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Making a puzzle harder by adding a number

Everything about Sudoku that doesn't fit in one of the other sections
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Postby JPF » Mon Apr 24, 2006 9:13 pm

ravel wrote:I get one unique solution, 2 multiple and the rest 0 solutions for different numbers for x.

That's the point.
I gave you the assurance of a unique solution.
So, you don't need the exact value of x, because there is only one x giving 1 solution.
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Postby JPF » Mon Apr 24, 2006 10:19 pm

BTW, 2 numbers (maybe more ?) can be repaced by x :
Code: Select all
 6 . . | 3 1 9 | . . x
 . 1 . | 2 . 4 | . 5 .
 . . . | . . . | . . .
-------+-------+-------
 1 8 . | . . . | . 6 9
 7 . . | . 2 . | . . 1
 2 4 . | . . . | . 7 5
-------+-------+-------
 . . . | . . . | . . .
 . 6 . | 1 . 8 | . 3 .
 x . . | 7 5 3 | . . 6



How does it work with the usual solving techniques ?
How many numbers can we replace by x ?

JPF
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Postby ab » Mon Apr 24, 2006 10:19 pm

rep'nA wrote:...I find no technique in Sudoku more elegant than uniqueness reductions.


I'm educated to degree level in maths, but couldn't disagree with you more! I only like to use techniques that rely on logic and not the assumption that the puzzle has a unique solution.

If you create a sudoku by hand you can't use techniques that rely on the uniqueness of the solution to build your puzzle, but you can use any technique that doesn't rely on uniqueness.

I do like JPF's puzzle though:)
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Postby vidarino » Tue Apr 25, 2006 7:28 am

ab wrote:If you create a sudoku by hand you can't use techniques that rely on the uniqueness of the solution to build your puzzle, but you can use any technique that doesn't rely on uniqueness.


Well, that's because you don't have a guarantee on uniqueness while you're creating the puzzle, and hence can not use techniques that rely on it. (Reaching that point (uniqueness) is the whole goal of the creation process, even...:) )

However, when the puzzle has been created, and its uniqueness verified, I have no problems utilizing that fact while solving it. I tell myself that "if that cell isn't N the puzzle would be unsolvable", and since I know it is solvable, ding.:)
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Postby ravel » Tue Apr 25, 2006 7:53 am

JPF,

i have 2 problems with the puzzles with x-candidates.

The one is that i only would have the chance to find all right numbers without t&e, if (all combinations of) wrong numbers would give 0 solutions. Then it would be very similar to normal sudoku.

The second is, that a unique puzzle i got from your sudoku above is so hard that i would solve it using an AUR.
[Edit: This is not the case, i made a mistake.]
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Postby Smythe Dakota » Tue Apr 25, 2006 11:29 am

vidarino wrote:.... However, when the puzzle has been created, and its uniqueness verified, I have no problems utilizing that fact while solving it. I tell myself that "if that cell isn't N the puzzle would be unsolvable", and since I know it is solvable, ding.:)

Is it not also true (at least with Pappocom-published puzzles) that minimality (non-redundancy of the clue set) ia assured? If so, how do you feel about using THAT fact to help solve a puzzle?

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Postby vidarino » Tue Apr 25, 2006 11:58 am

Smythe Dakota wrote:Is it not also true (at least with Pappocom-published puzzles) that minimality (non-redundancy of the clue set) ia assured? If so, how do you feel about using THAT fact to help solve a puzzle?


Interesting idea. I don't think there have been found any techniques that uses minimality as a base for a deduction, though. (But I'd be delighted to be proven wrong.)

I can't comment on the minimality of Pappocom's puzzles, but not too many published puzzles are fully minimal, only minimal within the symmetric pattern. (I.e. individual clues may or may not be redundant, but not a whole orbit.)

However, I wouldn't have any political reasons not to use that information, should it be presented to me.:)
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Postby RW » Tue Apr 25, 2006 12:45 pm

ab wrote:
rep'nA wrote:
...I find no technique in Sudoku more elegant than uniqueness reductions.


I'm educated to degree level in maths, but couldn't disagree with you more! I only like to use techniques that rely on logic and not the assumption that the puzzle has a unique solution.


