dailysudoku.com

ravel · Guest

You might be interested that i finally found a puzzle that becomes harder, when a clue is added. See here

Marty R. · Posted: Fri Apr 21, 2006 3:57 pm Post subject:

Ravel, how many types of URs are there? Can you provide a link to somewhere that defines these types?

Steve R · Posted: Fri Apr 21, 2006 4:08 pm Post subject: Harder with another clue

A very interesting point.

I think what you are saying is that it is easier for a human solver to spot the unique rectangle in r35c46 here:

David Bryant · Joined: 29 Jul 2005 Posts: 559 Location: Denver, Colorado

Steve, I think the point is that most human solvers are accustomed to look for a "non-unique rectangle" none of whose corners have yet been resolved. It's also probable that most human solvers don't tend to think very hard about the cells that have already been resolved.

There's an interesting example of this second kind of "nearly resolved deadly pattern" over on the "Nightmare" discussion forum. dcb

ravel · Guest

Marty,
this site explains types 1-4 very good, see also the original thread here.
See here for type 5.
Since Keiths "unique x-wing" there is a discussion here about types 6-9.

Steve and David,
the point is, that you definitely cannot use the (unvisible) UR, when the 9 is given. A solution with 4-9-4-9 would be unique for this sudoku, since a second solution with 9-4-9-4 in the rectangle cells then simply is not possible. Therefore you have to use at least forcing chains to solve the puzzle.

ravel · Joined: 21 Apr 2006 Posts: 536

So, this was what i needed to register finally - i hate it when i cannot edit typos or wrong copies Wink

Marty, the right link to the original thread is this one

Steve R · Posted: Fri Apr 21, 2006 10:12 pm Post subject: Harder with another clue

Ravel

Well said. It’s a good example, too.

The penny did finally drop when I was driving back a few minutes ago. The rest of the journey was spent wondering how it could be that the direction (a) “this puzzle has a unique solution” is of greater utility than the direction (b) “this puzzle has a unique solution and r3c6 contains 9.”

I still harbour suspicions that something useful lurks beneath the paradox.

Steve

ravel · Joined: 21 Apr 2006 Posts: 536

David Bryant · Joined: 29 Jul 2005 Posts: 559 Location: Denver, Colorado

keith · Posted: Tue Apr 25, 2006 9:58 pm Post subject: Not quite logical

David,

A nice turn of phrase! Unraveling, indeed!

The problem here is that Ravel's puzzle was created by adding an initial value (clue) to an already valid (unique) puzzle.

It is by no means true, in general, that you can remove a clue from any puzzle and still have a valid puzzle.

Remember that thread we had over puzzles with a small number of multiple solutions (last December?)? And, you found a puzzle with 2 or 3 or 4 solutions? It would be interesting to see if adding a clue (or two) to that puzzle provides a demonstration that uniqueness cannot be used on an initial value square.

Best wishes,

Keith

TKiel · Joined: 22 Feb 2006 Posts: 292 Location: Kalamazoo, MI

keith · Posted: Tue Apr 25, 2006 11:24 pm Post subject: Thought experiments

Tracy,

I agree that many puzzles have redundant clues, to make them easier or to make them symmetric. But, you can absolutely not think that removing a clue will result in a valid puzzle:

Experiment No. 1:

We have all seen puzzles in which only 8 numbers are represented in the initial pattern.

I believe I have seen a few puzzles in which only 8 numbers are represented, and one of them is represented only once.

Remove this one, and the puzzle must have at least two solutions. (Interchange each of the numbers not in the original pattern.)

Experiment No. 2:

A) Given a valid (unique) puzzle, remove a clue.

B) If the resulting puzzle is valid (unique), go to A).

Experiment No. 3: (A road to fame)

Remove any clue from any 17-clue Sudoku, and find a valid 16-clue Sudoku.

I must admit, I am not considering symmetry of the initial clues. This is a cosmetic (not a mathematical) requirement.

Best wishes,

Keith

TKiel · Joined: 22 Feb 2006 Posts: 292 Location: Kalamazoo, MI

keith · Posted: Wed Apr 26, 2006 11:45 pm Post subject:

Tracy,

Let's go back.

David proposed that if a puzzle has an initial clue which does not allow a uniqueness technique, remove that clue and use the uniqueness technique anyway.

I said that removing a clue from a unique puzzle does not necessarily result in another unique puzzle, so David's proposal is not a generally valid solution technique.

I hope you're enjoying the gorgeous weather in our part of the world!

Best wishes

Keith

TKiel · Joined: 22 Feb 2006 Posts: 292 Location: Kalamazoo, MI

Keith,

Now it makes sense to me. We weren't talking about the same thing.

Is there any place you'd rather be in the springtime than Michigan? I can't think of one.