Example Sudoku - Hard Level - 27 Givens - Step-by-Step Solution

Every Sudoku we create has a unique solution which can be reached by logic alone. The difficulty of a puzzle is determined by the depth of logic required. Our puzzles never require "trial and error", which is easy for computers but tedious for people.

But you don't have to believe us! Every Sudoku puzzle we provide comes with its step-by-step solution, such as the hard example shown below. The step-by-step shows one way to solve puzzle using only logical reasoning. Naturally each puzzle can be solved in many different ways, but every way leads to the same solution.

With our step-by-step solutions, you can be confident that your readers will enjoy solving your Sudokus with pencil and paper, and will never be frustrated by logical dead ends.

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Step 0

Starting puzzle

Step 1

The number 3 does not yet appear in row A. Due to other 3s on the grid, the only place it can go is cell A9.

Step 2

The number 6 does not yet appear in row I. Due to other 6s on the grid, the only place it can go is cell I8.

Step 3

The number 3 does not yet appear in column 2. Due to other 3s on the grid, the only place it can go is cell H2.

Step 4

The number 9 does not yet appear in column 8. Due to other 9s on the grid, the only place it can go is cell H8.

Step 5

The number 7 is missing from box A7-C9 and its only possible position is cell C7.

Step 6

The number 6 is missing from row E and its only possible position is cell E6.

Step 7

Because of the number 6 just placed, the only position in row D for another 6 is cell D3.

Step 8

Because of the number 6 just placed, the only position in column 1 for another 6 is cell B1.

Step 9

Because of the number 6 just placed, the only position in row C for another 6 is cell C5.

Step 10

The number 4 is missing from row E and its only possible position is cell E4.

Step 11

Because of the number 4 just placed, the only position in row F for another 4 is cell F7.

Step 12

The number 8 does not yet appear in column 7. Due to other 8s on the grid, the only place it can go is cell D7.

Step 13

The number 5 is missing from box D7-F9 and its only possible position is cell D8.

Step 14

In box A7-C9, the missing 1 can only go in cell B7 or B8. All of these cells are in row B. Therefore 1 can be eliminated from other cells in row B including B2, B3, B4. The remaining possibilities are marked with small numbers.

Step 15

In box A7-C9, the missing 2 can only go in cell B7 or B8. All of these cells are in row B. Therefore 2 can be eliminated from other cells in row B including B3, B4. The remaining possibilities are marked with small numbers.

Step 16

In box G1-I3, the missing 4 can only go in cell G3 or H3. All of these cells are in column 3. Therefore 4 can be eliminated from other cells in column 3 including A3, B3. The remaining possibilities are marked with small numbers.

Step 17

The number 4 is missing from row B and its only possible position is cell B2.

Step 18

The number 8 does not yet appear in column 2. Due to other 8s on the grid, the only place it can go is cell C2.

Step 19

Because of the number 8 just placed, the only position in row B for another 8 is cell B4.

Step 20

Because of the number 8 just placed, the only position in column 6 for another 8 is cell F6.

Step 21

The number 5 is missing from row B and its only possible position is cell B3.

Step 22

The number 5 is missing from box G1-I3 and its only possible position is cell I1.

Step 23

Because of the number 5 just placed, the only position in column 2 for another 5 is cell F2.

Step 24

The number 5 does not yet appear in column 7. Due to other 5s on the grid, the only place it can go is cell H7.

Step 25

The number 2 is missing from column 7 and its only possible position is cell B7.

Step 26

Because of the number 2 just placed, the only position in column 8 for another 2 is cell G8.

Step 27

Because of the number 2 just placed, the only position in row H for another 2 is cell H6.

Step 28

B8 is the last empty cell in box A7-C9 and the missing number is 1.

Step 29

I7 is the last empty cell in column 7 and the missing number is 1.

Step 30

Because of the number 1 just placed, the only position in column 9 for another 1 is cell D9.

Step 31

E8 is the last empty cell in box D7-F9 and the missing number is 7.

Step 32

Because of the number 7 just placed, the only position in column 9 for another 7 is cell I9.

Step 33

H9 is the last empty cell in box G7-I9 and the missing number is 4.

Step 34

E2 is the last empty cell in row E and the missing number is 1.

Step 35

H3 is the last empty cell in row H and the missing number is 1.

Step 36

Because of the number 1 just placed, the only position in column 1 for another 1 is cell A1.

Step 37

G3 is the last empty cell in box G1-I3 and the missing number is 4.

Step 38

F1 is the last empty cell in column 1 and the missing number is 2.

Step 39

Because of the number 2 just placed, the only position in column 3 for another 2 is cell A3.

Step 40

Because of the number 2 just placed, the only position in row C for another 2 is cell C4.

Step 41

Because of the number 2 just placed, the only position in row D for another 2 is cell D5.

Step 42

A2 is the last empty cell in box A1-C3 and the missing number is 7.

Step 43

F3 is the last empty cell in column 3 and the missing number is 7.

Step 44

C6 is the last empty cell in row C and the missing number is 1.

Step 45

The number 3 does not yet appear in row D. Due to other 3s on the grid, the only place it can go is cell D4.

Step 46

Because of the number 3 just placed, the only position in column 5 for another 3 is cell I5.

Step 47

D6 is the last empty cell in row D and the missing number is 7.

Step 48

Because of the number 7 just placed, the only position in column 4 for another 7 is cell G4.

Step 49

The number 1 does not yet appear in row G. Due to other 1s on the grid, the only place it can go is cell G5.

Step 50

Because of the number 1 just placed, the only position in column 4 for another 1 is cell F4.

Step 51

F5 is the last empty cell in box D4-F6 and the missing number is 9.

Step 52

G6 is the last empty cell in row G and the missing number is 5.

Step 53

Because of the number 5 just placed, the only position in column 4 for another 5 is cell A4.

Step 54

I4 is the last empty cell in column 4 and the missing number is 9.

Step 55

Because of the number 9 just placed, the only position in column 6 for another 9 is cell A6.

Step 56

A5 is the last empty cell in box A4-C6 and the missing number is 4.

Step 57

I6 is the last empty cell in column 6 and the missing number is 4. Congratulations - the puzzle is solved!