I seriously don't understand why this conversation is neccessary. In every source I can find, the basic rules for a sudoku are:

1. Every number 1-9 has to appear once in every row, column and box
2. There is only one solution

Why would it be less logical to assume the second rule to be true than to assume the first rule is true? If you play by the rules any technique that assumes an unique solution is as logical as any technique that assumes that every number appears once in every row. Sure, you can construct a 9x9 grid with multiple solutions that would satisfy the first rule of a sudoku puzzle, but everybody on this forum agrees that such a grid cannot be called a sudoku, it is something else. I do not care if the technique doesn't apply in "something else", as long as it is a valid logical technique in every sudoku puzzle.

Smythe Dakota wrote:Is it not also true (at least with Pappocom-published puzzles) that minimality (non-redundancy of the clue set) ia assured? If so, how do you feel about using THAT fact to help solve a puzzle?


Very interesting idea, could develop into something nice. I would absolutely use such a technique if the minimality was assured. If the creator provides a fact about a puzzle, why should I question that and not assume it to be true?

RW
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Postby TTHsieh » Sat Aug 02, 2008 2:20 pm

    Making a puzzle harder by adding a number into a diabolic cell (diabolic cell vs magic cell).
    here are some:
Code: Select all
________________________________________________________________________________________________

.....1.2.....3..45......6.71....57..48..2..96..96....35.8......32..4.....7.8..... # 4.5/2.3/2.3
.....1.23....4..56......7.81....68..53..2..97..97....46.3......42..5.....8.3..... # 7.2/2.3/2.3
        ^
..12..3..2..4.......561..7.68.........2.4.9.........53.3..521.......4..8..9..15.. # 4.5/2.0/2.0
..12..3..2..4.......561..7.68........52.4.9.........53.3..521.......4..8..9..15.. # 9.0/1.2/1.2
                                     ^
....1.2...34..56..7.......5..17.....8..651..4.....25..4.......3..72..19...3.6.... # 4.6/2.8/2.6
....1.2...34..56..7.......5..17.....8..651..4.....25..4.......3..723.19...3.6.... # 7.2/1.5/1.5
                                                                   ^
...1...23...4.56.....72..8..7......842.....355......9..8..71.....76.9...63...2... # 4.7/2.6/2.6
...1...23...4.56.....72..8..7......842.....355......9..8..71.5...76.9...63...2... # 5.6/1.2/1.2
                                                             ^
..12.....34.5.6.....6.7...54....89...9.....1...87....28...3.4.....8.7.21.....23.. # 4.7/3.6/3.0
..12.....34.5.6..8..6.7...54....89...9.....1...87....28...3.4.....8.7.21.....23.. # 6.6/1.2/1.2
                 ^
..1.2...34..5...6......74..1....86....9...7....87....9..28......9...2..15...3.9.. # 4.7/2.8/2.8
..1.2...34..5...6......74..1....86....9...7....87....9..28....6.9...2..15...3.9.. # 7.0/2.8/2.8
                                                              ^
.123.......4..5..65.....7...8.9.32.............18.2.9...9.....74..7..5.......463. # 4.7/2.0/2.0
.123.7.....4..5..65.....7...8.9.32.............18.2.9...9.....74..7..5.......463. # 7.1/2.0/2.0
     ^
.1......23..4..56..4...7.....7..1.5..8.5.4.2..6.7..9.....9...3..28..6..96......8. # 4.7/2.8/2.6
.1....4.23..4..56..4...7.....7..1.5..8.5.4.2..6.7..9.....9...3..28..6..96......8. # 7.2/2.8/2.6
      ^
12....3..4....5.67..7....1......8..4...723...2..5......8....9..73.8....6..5....81 # 4.7/2.0/2.0
12....3..4....5.67..7....1......8..4...723.9.2..5......8....9..73.8....6..5....81 # 7.3/2.0/2.0
                                           ^
1......23...4..5.6...5.34..7....18...2.....6...93....2..39.6...4.7..8...59......8 # 4.7/4.7/2.6
15.....23...4..5.6...5.34..7....18...2.....6...93....2..39.6...4.7..8...59......8 # 8.3/1.2/1.2
 ^
12....3..4....5.67..7....1......8..4...723...2..5......8....9..73.8....6..5....81 # 4.7/2.0/2.0
12....3..4....5.67..7....1......8..4...7236..2..5......8....9..73.8....6..5....81 # 8.5/2.0/2.0
                                          ^
..1..2.3.....3..4....5..67.2..8.1.....4...8.....4.5..1.89..4....7..5.....6.9..5.. # 5.0/1.2/1.2
1.2..3.4.....4..5....6..71.3..8.2.....5...8.....5.6..2.89..5....1..6.....7.9..6.. # 5.7/1.2/1.2
^
..1..2..3.4...3..5...6..17..84..5...............1..42..29..1...4..7...6.6..4..5.. # 5.2/1.2/1.2
..1..2..3.4...3..56..7..18..94..5...............1..42..26..1...4..8...7.7..4..5.. # 5.6/1.2/1.2
                  ^
..1...2.....3.4...5...1...6.3.5.7.6...5...8...4.8.3.5.7...2...9...4.8.....6...1.. # 5.2/2.6/2.6
..1...2.....3.4...5...1...6.3.5.7.6...5...8..14.8.3.5.7...2...9...4.8.....6...1.. # 7.3/1.5/1.5
                                             ^
....1.2...34....1.5..4....3.4.5....1..6...3..3....2.6.6....7..5.8....17...2.8.... # 5.6/4.0/3.2
....1.2...34....1.5..4....3.4.5....1..6...3..3...72.6.6....7..5.8....17...2.8.... # 6.6/3.8/2.6
                                                 ^
..1...2.....3.4...5...6...7.8.4.3.6...4...8...2.6.8.3.2...3...1...8.9.....9...5.. # 5.6/3.4/3.0
..1..23.....4.5...6...7...2.8.5.4.7...5...8...3.7.8.4.3...4...1...8.9.....9...6.. # 7.1/3.4/3.0
     ^
.1.2..34...4.5......61....7..7....8.9.......1.8....9..2....54......7.8...45..6.9. # 5.6/3.0/2.6
.1.2..34...4.5......614...7..7....8.9.......1.8....9..2....54......7.8...45..6.9. # 7.2/3.0/2.6
                      ^
.1.2....3..4..3.2.....4.1...5...6..47.......28..9...1...3.5.....2.8..6..5....1.7. # 5.6/3.6/2.6
12.3....4..5..4.3.....5.2...6...7..58.......39..1...2...4.6.....3.9..7..6....2.8. # 7.3/2.3/2.3
^
..1...2.....3.4...3...5...6.7.5.8.6...8...9...3.2.7.8.4...7...5...1.5.....2...3.. # 5.7/2.5/2.5
..1...2.....3.4...3...5...6.7.5.8.6...8...9...3.2.7.8.4...7...5...1.5.....24..3.. # 6.6/2.3/2.3
                                                                           ^
1...2...3.3.....4...5.6.7.....2.4...8.9...4.7...8.5.....6.1.8...7.....2.3...5...6 # 5.9/1.5/1.5
1...2...3.3.....4...5.6.7.....2.4...8.9...4.7...8.5.....691.8...7.....2.3...5...6 # 6.8/1.5/1.5

