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Daily Sudoku — 25 July 2026

The puzzle

  • 25 July 2026
  • Hard
  • 30 clues
Puzzle
587·····9
·1···56·4
4···1·7·5
·········
3695····8
··5478·6·
········2
·5····19·
6··8···47
Solution
587634219
912785634
436219785
874963521
369521478
125478963
743196852
258347196
691852347

Solve it in the app to get on the board

Step-by-step solution

Every cell below is filled by the same hint engine the app uses, in the order it can be deduced — 51 steps using 2 techniques.

Techniques used

  • Hidden Single — inside one row, column or box this digit fits in only one cell, so it must go there
  • Naked Single — every other digit is already used in this cell's row, column or box, so only one candidate is left
  1. R3C3 = 6 · Hidden SingleIn the top-left 3×3 box, 6 fits in only one cell. Looking at the other empty cells:- Because row 2 already has a 6, R2C1 and R2C3 cannot hold 6.- Because column 2 already has a 6, R3C2 cannot hold 6.So 6 must go in R3C3.
  2. R2C4 = 7 · Hidden SingleIn the top-centre 3×3 box, 7 fits in only one cell. Looking at the other empty cells:- Because row 1 already has a 7, R1C4, R1C5 and R1C6 cannot hold 7.- Because column 5 already has a 7, R2C5 cannot hold 7.- Because row 3 already has a 7, R3C4 and R3C6 cannot hold 7.So 7 must go in R2C4.
  3. R2C5 = 8 · Hidden SingleIn the top-centre 3×3 box, 8 fits in only one cell. Looking at the other empty cells:- Because row 1 already has a 8, R1C4, R1C5 and R1C6 cannot hold 8.- Because column 4 already has a 8, R3C4 cannot hold 8.- Because column 6 already has a 8, R3C6 cannot hold 8.So 8 must go in R2C5.
  4. R1C8 = 1 · Hidden SingleIn the top-right 3×3 box, 1 fits in only one cell. Looking at the other empty cells:- Because column 7 already has a 1, R1C7 cannot hold 1.- Because row 2 already has a 1, R2C8 cannot hold 1.- Because row 3 already has a 1, R3C8 cannot hold 1.So 1 must go in R1C8.
  5. R3C8 = 8 · Hidden SingleIn the top-right 3×3 box, 8 fits in only one cell. Looking at the other empty cells:- Because row 1 already has a 8, R1C7 cannot hold 8.- Because row 2 already has a 8, R2C8 cannot hold 8.So 8 must go in R3C8.
  6. R8C9 = 6 · Hidden SingleIn the bottom-right 3×3 box, 6 fits in only one cell. Looking at the other empty cells:- Because column 7 already has a 6, R7C7 cannot hold 6.- Because column 8 already has a 6, R7C8 cannot hold 6.- Because row 9 already has a 6, R9C7 cannot hold 6.So 6 must go in R8C9.
  7. R7C7 = 8 · Hidden SingleIn the bottom-right 3×3 box, 8 fits in only one cell. Looking at the other empty cells:- Because column 8 already has a 8, R7C8 cannot hold 8.- Because row 9 already has a 8, R9C7 cannot hold 8.So 8 must go in R7C7.
  8. R2C1 = 9 · Hidden SingleIn row 2, 9 fits in only one cell. Looking at the other empty cells:- Because column 3 already has a 9, R2C3 cannot hold 9.- Because column 8 already has a 9, R2C8 cannot hold 9.So 9 must go in R2C1.
  9. R5C6 = 1 · Hidden SingleIn row 5, 1 fits in only one cell. Looking at the other empty cells:- Because column 5 already has a 1, R5C5 cannot hold 1.- Because column 7 already has a 1, R5C7 cannot hold 1.- Because column 8 already has a 1, R5C8 cannot hold 1.So 1 must go in R5C6.
  10. R7C4 = 1 · Hidden SingleIn the bottom-centre 3×3 box, 1 fits in only one cell. Looking at the other empty cells:- Because column 5 already has a 1, R7C5 and R9C5 cannot hold 1.- Because column 6 already has a 1, R7C6 and R9C6 cannot hold 1.- Because row 8 already has a 1, R8C4, R8C5 and R8C6 cannot hold 1.So 1 must go in R7C4.
  11. R9C3 = 1 · Hidden SingleIn the bottom-left 3×3 box, 1 fits in only one cell. Looking at the other empty cells:- Because row 7 already has a 1, R7C1, R7C2 and R7C3 cannot hold 1.- Because row 8 already has a 1, R8C1 and R8C3 cannot hold 1.- Because column 2 already has a 1, R9C2 cannot hold 1.So 1 must go in R9C3.
