* Cell r3c5 is the only valid location in column 5 for digit 5

- Removing candidate 5 from r3c1 r3c2

* Cell r8c4 is the only valid location in row 8 for digit 9

* Cell r7c5 is the only valid location in block 8 for digit 7

- Removing candidate 7 from r7c2 r7c3 r4c5 r6c5

Box/Line: In row 4, the only valid positions for digit 7 are r4c2 r4c3

- Removing candidate 7 from block 4 r5c1 r5c3 r6c1 r6c2

## All Logic Strategies exhausted at top level. Starting new branch level 1.

## Choosing cell having fewest candidates: r5c3: [5,6]

## Level 1, trying r5c3=5: Leads to contradiction. Backtracking...

## Level 1, trying r5c3=6: Leads to solution.

* Cell r5c3=6 by trial & error

Sparse Subset: In row 5, the digits 3 7 8 must go in cells r5c4 r5c6 r5c7 (unspecified order)

These digits can then be eliminated from the other cells in row 5

- Removing candidate(s) 3 from cell r5c1

- Removing candidate(s) 3 from cell r5c9

## All Logic Strategies exhausted at level 1. Starting new branch level 2.

## Choosing cell having fewest candidates: r5c6: [3,8]

## Level 2, trying r5c6=3: Leads to solution.

* Cell r5c6=3 by trial & error

* Cell r5c7=7 by simple elimination.

* Cell r5c4=8 by simple elimination.

* Cell r2c4 is the only valid location in column 4 for digit 3

- Removing candidate 3 from r2c7 r2c9

* Cell r6c4 is the only valid location in row 6 for digit 7

X-wing: In columns 1 & 7, digit 3 must go in row 6 or 9

Therefore candidate 3 can be removed from all other cells in rows 6 & 9

Removing candidate 3 from r6c2 r9c2 r6c8 r9c8

## All Logic Strategies exhausted at level 2. Starting new branch level 3.

## Choosing cell having fewest candidates: r5c1: [5,9]

## Level 3, trying r5c1=5: Leads to contradiction. Backtracking...

## Level 3, trying r5c1=9: Leads to solution.

* Cell r5c1=9 by trial & error

* Cell r5c9=5 by simple elimination.

* Cell r7c8 is the only valid location in column 8 for digit 5

- Removing candidate 5 from r7c2 r7c3

* Cell r7c3 now has only one possible value: 4

- Removing candidate 4 from r7c2 r7c6 r1c3 r2c3 r9c2

* Cell r7c6 is the only valid location in row 7 for digit 6

- Removing candidate 6 from r4c6 r8c6 r9c5

* Cell r9c4 is the only valid location in row 9 for digit 4

- Removing candidate 4 from r3c4

* Cell r3c4 now has only one possible value: 1

- Removing candidate 1 from r3c7 r3c8 r1c5 r1c6 r2c6

Sparse Subset: In column 2, the digits 2 3 5 7 8 must go in cells r4c2 r6c2 r7c2 r8c2 r9c2 (unspecified order)

These digits can then be eliminated from the other cells in column 2

- Removing candidate(s) 2 7 8 from cell r1c2

- Removing candidate(s) 2 8 from cell r3c2

In column 2, the only valid positions for digit 8 are r7c2 r8c2 r9c2

- Removing candidate 8 from block 7 r8c1 r9c1

## All Logic Strategies exhausted at level 3. Starting new branch level 4.

## Choosing cell having fewest candidates: r9c5: [1,8]

## Level 4, trying r9c5=1: Leads to solution.

* Cell r9c5=1 by trial & error

* Cell r8c6=8 by simple elimination.

* Cell r4c6 is the only valid location in column 6 for digit 1

- Removing candidate 1 from r4c8 r4c9

* Cell r1c5 is the only valid location in column 5 for digit 8

- Removing candidate 8 from r1c1 r1c8 r1c9

## All Logic Strategies exhausted at level 4. Starting new branch level 5.

## Choosing cell having fewest candidates: r1c1: [2,7]

## Level 5, trying r1c1=2: Leads to contradiction. Backtracking...

## Level 5, trying r1c1=7: Leads to solution.

* Cell r1c1=7 by trial & error

## All Logic Strategies exhausted at level 5. Starting new branch level 6.

## Choosing cell having fewest candidates: r1c2: [4,9]

## Level 6, trying r1c2=4: Leads to contradiction. Backtracking...

## Level 6, trying r1c2=9: Leads to solution.

* Cell r1c2=9 by trial & error

* Cell r3c2=4 by simple elimination.

* Cell r3c7=2 by simple elimination.

* Cell r3c1=8 by simple elimination.

* Cell r3c8=9 by simple elimination.

