# Steps to Solve Tough Sudoku of 1-Feb-2007 with Proof

The following is an illustrated proof for the Tough Sudoku of February 1, 2007. Since this proof uses coloring and a Y wing, 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:

• a5 = 1% box
• i5 = 2% box
Unique Possibilities get the puzzle to 25 cells solved. (UP 25)

### Puzzle at UP 25 ### Hidden Pair 28 Hidden Pairs are often easy to locate before entering the possibilities. The highit cells reveal:

• Hidden pair 28 at a23
• Forces a23=28
• Forbids a789=28

Now, a few Unique Possibilities:

• b3 = 4% box
• b6 = 6% cell
• e6 = 5% cell
• e7 = 6% cell
• a8 = 6% rcbox

### Possibility Matrix at UP 30 ### Locked 7's There are many possible steps to take at this point. I have chosen to only illustrate the easiest required steps (IMHO) to solve this puzzle

Illustrated here is:

• Locked 7's at ac1
• Forbids dgh1=7
Yielding one more Unique Possibility:
• d2=7% box & column

### Possibility Matrix at UP 31 ### Locked 9's Again, there are many possible steps to take at this point. As is often the case, the next two steps were available at puzzle start.

Illustrated here is:

• Locked 9's at c45
• Forbids c189=9
Yielding the next step.

### Coloring with 9's Key:

Black boxes =
coloring endpoints
Black lines =
Red line =
Yellow marks =
elimination targets

Illustrated here is coloring on 9's, as a forbidding chain on 9's:

• fc on 9's: d1 == a1 -- a9 == f9
• Forbids d8,f23=9

Yielding a few more Unique possibilites:

• d8 = 4% cell
• d7 = 2% cell
• c9 = 2% row, column & box
• f6 = 2% row, column & box
• d6 = 3% row & box
• d4 = 8% column & box
• g6 = 8% row & box

### Possibility Matrix at UP 38 Again, there are many possible steps to take at this point.

Instead of illustrating all of them, which would take some time, next I will show one step that unlocks the puzzle.

### Y wing at UP 38 Key as before. The three strong cells:

1. b2 = 39
2. f2=36
3. d1=69
Form the Y wing, with f2=36 as the vertex. Forbids a1=9.

The puzzle now unlocks with unique values in the cells to the end. (% cell).

### Solved Puzzle ### Proof

Here is the proof in my usual style:

1. Start at 23 filled - the given puzzle. Unique Possibilities to 25 filled. (UP 25).
2. Hidden pair 28 at a23 forbids a79=2, a78=8, a2=79, a3=479 UP 30
3. Locked 7's at ac1 forbids dgh1=7 UP 31
1. Locked 9's at c45 forbids c189=9
2. fc on 9's: d1 == a1 -- a9 == f9 forbids d8,f23=9 UP 38
4. Y wing b2=93, f2=36, d1=69 forbids a1=9 UP 81
• Sets: 2+1+1+2+3 = 9
• Max depth 3 at step 5
• Rating: 2(.01) + 2(.03) + .07 = .15

Find information about me, Steve, at the first page of this blog and My Page at sudoku.com.au. 