## Sudoku's strange ~~

Everything about Sudoku that doesn't fit in one of the other sections

### Sudoku's strange ~~

I use SE to find 6x6 puzzle:
Code: Select all
`000000789000000789789789789000000789000000789897897789000000789000000789978978789`

Then type in 1~6 at 0.
like

Code: Select all
`100200789003000789897897789040006789500010789978978789000300789004005789789789789`

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:
Code: Select all
`100200 003000 040006 500010 000300 004005`

Code: Select all
`156234 423651 341526 562413 615342 234165`

Second I cancel a number of "4" at R8
Code: Select all
`100200 003000 040006 500010 000300 000005`

After F3,F4 many times
SE tell me R7C6 and R8C4 can't put in any number, and
Code: Select all
`154263 623154 241536 536412 415320 362045`

Why this condition will happen?
Eioru

Posts: 182
Joined: 16 August 2006

Code: Select all
`1..2..789..3...789897897789.4...67895...1.789978978789...3..789..4..5789789789789`

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

and thus makes an incorrect exclusion
(excluding 6 at r7c12)

this is the second answer -
Code: Select all
`154263623154241536536412465321312645`

Pat

Posts: 3637
Joined: 18 July 2005

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.
Eioru

Posts: 182
Joined: 16 August 2006

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

Code: Select all
`.-------------------.------------------.------------------.| 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    |'-------------------'------------------'------------------'`

Code: Select all
`...2.1..3     ...7.5...     ..3...9..     58.....62     .........     76.....58     ..1...4..     ...6.9...     2..4.8..9`
wintder

Posts: 297
Joined: 24 April 2007

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.)

Code: Select all
` *-----------------------* | . 1 . | . . . | . 2 . | | . . . | . . . | . . . | | . 2 . | . . . | . 1 . | |-------+-------+-------| | . . . | . . . | . . . | | . . . | . . . | . . . | | . . . | . . . | . . . | |-------+-------+-------| | . . . | . . . | . . . | | . . . | . . . | . . . | | . . . | . . . | . . . | *-----------------------*`
daj95376
2014 Supporter

Posts: 2624
Joined: 15 May 2006

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:

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?
udosuk

Posts: 2698
Joined: 17 July 2005

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
Smythe Dakota

Posts: 546
Joined: 11 February 2006