* Cell r8c9 is the only valid location in column 9 for digit 2

- Removing candidate 2 from r8c1 r8c2 r8c3

* Cell r1c6 is the only valid location in row 1 for digit 4

- Removing candidate 4 from r2c6

* Cell r2c6 now has only one possible value: 2

- Removing candidate 2 from r2c1 r2c3

* Cell r2c7 is the only valid location in row 2 for digit 4

* Cell r9c8 is the only valid location in column 8 for digit 8

- Removing candidate 8 from r9c2 r7c9

* Cell r9c2 now has only one possible value: 2

- Removing candidate 2 from r9c1 r4c2 r6c2

* Cell r6c2 now has only one possible value: 5

- Removing candidate 5 from r6c1 r8c2

* Cell r8c2 now has only one possible value: 7

- Removing candidate 7 from r8c3 r4c2

* Cell r8c3 now has only one possible value: 5

- Removing candidate 5 from r8c1 r2c3

* Cell r8c1 now has only one possible value: 6

- Removing candidate 6 from r8c7 r9c1

* Cell r8c7 now has only one possible value: 1

- Removing candidate 1 from r6c7

* Cell r9c1 now has only one possible value: 3

- Removing candidate 3 from r9c7 r6c1 r7c2

* Cell r9c7 now has only one possible value: 6

- Removing candidate 6 from r6c7

* Cell r6c7 now has only one possible value: 3

- Removing candidate 3 from r4c8 r4c9

* Cell r4c8 now has only one possible value: 6

- Removing candidate 6 from r4c5 r6c8

* Cell r4c5 now has only one possible value: 2

- Removing candidate 2 from r4c3 r6c5

* Cell r4c3 now has only one possible value: 7

* Cell r6c5 now has only one possible value: 6

* Cell r6c8 now has only one possible value: 1

- Removing candidate 1 from r1c8

* Cell r1c8 now has only one possible value: 3

- Removing candidate 3 from r1c9

* Cell r1c9 now has only one possible value: 1

- Removing candidate 1 from r1c3 r2c9

* Cell r1c3 now has only one possible value: 2

* Cell r2c9 now has only one possible value: 8

- Removing candidate 8 from r2c1

* Cell r2c1 now has only one possible value: 5

* Cell r4c9 now has only one possible value: 9

* Cell r6c1 now has only one possible value: 2

* Cell r7c2 now has only one possible value: 8

* Cell r2c3 now has only one possible value: 1

* Cell r4c2 now has only one possible value: 3

* Cell r7c9 now has only one possible value: 3

Summary (Combining Trial & Error with Logic Strategies):

792 684 531

561 392 478

843 157 296

437 521 869

916 843 725

258 769 314

184 276 953

675 938 142

329 415 687

Final Cell Values by Solve Order:

Initial (Clue) Values:

r1c4=6, r1c7=5, r2c2=6, r2c5=9, r2c8=7, r3c3=3, r3c6=7, r3c9=6, r4c1=4, r4c4=5, r4c7=8, r5c2=1, r5c5=4, r5c8=2, r6c3=8, r6c6=9, r6c9=4, r7c1=1, r7c4=2, r7c7=9, r8c5=3, r8c8=4, r9c3=9, r9c6=5, r9c9=7

Solved:

r3c5=5, r8c4=9, r7c5=7, *r5c3=6, *r5c6=3, r5c7=7, r5c4=8, r2c4=3, r6c4=7, *r5c1=9, r5c9=5, r7c8=5, r7c3=4, r7c6=6, r9c4=4, r3c4=1, *r9c5=1, r8c6=8, r4c6=1, r1c5=8, *r1c1=7, *r1c2=9, r3c2=4, r3c7=2, r3c1=8, r3c8=9, r8c9=2, r1c6=4, r2c6=2, r2c7=4, r9c8=8, r9c2=2, r6c2=5, r8c2=7, r8c3=5, r8c1=6, r8c7=1, r9c1=3, r9c7=6, r6c7=3, r4c8=6, r4c5=2, r4c3=7, r6c5=6, r6c8=1, r1c8=3, r1c9=1, r1c3=2, r2c9=8, r2c1=5, r4c9=9, r6c1=2, r7c2=8, r2c3=1, r4c2=3, r7c9=3

* Asterisk indicates trial & error assignment used when all logic strategies have been exhausted.

Deepest recursion: 8

Total steps including dead branches: 2047

Total patterns searched including dead branches: 67

Total patterns found including dead branches: 8078

Total patterns found resulting in candidate elimination including dead branches: 171

Unlimited depth search Backdoor values: r5c3=6 r5c6=3 r5c1=9 r9c5=1 r1c1=7 r1c2=9

Total solution time: 495.20 milliseconds