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 Sudoku Techniques.
Puzzle at 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
The highlit cells force
- Hidden Pair 13 at i79 forbids:
This solves one more cell:
The puzzle is now at 27 cells solved. (UP 27)
Locked 4's - Twice
Illustrated to the left are two sets of Locked 4's:
- Locked 4's at i23
- Locked 4's at g456
Locked 5's
If you compare the last two illustrated forbiddings, you should also see:
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
Some potential 7's can be eliminated:
- Locked 7's at de3
- Locked 7's at ac9
Naked Quad 2589 equivalent to Hidden Triple 237
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 at def3
- Then, Locked 2's at c56
Wrap around Y wing style
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
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.
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
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
Proof in the usual style is omitted, as the Super Bowl partying is getting too close