  12. R5C7 = 4 · Hidden SingleIn row 5, 4 fits in only one cell. Looking at the other empty cells:- Because the centre 3×3 box already has a 4, R5C5 cannot hold 4.- Because column 8 already has a 4, R5C8 cannot hold 4.So 4 must go in R5C7.
  13. R5C8 = 7 · Hidden SingleIn row 5, 7 fits in only one cell. Looking at the other empty cells:- Because column 5 already has a 7, R5C5 cannot hold 7.So 7 must go in R5C8.
  14. R5C5 = 2 · Naked SingleLooking at R5C5:- Row 5 already has 1, 3, 4, 5, 6, 7, 8 and 9 → ruled out.So this cell can only be 2.
  15. R6C7 = 9 · Hidden SingleIn row 6, 9 fits in only one cell. Looking at the other empty cells:- Because column 1 already has a 9, R6C1 cannot hold 9.- Because the middle-left 3×3 box already has a 9, R6C2 cannot hold 9.- Because column 9 already has a 9, R6C9 cannot hold 9.So 9 must go in R6C7.
  16. R6C9 = 3 · Hidden SingleIn row 6, 3 fits in only one cell. Looking at the other empty cells:- Because column 1 already has a 3, R6C1 cannot hold 3.- Because the middle-left 3×3 box already has a 3, R6C2 cannot hold 3.So 3 must go in R6C9.
  17. R4C9 = 1 · Naked SingleLooking at R4C9:- Column 9 already has 2, 3, 4, 5, 6, 7, 8 and 9 → ruled out.So this cell can only be 1.
  18. R6C1 = 1 · Hidden SingleIn the middle-left 3×3 box, 1 fits in only one cell. Looking at the other empty cells:- Because row 4 already has a 1, R4C1, R4C2 and R4C3 cannot hold 1.- Because column 2 already has a 1, R6C2 cannot hold 1.So 1 must go in R6C1.
  19. R6C2 = 2 · Naked SingleLooking at R6C2:- Row 6 already has 1, 3, 4, 5, 6, 7, 8 and 9 → ruled out.So this cell can only be 2.
  20. R2C3 = 2 · Hidden SingleIn the top-left 3×3 box, 2 fits in only one cell. Looking at the other empty cells:- Because column 2 already has a 2, R3C2 cannot hold 2.So 2 must go in R2C3.
  21. R2C8 = 3 · Naked SingleLooking at R2C8:- Row 2 already has 1, 2, 4, 5, 6, 7, 8 and 9 → ruled out.So this cell can only be 3.
  22. R3C2 = 3 · Naked SingleLooking at R3C2:- Row 3 already has 1, 4, 5, 6, 7 and 8 → ruled out.- Column 2 already has 2 → ruled out.- The top-left 3×3 box already has 9 → ruled out.So this cell can only be 3.
  23. R1C7 = 2 · Naked SingleLooking at R1C7:- Row 1 already has 1, 5, 7, 8 and 9 → ruled out.- Column 7 already has 4 and 6 → ruled out.- The top-right 3×3 box already has 3 → ruled out.So this cell can only be 2.
  24. R4C8 = 2 · Hidden SingleIn the middle-right 3×3 box, 2 fits in only one cell. Looking at the other empty cells:- Because column 7 already has a 2, R4C7 cannot hold 2.So 2 must go in R4C8.
  25. R7C8 = 5 · Naked SingleLooking at R7C8:- Row 7 already has 1, 2 and 8 → ruled out.- Column 8 already has 3, 4, 6, 7 and 9 → ruled out.So this cell can only be 5.
  26. R4C7 = 5 · Naked SingleLooking at R4C7:- Row 4 already has 1 and 2 → ruled out.- Column 7 already has 4, 6, 7, 8 and 9 → ruled out.- The middle-right 3×3 box already has 3 → ruled out.So this cell can only be 5.
  27. R9C7 = 3 · Naked SingleLooking at R9C7:- Row 9 already has 1, 4, 6, 7 and 8 → ruled out.- Column 7 already has 2, 5 and 9 → ruled out.So this cell can only be 3.
  28. R8C1 = 2 · Hidden SingleIn the bottom-left 3×3 box, 2 fits in only one cell. Looking at the other empty cells:- Because row 7 already has a 2, R7C1, R7C2 and R7C3 cannot hold 2.- Because column 3 already has a 2, R8C3 cannot hold 2.- Because column 2 already has a 2, R9C2 cannot hold 2.So 2 must go in R8C1.
  29. R8C3 = 8 · Hidden SingleIn the bottom-left 3×3 box, 8 fits in only one cell. Looking at the other empty cells:- Because row 7 already has a 8, R7C1, R7C2 and R7C3 cannot hold 8.- Because row 9 already has a 8, R9C2 cannot hold 8.So 8 must go in R8C3.