.1..2..34...1.......567.....8....94...3...2...91....6.....457.......9...82..1..9. # 6.6/2.3/2.3
.1..2..34...1.4.....567.....8....94...3...2...91....6.....457.......9...82..1..9. # 7.2/2.0/2.0
              ^
1....23...4..5......54...6...6..1..72.......13..2..6...8...45......8..9...95....8 # 6.6/4.5/2.6
1....234..4..5......54...6...6..1..72.......13..2..6...8...45......8..9...95....8 # 7.8/1.2/1.2
       ^
1......2......34.5.34......4...67.8.3...8...1.8.39...6......17.6.98......5......2 # 6.6/2.6/2.6
1......2......34.5.34......4...67.8.3...8...1.8.39..46......17.6.98......5......2 # 8.3/2.5/2.5
                                                    ^
.1.2..3...45.3......6..7....6...4.5...8...7...2.1...6....9..1......5.67...2..3.8. # 6.7/3.4/2.8
.1.2..3...45.3......6..7....6...4.5...8...7...2.1...6....9..1......5.67...2..398. # 7.1/1.5/1.5
                                                                              ^
1....2.3..4.........564...7..81...5.5.......8.2...91..9...162.........9..8.9....5 # 6.7/4.5/3.4
1....2.3..4.........564...7..81...5.5.......8.2.5.91..9...162.........9..8.9....5 # 7.2/1.2/1.2
                                                ^
...1....23..4...56.....78...3.7...4.9.......7.6...2.3...59.....67...5..12....6... # 6.7/6.6/3.4
...1....23..4...56.....78...3.7...4.9......67.6...2.3...59.....67...5..12....6... # 7.3/1.2/1.2
                                           ^
1.2..........3.4...4..56.7..8.9....3..3...5..2....3.6..9.61..5...4.8..........6.8 # 6.7/3.2/3.2
123..........4.5...5..26.7..8.9....4..4...2..3....4.6..9.61..2...5.8..........6.8 # 7.6/1.2/1.2
 ^
...1.2..3.4..5....6..7..8.......5.6.3.4...5.7.2.9.......7..3..8....8..1.9..5.6... # 6.7/4.5/2.6
...1.2..3.4..5....6..7..8.......5.6.3.4...5.7.2.9.......7..3..84...8..1.9..5.6... # 8.5/2.3/2.3
                                                               ^

