Classic Sudoku, solved step by step — with the logic explained

Here is a complete walkthrough of a classic 30-clue Sudoku. It takes 51 logical moves, and every single one is forced — solvable with just two beginner techniques, hidden singles and naked singles. No guessing, ever.

The puzzle & the solution

Givens are shown in black; every blue digit is one we deduce below.

Reading the coordinates

Each step names a cell as R(row)C(column) — counted from the top-left. For example R1C6 means row 1, column 6.

The 51 steps

Follow them in order. Each step fills one cell and explains exactly why that digit is forced.

1. R1C6 = 8 Hidden single
   Look across its 3×3 box: 8 can only fit in R1C6. Even though that cell could take other digits on its own, 8 has nowhere else to go in its 3×3 box.
2. R1C4 = 6 Hidden single
   Look across its 3×3 box: 6 can only fit in R1C4. Even though that cell could take other digits on its own, 6 has nowhere else to go in its 3×3 box.
3. R3C7 = 5 Hidden single
   Look across its 3×3 box: 5 can only fit in R3C7. Even though that cell could take other digits on its own, 5 has nowhere else to go in its 3×3 box.
4. R6C3 = 3 Hidden single
   Look across its 3×3 box: 3 can only fit in R6C3. Even though that cell could take other digits on its own, 3 has nowhere else to go in its 3×3 box.
5. R5C3 = 6 Hidden single
   Look across its 3×3 box: 6 can only fit in R5C3. Even though that cell could take other digits on its own, 6 has nowhere else to go in its 3×3 box.
6. R4C3 = 9 Hidden single
   Look across its 3×3 box: 9 can only fit in R4C3. Even though that cell could take other digits on its own, 9 has nowhere else to go in its 3×3 box.
7. R6C4 = 9 Hidden single
   Look across its 3×3 box: 9 can only fit in R6C4. Even though that cell could take other digits on its own, 9 has nowhere else to go in its 3×3 box.
8. R6C7 = 8 Hidden single
   Look across its 3×3 box: 8 can only fit in R6C7. Even though that cell could take other digits on its own, 8 has nowhere else to go in its 3×3 box.
9. R2C9 = 8 Hidden single
   Look across its 3×3 box: 8 can only fit in R2C9. Even though that cell could take other digits on its own, 8 has nowhere else to go in its 3×3 box.
10. R8C2 = 8 Hidden single
    Look across its 3×3 box: 8 can only fit in R8C2. Even though that cell could take other digits on its own, 8 has nowhere else to go in its 3×3 box.
11. R7C1 = 9 Hidden single
    Look across its 3×3 box: 9 can only fit in R7C1. Even though that cell could take other digits on its own, 9 has nowhere else to go in its 3×3 box.
12. R9C6 = 6 Hidden single
    Look across its 3×3 box: 6 can only fit in R9C6. Even though that cell could take other digits on its own, 6 has nowhere else to go in its 3×3 box.
13. R9C4 = 2 Hidden single
    Look across its 3×3 box: 2 can only fit in R9C4. Even though that cell could take other digits on its own, 2 has nowhere else to go in its 3×3 box.
14. R3C6 = 2 Hidden single
    Look across its 3×3 box: 2 can only fit in R3C6. Even though that cell could take other digits on its own, 2 has nowhere else to go in its 3×3 box.
15. R3C5 = 4 Hidden single
    Look across its 3×3 box: 4 can only fit in R3C5. Even though that cell could take other digits on its own, 4 has nowhere else to go in its 3×3 box.
16. R9C7 = 1 Hidden single
    Look across its 3×3 box: 1 can only fit in R9C7. Even though that cell could take other digits on its own, 1 has nowhere else to go in its 3×3 box.
17. R1C8 = 1 Hidden single
    Look across its 3×3 box: 1 can only fit in R1C8. Even though that cell could take other digits on its own, 1 has nowhere else to go in its 3×3 box.
18. R1C7 = 9 Hidden single
    Look across its 3×3 box: 9 can only fit in R1C7. Even though that cell could take other digits on its own, 9 has nowhere else to go in its 3×3 box.
19. R5C8 = 9 Hidden single
    Look across its 3×3 box: 9 can only fit in R5C8. Even though that cell could take other digits on its own, 9 has nowhere else to go in its 3×3 box.
20. R4C8 = 2 Hidden single
    Look across its 3×3 box: 2 can only fit in R4C8. Even though that cell could take other digits on its own, 2 has nowhere else to go in its 3×3 box.
21. R1C9 = 2 Hidden single
    Look across its 3×3 box: 2 can only fit in R1C9. Even though that cell could take other digits on its own, 2 has nowhere else to go in its 3×3 box.
22. R5C2 = 2 Hidden single
    Look across its 3×3 box: 2 can only fit in R5C2. Even though that cell could take other digits on its own, 2 has nowhere else to go in its 3×3 box.
