The New Sudoku Players' Forum

[Eioru]

I use SE to find 6x6 puzzle:

Code: Select all

000000789
000000789
789789789
000000789
000000789
897897789
000000789
000000789
978978789

It doesn't care about 7,8,9.
Then type in 1~6 at 0.
like

Code: Select all

100200789
003000789
897897789
040006789
500010789
978978789
000300789
004005789
789789789

Then just use F3 and F4 to find the answer.
The right puzzles should be got step by SE.
If SE tell you "The value 7 appears more than once in the same block." ,it is said the puzzle can't be complete.

Then I use the top puzzle:

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100200 003000 040006 500010 000300 004005

the answer is

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156234 423651 341526 562413 615342 234165

Second I cancel a number of "4" at R8

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100200 003000 040006 500010 000300 000005

After F3,F4 many times
SE tell me R7C6 and R8C4 can't put in any number, and

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154263 623154 241536 536412 415320 362045

Why this condition will happen?

[Pat]

your first puzzle

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1..2..789
..3...789
897897789

.4...6789
5...1.789
978978789

...3..789
..4..5789
789789789

has exactly one answer


by removing the clue r8c3 = 4
you got a puzzle with two answers

SuDoku Explainer assumes Uniqueness-Of-Answer
and thus makes an incorrect exclusion
(excluding 6 at r7c12)
- which kills both answers

this is the second answer -

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154263
623154

241536
536412

465321
312645

[Eioru]

Code: Select all

...2.1..3     ...2....3
...7.5...     ...7.5...
..3...9..     ..3...9..
58.....62     58.....62
.........     .........
76.....58     76.....58
..1...4..     ..1...4..
...6.9...     ...6.9...
2..4.8..9     2..4.8..9

SE=7.2

but when take 1 from R1C6 (Right puzzle) SE=6.6.

[wintder]

That is a funny one! The one added removes a potential Uniqueness move that otherwise requires a forcing chain or two.

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.-------------------.------------------.------------------.
| 68-14  1457  5678 | 2     9     14   | 568   1478  3    |
| 14689  1249  68   | 7     3     5    | 268   1248  16   |
| 14     257   3    | 8     6     14   | 9     27    57   |
:-------------------+------------------+------------------:
| 5      8     49   | 19    47    37   | 13    6     2    |
| 13     13    2    | 5     8     6    | 7     9     4    |
| 7      6     49   | 19    24    23   | 13    5     8    |
:-------------------+------------------+------------------:
| 689    579   1    | 3     257   27   | 4     278   567  |
| 348    3457  578  | 6     1257  9    | 258   12378 157  |
| 2      357   567  | 4     157   8    | 56    137   9    |
'-------------------'------------------'------------------'

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...2.1..3     
...7.5...     
..3...9..     
58.....62     
.........     
76.....58     
..1...4..     
...6.9...     
2..4.8..9


[daj95376]

Well, this opens up an interesting question. Does anyone have an example of a solution where the vertices of a UR pattern consist of just two values? (Of course, one of the vertices must be a given.)

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 *-----------------------*
 | . 1 . | . . . | . 2 . |
 | . . . | . . . | . . . |
 | . 2 . | . . . | . 1 . |
 |-------+-------+-------|
 | . . . | . . . | . . . |
 | . . . | . . . | . . . |
 | . . . | . . . | . . . |
 |-------+-------+-------|
 | . . . | . . . | . . . |
 | . . . | . . . | . . . |
 | . . . | . . . | . . . |
 *-----------------------*


[udosuk]

This phenomenon has popped up time and time again, such as in the following thread more than a year ago:

http://forum.enjoysudoku.com/viewtopic.php?t=3907

So in other words, we have the following Uniqueness Paradox:

Uniqueness Paradox

If uniqueness is not guaranteed, then a Sudoku puzzle always becomes easier if you add one or more initial givens.

However, if uniqueness can be assumed, then it's possible for a Sudoku puzzle to have a higher difficulty if you add one or more initial givens.

How's that sound?

[Smythe Dakota]

Well, suppose you give someone a puzzle with no 4's and no 7's, and tell him the solution is unique. If he believes you, he'll immediately conclude there's no solution, because if there were, there would be a second solution just by replacing all 4's with 7's and vice versa.

It's not so paradoxical. It's just that, with uniqueness logic, you're outside the realm of ordinary reasoning, and into the realm of meta-reasoning.

Bill Smythe