Interactive Sudoku Tutorial 2: Learn by Playing

Here is a hard Sudoku. We have solved this puzzle step-by-step by using various techniques.

To practice more, go to Download and find your favorite difficulty level.

Show me the Final Solution directly.

In block B8, the only cell where the digit “2” can be placed is (I6). Therefore, this cell (I6) must be 2.

In block B9, the only cell where the digit “6” can be placed is (H9). Therefore, this cell (H9) must be 6.

In block B2, the only cell where the digit “7” can be placed is (C6). Therefore, this cell (C6) must be 7.

In column 7, the only cell where the digit “7” can be placed is (E7). Therefore, this cell (E7) must be 7.

In block B2, the only cell where the digit “9” can be placed is (B5). Therefore, this cell (B5) must be 9.

In block B5, the only cell where the digit “9” can be placed is (D6). Therefore, this cell (D6) must be 9.

In block B6, the only cell where the digit “9” can be placed is (F9). Therefore, this cell (F9) must be 9.

In column 7, the only cell where the digit “2” can be placed is (G7). Therefore, this cell (G7) must be 2.

In row G, the only cell where the digit “5” can be placed is (G8). Therefore, this cell (G8) must be 5.

In block B3, the only cell where the digit “5” can be placed is (C7). Therefore, this cell (C7) must be 5.

In column 6, the only cell where the digit “5” can be placed is (H6). Therefore, this cell (H6) must be 5.

In block B2, the only cell where the digit “6” can be placed is (C5). Therefore, this cell (C5) must be 6.

In block B9, the only cell where the digit “9” can be placed is (I7). Therefore, this cell (I7) must be 9.

In block B7, the only cell where the digit “9” can be placed is (G1). Therefore, this cell (G1) must be 9.

In block B8, the only cell where the digit “1” can be placed is (H5). Therefore, this cell (H5) must be 1.

In column 6, the only cell where the digit “1” can be placed is (E6). Therefore, this cell (E6) must be 1.

The only possible candidate for cell (C4) is 4. All other 8 digits appear at least once in the related area (i.e., in the same row (R3), in the same column (4) or in the same block (B2)). Therefore, this cell (C4) must be 4.

In block B1, the two green cells (C2) and (C3) have the same two possibilities 3 and 8, so these two digits each will occupy one of those two green cells and cannot be possibilities for any other cells in the same block.

In column 8, candidate 1s are marked in red and they all fall in block B3. So, in block B3, the digit “1” must be one of those marked in red and cannot be a candidate for any other cells in the same block.

In column 3, candidate 4s are marked in red and they all fall in block B4. So, in block B4, the digit “4” must be one of those marked in red and cannot be a candidate for any other cells in the same block.

Cell (A5) has 2 possibilities “2” and “5”. In either case, digit “5” cannot be a candidate for cell (B2).
Case 1
Step A: Suppose (A5) is 2
Step B: (A2) cannot be 2
Step C: (B2) must be 2
Step D: (B2) cannot be 5

Case 2
Step a: Suppose (A5) is 5
Step b: (D5) cannot be 5
Step c: (D2) must be 5
Step d: (B2) cannot be 5

If cell (B2) is “7”, digit “4” will not be in any cells of row R6. Therefore, cell (B2) cannot be “7”.

Step A: Suppose (B2) is 7
Step B: (B2) cannot be 2, (B3) cannot be 7
Step C: (B4) must be 2, (F3) must be 7
Step D: (F4) cannot be 2, (F3) cannot be 4
Step E: (F8) must be 2
Step F: (F8) cannot be 4

The only candidate for cell (B2) is 2. Therefore, this cell must be 2. All other 2(s) in the orange area can be removed.

Case 1
Step A: Suppose (B3) is 6
Step B: (B3) cannot be 7
Step C: (F3) must be 7
Step D: (F3) cannot be 4
Step E: (F8) must be 4
Step F: (F8) cannot be 3

Case 2
Step a: Suppose (B3) is 7
Step b: (A1) cannot be 7, (A2) cannot be 7
Step c: (A9) must be 7
Step d: (A9) cannot be 3
Step e: (A8) must be 3
Step f: (F8) cannot be 3

Case 1
Step A: Suppose (C3) is 3
Step B: (G3) cannot be 3
Step C: (G3) must be 1
Step D: (I2) cannot be 1
Step E: (D2) must be 1
Step F: (D2) cannot be 3

Case 2
Step a: Suppose (C3) is 8
Step b: (C3) cannot be 3
Step c: (C2) must be 3
Step d: (D2) cannot be 3

Case 1
Step A: Suppose (A9) is 3
Step B: (D9) cannot be 3, (G9) cannot be 3
Step C: (G3) must be 3
Step D: (D3) cannot be 3
Step E: (D7) must be 3
Step F: (E8) cannot be 3

Case 2
Step a: Suppose (A9) is 7
Step b: (A9) cannot be 3
Step c: (A8) must be 3
Step d: (E8) cannot be 3

In block B6, candidate 3s are marked in red and they all fall in row R4. So, in row R4, the digit “3” must be one of those marked in red and cannot be a candidate for any other cells in the same row.