23. R2C3 = 2 Hidden single
    Look across its 3×3 box: 2 can only fit in R2C3. Even though that cell could take other digits on its own, 2 has nowhere else to go in its 3×3 box.
24. R2C2 = 7 Hidden single
    Look across its 3×3 box: 7 can only fit in R2C2. Even though that cell could take other digits on its own, 7 has nowhere else to go in its 3×3 box.
25. R6C8 = 5 Hidden single
    Look across its 3×3 box: 5 can only fit in R6C8. Even though that cell could take other digits on its own, 5 has nowhere else to go in its 3×3 box.
26. R4C2 = 5 Hidden single
    Look across its 3×3 box: 5 can only fit in R4C2. Even though that cell could take other digits on its own, 5 has nowhere else to go in its 3×3 box.
27. R4C7 = 4 Hidden single
    Look across its 3×3 box: 4 can only fit in R4C7. Even though that cell could take other digits on its own, 4 has nowhere else to go in its 3×3 box.
28. R2C8 = 4 Hidden single
    Look across its 3×3 box: 4 can only fit in R2C8. Even though that cell could take other digits on its own, 4 has nowhere else to go in its 3×3 box.
29. R6C6 = 4 Hidden single
    Look across its 3×3 box: 4 can only fit in R6C6. Even though that cell could take other digits on its own, 4 has nowhere else to go in its 3×3 box.
30. R4C6 = 1 Hidden single
    Look across its 3×3 box: 1 can only fit in R4C6. Even though that cell could take other digits on its own, 1 has nowhere else to go in its 3×3 box.
31. R7C3 = 1 Hidden single
    Look across its 3×3 box: 1 can only fit in R7C3. Even though that cell could take other digits on its own, 1 has nowhere else to go in its 3×3 box.
32. R8C1 = 2 Hidden single
    Look across its 3×3 box: 2 can only fit in R8C1. Even though that cell could take other digits on its own, 2 has nowhere else to go in its 3×3 box.
33. R9C3 = 5 Hidden single
    Look across its 3×3 box: 5 can only fit in R9C3. Even though that cell could take other digits on its own, 5 has nowhere else to go in its 3×3 box.
34. R8C7 = 6 Hidden single
    Look across its 3×3 box: 6 can only fit in R8C7. Even though that cell could take other digits on its own, 6 has nowhere else to go in its 3×3 box.
35. R7C4 = 5 Hidden single
    Look across column 4: 5 can only fit in R7C4. Even though that cell could take other digits on its own, 5 has nowhere else to go in column 4.
36. R1C3 = 4 Naked single
    R1C3 has just one candidate left — 4. Its row, column and box already contain the other eight digits.
37. R2C7 = 3 Naked single
    R2C7 has just one candidate left — 3. Its row, column and box already contain the other eight digits.
38. R3C1 = 1 Naked single
    R3C1 has just one candidate left — 1. Its row, column and box already contain the other eight digits.
39. R3C4 = 3 Naked single
    R3C4 has just one candidate left — 3. Its row, column and box already contain the other eight digits.
40. R3C9 = 7 Naked single
    R3C9 has just one candidate left — 7. Its row, column and box already contain the other eight digits.
41. R4C4 = 7 Naked single
    R4C4 has just one candidate left — 7. Its row, column and box already contain the other eight digits.
42. R5C5 = 5 Naked single
    R5C5 has just one candidate left — 5. Its row, column and box already contain the other eight digits.
43. R5C7 = 7 Naked single
    R5C7 has just one candidate left — 7. Its row, column and box already contain the other eight digits.
44. R6C2 = 1 Naked single
    R6C2 has just one candidate left — 1. Its row, column and box already contain the other eight digits.
45. R7C5 = 3 Naked single
    R7C5 has just one candidate left — 3. Its row, column and box already contain the other eight digits.
46. R7C6 = 7 Naked single
    R7C6 has just one candidate left — 7. Its row, column and box already contain the other eight digits.
47. R7C9 = 4 Naked single
    R7C9 has just one candidate left — 4. Its row, column and box already contain the other eight digits.
48. R8C3 = 7 Naked single
    R8C3 has just one candidate left — 7. Its row, column and box already contain the other eight digits.
49. R8C8 = 3 Naked single
    R8C8 has just one candidate left — 3. Its row, column and box already contain the other eight digits.
50. R9C1 = 3 Naked single
    R9C1 has just one candidate left — 3. Its row, column and box already contain the other eight digits.
51. R9C2 = 4 Naked single
    R9C2 has just one candidate left — 4. Its row, column and box already contain the other eight digits.

The two techniques used

FAQ