TTHsieh
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Postby daj95376 » Sat Aug 02, 2008 2:51 pm

You did more than add one cell in these examples.

Code: Select all
.....1.2.....3..45......6.71....57..48..2..96..96....35.8......32..4.....7.8..... # 4.5/2.3/2.3
.....1.23....4..56......7.81....68..53..2..97..97....46.3......42..5.....8.3..... # 7.2/2.3/2.3
        ^
..1..2.3.....3..4....5..67.2..8.1.....4...8.....4.5..1.89..4....7..5.....6.9..5.. # 5.0/1.2/1.2
1.2..3.4.....4..5....6..71.3..8.2.....5...8.....5.6..2.89..5....1..6.....7.9..6.. # 5.7/1.2/1.2
^
..1..2..3.4...3..5...6..17..84..5...............1..42..29..1...4..7...6.6..4..5.. # 5.2/1.2/1.2
..1..2..3.4...3..56..7..18..94..5...............1..42..26..1...4..8...7.7..4..5.. # 5.6/1.2/1.2
                  ^
..1...2.....3.4...5...6...7.8.4.3.6...4...8...2.6.8.3.2...3...1...8.9.....9...5.. # 5.6/3.4/3.0
..1..23.....4.5...6...7...2.8.5.4.7...5...8...3.7.8.4.3...4...1...8.9.....9...6.. # 7.1/3.4/3.0
     ^
.1.2....3..4..3.2.....4.1...5...6..47.......28..9...1...3.5.....2.8..6..5....1.7. # 5.6/3.6/2.6
12.3....4..5..4.3.....5.2...6...7..58.......39..1...2...4.6.....3.9..7..6....2.8. # 7.3/2.3/2.3
^
1.2..........3.4...4..56.7..8.9....3..3...5..2....3.6..9.61..5...4.8..........6.8 # 6.7/3.2/3.2
123..........4.5...5..26.7..8.9....4..4...2..3....4.6..9.61..2...5.8..........6.8 # 7.6/1.2/1.2
 ^
_______________________________________________________________________________________________
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Postby TTHsieh » Sat Aug 02, 2008 3:17 pm

Sorry, permutation error.
Code: Select all
.....1.2.....4..56......7.81....68..53..2..97..97....46.3......42..5.....8.3..... # 4.5/2.3/2.3
.....1.23....4..56......7.81....68..53..2..97..97....46.3......42..5.....8.3..... # 7.2/2.3/2.3
        ^
..2..3.4.....4..5....6..71.3..8.2.....5...8.....5.6..2.89..5....1..6.....7.9..6.. # 5.0/1.2/1.2
1.2..3.4.....4..5....6..71.3..8.2.....5...8.....5.6..2.89..5....1..6.....7.9..6.. # 5.7/1.2/1.2
^
..1..2..3.4...3..5...7..18..94..5...............1..42..26..1...4..8...7.7..4..5.. # 5.2/1.2/1.2
..1..2..3.4...3..56..7..18..94..5...............1..42..26..1...4..8...7.7..4..5.. # 5.6/1.2/1.2
                  ^
..1...3.....4.5...6...7...2.8.5.4.7...5...8...3.7.8.4.3...4...1...8.9.....9...6.. # 5.6/3.4/3.0
..1..23.....4.5...6...7...2.8.5.4.7...5...8...3.7.8.4.3...4...1...8.9.....9...6.. # 7.1/3.4/3.0
     ^
.2.3....4..5..4.3.....5.2...6...7..58.......39..1...2...4.6.....3.9..7..6....2.8. # 5.6/3.6/2.6
12.3....4..5..4.3.....5.2...6...7..58.......39..1...2...4.6.....3.9..7..6....2.8. # 7.3/2.3/2.3
^
1.3..........4.5...5..26.7..8.9....4..4...2..3....4.6..9.61..2...5.8..........6.8 # 6.7/3.2/3.2
123..........4.5...5..26.7..8.9....4..4...2..3....4.6..9.61..2...5.8..........6.8 # 7.6/1.2/1.2
 ^
________________________________________________________________________________________________