Case 1
Step A: Suppose (A8) is 1
Step B: (A8) cannot be 3
Step C: (H8) must be 3
Step D: (H7) cannot be 3
Step E: (H7) must be 8
Step F: (I9) cannot be 8

Case 2
Step a: Suppose (A8) is 3
Step b: (A8) cannot be 1
Step c: (B8) must be 1
Step d: (B8) cannot be 8
Step e: (B9) must be 8
Step f: (I9) cannot be 8

In row I, candidate 8s are marked in red and they all fall in block B7. So, in block B7, the digit “8” must be one of those marked in red and cannot be a candidate for any other cells in the same block.

If cell (A9) is “3”, digit “8” will not be in any cells of column C2. Therefore, cell (A9) cannot be “3”.

Step A: Suppose (A9) is 3
Step B: (A9) cannot be 7, (G9) cannot be 3
Step C: (B9) must be 7, (G3) must be 3
Step D: (B9) cannot be 8, (G3) cannot be 1, (C3) cannot be 3
Step E: (C2) must be 3, (I2) must be 1, (D9) must be 8
Step F: (C2) cannot be 8, (I2) cannot be 8, (D2) cannot be 8

The only candidate for cell (A9) is 7. Therefore, this cell must be 7. All other 7(s) in the orange area can be removed.

The only candidate for cell (B9) is 8. Therefore, this cell must be 8. All other 8(s) in the orange area can be removed.

The only candidate for cell (B8) is 1. Therefore, this cell must be 1. All other 1(s) in the orange area can be removed.

The only candidate for cell (A8) is 3. Therefore, this cell must be 3. All other 3(s) in the orange area can be removed.

The only candidate for cell (B4) is 5. Therefore, this cell must be 5. All other 5(s) in the orange area can be removed.

The only candidate for cell (A5) is 2. Therefore, this cell must be 2. All other 2(s) in the orange area can be removed.

The only candidate for cell (A4) is 1. Therefore, this cell must be 1.

The only candidate for cell (E5) is 4. Therefore, this cell must be 4. All other 4(s) in the orange area can be removed.

The only candidate for cell (D5) is 5. Therefore, this cell must be 5. All other 5(s) in the orange area can be removed.

Case 1
Step A: Suppose (D2) is 1
Step B: (D3) cannot be 1
Step C: (G3) must be 1
Step D: (G3) cannot be 3
Step E: (G9) must be 3
Step F: (D9) cannot be 3, (H7) cannot be 3

Case 2
Step a: Suppose (D2) is 8
Step b: (D7) cannot be 8
Step c: (D7) must be 3
Step d: (D9) cannot be 3, (H7) cannot be 3

The only candidate for cell (D9) is 4. Therefore, this cell must be 4. All other 4(s) in the orange area can be removed.

The only candidate for cell (F8) is 2. Therefore, this cell must be 2. All other 2(s) in the orange area can be removed.

The only candidate for cell (E8) is 8. Therefore, this cell must be 8. All other 8(s) in the orange area can be removed.

The only candidate for cell (D7) is 3. Therefore, this cell must be 3.

The only candidate for cell (F4) is 3. Therefore, this cell must be 3. All other 3(s) in the orange area can be removed.

The only candidate for cell (E4) is 2. Therefore, this cell must be 2.

The only candidate for cell (H7) is 8. Therefore, this cell must be 8.

The only candidate for cell (H8) is 4. Therefore, this cell must be 4. All other 4(s) in the orange area can be removed.

The only candidate for cell (I9) is 1. Therefore, this cell must be 1. All other 1(s) in the orange area can be removed.

The only candidate for cell (G9) is 3. Therefore, this cell must be 3. All other 3(s) in the orange area can be removed.

The only candidate for cell (G3) is 1. Therefore, this cell must be 1. All other 1(s) in the orange area can be removed.

The only candidate for cell (D3) is 8. Therefore, this cell must be 8. All other 8(s) in the orange area can be removed.

The only candidate for cell (C3) is 3. Therefore, this cell must be 3. All other 3(s) in the orange area can be removed.

The only candidate for cell (C2) is 8. Therefore, this cell must be 8. All other 8(s) in the orange area can be removed.

The only candidate for cell (D2) is 1. Therefore, this cell must be 1.

The only candidate for cell (E3) is 6. Therefore, this cell must be 6. All other 6(s) in the orange area can be removed.

The only candidate for cell (B3) is 7. Therefore, this cell must be 7. All other 7(s) in the orange area can be removed.

The only candidate for cell (B1) is 6. Therefore, this cell must be 6.

The only candidate for cell (E1) is 3. Therefore, this cell must be 3. All other 3(s) in the orange area can be removed.

The only candidate for cell (F3) is 4. Therefore, this cell must be 4.

The only candidate for cell (H1) is 7. Therefore, this cell must be 7. All other 7(s) in the orange area can be removed.

The only candidate for cell (F1) is 5. Therefore, this cell must be 5. All other 5(s) in the orange area can be removed.

The only candidate for cell (A1) is 4. Therefore, this cell must be 4. All other 4(s) in the orange area can be removed.

The only candidate for cell (A2) is 5. Therefore, this cell must be 5.

The only candidate for cell (F2) is 7. Therefore, this cell must be 7.

The only candidate for cell (H2) is 3. Therefore, this cell must be 3.

The only candidate for cell (I1) is 8. Therefore, this cell must be 8.

The only candidate for cell (I2) is 4. Therefore, this cell must be 4.

Final Solution