Proof of Super Bowl Sudoku


The following is an illustrated proof for the Tough Sudoku of February 5, 2007. Since this is Super Bowl Sunday where I live, I may have easily missed something(s). Regardless, the proof below has one very interesting step. Probably, it should be tackled either before the game, or perhaps much after the game. This is not a proof to be considered when one is, well, containing proof.

Since this proof uses a Y wing style plus a varietly of other techniques, you may need to refer to previous blog pages to understand this proof. Links to these pages are found to the right, under Previous Entries.

Puzzle at start


PUzzle start

A few Unique Possibilities:

  • h5 = 3% box
  • i4 = 8% box
  • h1 = 8% box & column
  • h9 = 6% column
Unique Possibilities get the puzzle to 26 cells solved. (UP 26)



Hidden Pair 13


Hidden pair 13 at UP 26

The highlit cells force

  • Hidden Pair 13 at i79 forbids:
    • i7=4
    • i9=5
    • g78=1
This solves one more cell:
  • g8 = 5% box
The puzzle is now at 27 cells solved. (UP 27)



Locked 4's - Twice


Two sets of Locked 4's

Illustrated to the left are two sets of Locked 4's:

  • Locked 4's at i23
    • forbids gh2=4
  • Locked 4's at g456
    • forbids g27=4



Locked 5's


Locked 5's and then Hidden Pair 45

  • Locked 5's at a13
    • forbids c23=5
If you compare the last two illustrated forbiddings, you should also see:
  • Hidden Pair 45 at fi2
    • forbids f2=12



Hidden Pair 13


Hidden Pair 13

Illustrated perhaps poorly on the left, note that 1 and 3 are locked into box e2 at cells de1.

  • Hidden pair 13 at de1
    • forbids b1=1
    • forbids de1=257



Locked 7's - Twice


Two instances of Locked 7's

Some potential 7's can be eliminated:

  • Locked 7's at de3
    • forbids ac3=7
  • Locked 7's at ac9
    • forbids a7=7



Naked Quad 2589 equivalent to Hidden Triple 237


Naked Quad - Hidden Triple

Illustrated to the left is the naked quad 2589 in column c. As noted in previous blog pages, if there is a naked set, there is also a hidden set, thus we have alternatively a hidden triple in column c at c289

  • Quad 2589 at c3456
    • forbids c2=29
    • forbids c8=89
    • forbids c9=29



Locked 2's - Twice


Locked 2's two instances

  • Locked 2's at def3
    • forbids abc3=2
  • Then, Locked 2's at c56
    • forbids a6b5=2



Wrap around Y wing style


Almost Hidden Pair 48 in a chain

This Forbidding Chain is a standard wrap around Y wing style. Looking for easy Y wing style eliminations like this simplifies many puzzles.

Key:

  • Black containers are strong sets
  • Black lines are strong links
  • Red lines are weak links
  • a6=8 == a6=4 -- b5=4 == b8=4 -- b8=8 == a78=8
    • forbids b8 = 19
    • forbids a3=8

An alternative name for the technique shown above has been recently defined in a Sudoku forum as Hub and Spoke. In that viewpoint:

  • Cell b8 is the hub
  • Strong 8's in box a8 are a spoke
  • Strong 4's in column b are another spoke
  • The Almost Locked Set, a6=48 is the rim
Of course, one can find this idea expressed in the blog page, Y wing styles, under my favorite type of Y wing style.



Another Hidden Pair 13


Hidden Pair 13

Illustrated to the left is the naked triple 489 in row 8, which of course also means there is a hidden pair 13 in row 8.

  • Hidden pair 13 at cd8
    • forbids d8=89



Naked Pair 13


Naked Pair 13

Some puzzles seem to have the same candidates interact with each other multiple times.

  • Naked pair 13 at d18
    • forbids d467=1
    • forbids d67=3


  • Naked Pair 28


    Pair 28

    Finally there seems to be some promise of actually solving some cells

  • Naked pair 28 at cd6
    • forbids ef6=2
    • forbids aef6=8
  • From this point, the puzzle cascades with either singletons in some container to the end.



    Solved Puzzle

    Done

    Proof in the usual style is omitted, as the Super Bowl partying is getting too close




    4 Comments
    Indicate which comments you would like to be able to see

    Boy did I take the wrong turn:

    a6=8 == a6=4 -- b5=4 == b8=4 (but then: ?!) -- h8=4 == h8=9 -- g7=9 == g7=7 -- g1=7 == g1=2 -- b2=2 == b2=6 -- b3=6 == {pair 89 at bc3}, forbids a3=8. Missing the wrap-around Y-wing style completely!

    Go Bears!
     |  |
    Hi Dave!
    I have been there!
    My 'best' work is done without the puzzle in front of me - not sure why that is the case.
     |  |
    lnvez hcqslz limbun dkcovj jfvp ctuji xldce
    06/Jun/07 4:57 PM
     |  |
    knztoc udvfh ashnpy dibnwqp panysljub gpxdveqcy agkjdhy http://www.zmgkpl.lzwdm.com
    06/Jun/07 4:58 PM
     |  |
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