Partial Sudoku

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

Partial Sudoku

Postby r.e.s. » Thu Oct 27, 2005 11:41 pm

Help! I partially solved a sudoku and saved the candidate grid at that stage. But then a gremlin:D blanked every cell that contained only one digit, leaving the following grid ...
Code: Select all
                38     | 368           36     |                   
  368    36            |        38     236    | 19     15     19 
                       |                      |                   
  ---------------------+----------------------+-------------------
  49            259    | 569           69     | 69            479
  1349   34            |        38            |        18     1489
  139    37     359    | 35689         369    | 169           1789
  ---------------------+----------------------+-------------------
                       |                      |                   
  3689   236    2389   | 39                   |        18     18 
  3489   34     389    | 39                   |                   

What is the solution to the original sudoku?
r.e.s.
 
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Joined: 31 August 2005

Postby Lardarse » Fri Oct 28, 2005 5:45 am

Ooh... This loks like a nice puzzle...
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Postby emm » Fri Oct 28, 2005 5:48 am

You naughty man - I had work to do this afternoon - but this was more fun!:D
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Postby MCC » Sat Oct 29, 2005 3:43 pm

r.e.s.

Here are the placements you've lost.

Code: Select all
5 1 . | . 9 . | 7 4 2
. . 4 | 7 . . | . . .
2 9 7 | 1 5 4 | 8 6 3
-----------------------
. 8 . | . 1 . | . 3 .
. . 6 | 2 . 7 | 5 . .
. . . | . 4 . | . 2 .
-----------------------
7 5 1 | 4 2 8 | 3 9 6
. . . | . 7 5 | 4 . .
. . . | . 6 1 | 2 7 5



mcc
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Postby tso » Sat Oct 29, 2005 4:56 pm

I like this rare variation.
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Postby r.e.s. » Sun Oct 30, 2005 10:30 pm

I was a bit surprised that by hand these can be rather tediously difficult to make so as to have enough blanked-out cells to be interesting, yet not so many that the resulting "partial candidate grid" no longer has a unique solution. (If it does have a unique solution, it's reasonable to call the partial candidate grid a "partial sudoku", since its solution is the same as that of the original sudoku.) As the solving of a given original sudoku proceeds step-by-step, the corresponding partial candidate grids will eventually cease having a unique solution -- for some sudokus, this occurs at the very start (so there is no "partial sudoku" possible at all), and for many others it occurs before enough cells get solved to provide enough blanks for an interesting puzzle.

On the other hand, it should be fairly easy to produce this type of puzzle as part of a standard sudoku solver program ... At any stage of the step-by-step solving, the program could check whether the partial candidate grid (with all single-candidate cells blanked) has a unique solution, and if so to offer the "partial sudoku" as an optional puzzle.
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