT trial and error. I don’t believe this topic would EVER have occurred to anyone if no one had ever tried to program a computer to create and solve Sudoku. I’ve NEVER come across this idea in the decades I’ve been doing Sudokus and the hundreds of different logic puzzles in the same genre. Some things that humans do easily might be more difficult to program at first. Not that it can’t be implemented -- or that it will even be difficult to do so -- only that apparently no one has yet. When someone does -- won’t everyone have to change their mind about what is and what isn’t logic and what is guessing? (I don’t really know how my TV’s remote control works -- to me, it is indistinguishable from magic. Maybe it is. But if a high-tech expert tells me it’s done with technology, who am I to insist that it’s magic?)
Ok, here’s the puzzle as printed:
- Code: Select all
. . 3 | 7 . 5 | . 2 6
. . . | 3 . . | 7 . 8
. . . | . 4 6 | . . .
-------+-------+------
. 2 . | . . . | 6 . 3
. . 7 | . . . | 1 . .
4 . 1 | . . . | . 7 .
-------+-------+------
. . . | 6 3 . | . . .
9 . 5 | . . 1 | . . .
3 8 . | 9 . 4 | 2 . .
Here’s what it looked like after doing all the currently accepted logical tactics:
- Code: Select all
. . 3 | 7 . 5 | 4 2 6
. . . | 3 . . | 7 . 8
7 . . | . 4 6 | . 3 1
-------+-------+------
5 2 . | 1 7 . | 6 4 3
. . 7 | 4 . . | 1 . .
4 . 1 | 5 . . | . 7 .
-------+-------+------
. . . | 6 3 7 | . . .
9 7 5 | . . 1 | 3 6 4
3 8 6 | 9 5 4 | 2 1 7
At this point, I made pencil marks in the cells that had exactly two possibilities:
- Code: Select all
1-8 1-9 3 | 7 . 5 | 4 2 6
. . . | 3 . . | 7 5-9 8
7 5-9 2-8 | 2-8 4 6 | 5-9 3 1
-------------+---------------+-------------
5 2 8-9 | 1 7 8-9 | 6 4 3
6-8 . 7 | 4 . . | 1 . .
4 . 1 | 5 . . | 8-9 7 2-9
-------------+---------------+-------------
1-2 1-4 2-4 | 6 3 7 | . . 5-9
9 7 5 | 2-8 2-8 1 | 3 6 4
3 8 6 | 9 5 4 | 2 1 7
I didn’t have to look for too long -- the solution was so simple:
- Code: Select all
1) r1c1 must be 1 or 8
2) if r1c1 is 1, then r7c1 is 2, then r7c3 is 4
3) if r1c1 is 8, then rcc3 is 2, then r7c3 is 4
Either way, r7c3 is 4, so r7c3 MUST BE 4!
With this cell filled, the puzzle is finished quickly by more common means.
Below, I’ve removed all extraneous information to make it as clear as possible:
- Code: Select all
1-8 . . | . . . | . . .
. . . | . . . | . . .
. . 2-8 | . . . | . . .
-------------+---------------+-------------
. . . | . . . | . . .
. . . | . . . | . . .
. . . | . . . | . . .
-------------+---------------+-------------
1-2 . 2-4 | . . . | . . .
. . . | . . . | . . .
. . . | . . . | . . .
*Though I don’t know, haven’t guess, don’t even *care* what the value of r1c1 is yet, haven’t touched pencil to paper, haven’t looked in the back of the book or into a crystal ball, haven’t flipped a coin, certainly didn’t TRY and ERROR -- I have proved r7c3=4 definitively, with very simple, rudimentary, iron clad logic -- the kind of critical, logical thinking they taught us in grade school.
Pappocom says I just guessed.
If only we could get the opinion of someone who worked in a field where one heard ‘logical arguments’ from opposing parties and then had to make ‘decisions’ based on the validity of these arguments -- I suppose one might call them ‘judgments’ -- someone trained to identify logical fallacy. If such a person existed, what would she or he say? I wonder if she or he would disallow logical conclusions such as this as ‘guess work’ in their place of work. If only there were such a magical person and such an honorable career.
One more thing -- generally, when I get to this point in a problem, I solve it the way I did above. Of course I could have seen it this way:
- Code: Select all
1) r7c3 must be 2 or 4
2) if r7c3 is 2,
then r7c1 is 1,
then r1c1 is 8,
then r3c3 is 2, which is a contradiction as I now have two 2’s in column 3.
3) therefore, r7c3 must be 4.
I don’t usually do it this way -- not because I have a problem with this type of iron clad logic -- but because usually the chain of reasoning is much longer this way, longer than I can follow in my head. In this particular case however, it’s probably just as obvious to most solvers.
As a non-programmer, it isn’t clear to me why this cannot be implemented and more and more I’m coming to believe it’s because people are allowing themselves to be convinced that it isn’t logic and shouldn’t be implemented. Everybody seems to be jumping on the bandwagon and adding disclaimers like -- “warning, these puzzles may require guessing to solve”, maybe without putting much thought to it.
The idea that using this type of logic makes solving too easy is terribly misleading. When Wayne says that doing this makes a Very Hard as easy as a Hard -- what I hear is that Very Hards are actually are NOT more difficult than Hards! We’re pretending they’re harder by pretending certain types of logic are voodoo. Restrict yourself to ANY subset of logical tactics and solving will be more difficult.
Subjectively, the part of solving a puzzle that is the most fun for me by far is the point at which I have to do what I’ve described above. Wayne says in multiple places that this isn’t fun. I’ve never seen him qualify that by saying “Personally, I don’t find that fun.”, but instead, he speaks for all. I hope people are deciding for themselves.
When asked how long it takes to solve a really difficult puzzle, Wayne said in the Times: “The very hardest? Put it this way. If you were on death row and were due to be executed in the morning, and your guard told you that if you could solve this puzzle you’d be free, then you’d die.”
Really? Assuming he was referring to a 9x9 Sudoku, and that by “morning”, he means no earlier than 6am, and scratch paper, pen and pencil is provided -- Bring it on.
(The puzzle is in the June 30th Los Angeles Times, but as this post is about solving technique rather than the TIMES I placed it here.)