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Postby TTHsieh » Sat Aug 02, 2008 5:47 pm

more examples.
Code: Select all
.1.2....4....56.1.6.....3..7..6...8...2...9...4...3..2..5.....8.9.86....4....5.7. # 6.9/6.6/6.6
.1.23...4....56.1.6.....3..7..6...8...2...9...4...3..2..5.....8.9.86....4....5.7. # 7.1/6.6/6.6
    ^
...1....2....3.45......2.67.8...7..95.......61..8...3.81.5......67.2....4....9... # 7.0/4.2/2.6
...1....2....3.45......2.67.83..7..95.......61..8...3.81.5......67.2....4....9... # 7.1/4.2/2.6
                             ^
.2.3....4..5..4.3.....6.2...7...8..96.......39..1...2...4.7.....3.8..1..7....2.5. # 7.0/4.5/2.6
12.3....4..5..4.3.....6.2...7...8..96.......39..1...2...4.7.....3.8..1..7....2.5. # 7.3/2.3/2.3
^
.1.....2..34.1....5.67..........238.1.......4.735..........87.2....4.61..9.....4. # 7.1/7.0/3.4
.1...5.2..34.1....5.67..........238.1.......4.735..........87.2....4.61..9.....4. # 7.2/7.0/3.4
     ^
..1...2.....3.4...5...6...7.6.4.8.2...2...9...3.6.2.8.7...8...1...1.6.....9...3.. # 7.1/4.6/2.6
..1...2.....3.4...5...6...7.6.4.8.2...25..9...3.6.2.8.7...8...1...1.6.....9...3.. # 7.4/3.2/2.6
                                       ^
..1....2....32...45....63..6..7..8...4.....1...9..8..5..64....29...57....8....7.. # 7.1/4.5/3.0
..1....2...732...45....63..6..7..8...4.....1...9..8..5..64....29...57....8....7.. # 8.2/2.3/2.3
           ^
1..2.......3..1...2.4.561........53.7.......6.89........289.6.5...7..4.......5..9 # 7.2/4.6/2.6
1..2...6...3..1...2.4.561........53.7.......6.89........289.6.5...7..4.......5..9 # 7.3/1.2/1.2
       ^
..12....32....3.4..5..4......6..7..8..8...6..7..4..1......9..8..3.5....26....19.. # 7.2/4.6/2.8
..12....32....3.4..5..4......6..7..8..8...6..7..46.1......9..8..3.5....26....19.. # 8.3/1.2/1.2
                                                 ^
1..2..3....4..3.5.....1...4.6...78...5.....9...29...7.6...3.....9.7..2....3..6..8 # 7.2/4.7/3.0
1..2..3....4..3.5.....1...4.6...78...5.....9...29...7.6...3..1..9.7..2....3..6..8 # 8.3/2.3/2.3
                                                             ^
________________________________________________________________________________________________

TTHsieh
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Postby JPF » Sat Aug 02, 2008 6:46 pm

I suppose that in all your examples, the lower ER uses at least one of the "Unique Solution" techniques.

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Postby daj95376 » Sat Aug 02, 2008 6:57 pm

[Withdrawn: Uniqueness comment incorrect.]
Last edited by daj95376 on Sun Aug 03, 2008 4:18 pm, edited 1 time in total.
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Postby TTHsieh » Sat Aug 02, 2008 11:03 pm

  • Up to now, "Unique Solution" techniques seem right.
  • daj95376, JPF, thanks.
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