  30. R4C1 = 8 · Hidden SingleIn the middle-left 3×3 box, 8 fits in only one cell. Looking at the other empty cells:- Because column 2 already has a 8, R4C2 cannot hold 8.- Because column 3 already has a 8, R4C3 cannot hold 8.So 8 must go in R4C1.
  31. R7C1 = 7 · Naked SingleLooking at R7C1:- Row 7 already has 1, 2, 5 and 8 → ruled out.- Column 1 already has 3, 4, 6 and 9 → ruled out.So this cell can only be 7.
  32. R4C2 = 7 · Hidden SingleIn the middle-left 3×3 box, 7 fits in only one cell. Looking at the other empty cells:- Because column 3 already has a 7, R4C3 cannot hold 7.So 7 must go in R4C2.
  33. R4C3 = 4 · Naked SingleLooking at R4C3:- Row 4 already has 1, 2, 5, 7 and 8 → ruled out.- Column 3 already has 6 and 9 → ruled out.- The middle-left 3×3 box already has 3 → ruled out.So this cell can only be 4.
  34. R7C3 = 3 · Naked SingleLooking at R7C3:- Row 7 already has 1, 2, 5, 7 and 8 → ruled out.- Column 3 already has 4, 6 and 9 → ruled out.So this cell can only be 3.
  35. R7C2 = 4 · Hidden SingleIn the bottom-left 3×3 box, 4 fits in only one cell. Looking at the other empty cells:- Because row 9 already has a 4, R9C2 cannot hold 4.So 4 must go in R7C2.
  36. R9C2 = 9 · Naked SingleLooking at R9C2:- Row 9 already has 1, 3, 4, 6, 7 and 8 → ruled out.- Column 2 already has 2 and 5 → ruled out.So this cell can only be 9.
  37. R9C6 = 2 · Hidden SingleIn the bottom-centre 3×3 box, 2 fits in only one cell. Looking at the other empty cells:- Because row 7 already has a 2, R7C5 and R7C6 cannot hold 2.- Because row 8 already has a 2, R8C4, R8C5 and R8C6 cannot hold 2.- Because column 5 already has a 2, R9C5 cannot hold 2.So 2 must go in R9C6.
  38. R9C5 = 5 · Naked SingleLooking at R9C5:- Row 9 already has 1, 2, 3, 4, 6, 7, 8 and 9 → ruled out.So this cell can only be 5.
  39. R3C4 = 2 · Hidden SingleIn the top-centre 3×3 box, 2 fits in only one cell. Looking at the other empty cells:- Because row 1 already has a 2, R1C4, R1C5 and R1C6 cannot hold 2.- Because column 6 already has a 2, R3C6 cannot hold 2.So 2 must go in R3C4.
  40. R3C6 = 9 · Naked SingleLooking at R3C6:- Row 3 already has 1, 2, 3, 4, 5, 6, 7 and 8 → ruled out.So this cell can only be 9.
  41. R8C6 = 7 · Hidden SingleIn the bottom-centre 3×3 box, 7 fits in only one cell. Looking at the other empty cells:- Because row 7 already has a 7, R7C5 and R7C6 cannot hold 7.- Because column 4 already has a 7, R8C4 cannot hold 7.- Because column 5 already has a 7, R8C5 cannot hold 7.So 7 must go in R8C6.
  42. R8C5 = 4 · Hidden SingleIn the bottom-centre 3×3 box, 4 fits in only one cell. Looking at the other empty cells:- Because row 7 already has a 4, R7C5 and R7C6 cannot hold 4.- Because column 4 already has a 4, R8C4 cannot hold 4.So 4 must go in R8C5.
  43. R8C4 = 3 · Naked SingleLooking at R8C4:- Row 8 already has 1, 2, 4, 5, 6, 7, 8 and 9 → ruled out.So this cell can only be 3.
  44. R1C6 = 4 · Hidden SingleIn the top-centre 3×3 box, 4 fits in only one cell. Looking at the other empty cells:- Because column 4 already has a 4, R1C4 cannot hold 4.- Because column 5 already has a 4, R1C5 cannot hold 4.So 4 must go in R1C6.
  45. R1C5 = 3 · Hidden SingleIn the top-centre 3×3 box, 3 fits in only one cell. Looking at the other empty cells:- Because column 4 already has a 3, R1C4 cannot hold 3.So 3 must go in R1C5.
  46. R1C4 = 6 · Naked SingleLooking at R1C4:- Row 1 already has 1, 2, 3, 4, 5, 7, 8 and 9 → ruled out.So this cell can only be 6.
  47. R4C4 = 9 · Naked SingleLooking at R4C4:- Row 4 already has 1, 2, 4, 5, 7 and 8 → ruled out.- Column 4 already has 3 and 6 → ruled out.So this cell can only be 9.
  48. R4C6 = 3 · Hidden SingleIn the centre 3×3 box, 3 fits in only one cell. Looking at the other empty cells:- Because column 5 already has a 3, R4C5 cannot hold 3.So 3 must go in R4C6.
  49. R4C5 = 6 · Naked SingleLooking at R4C5:- Row 4 already has 1, 2, 3, 4, 5, 7, 8 and 9 → ruled out.So this cell can only be 6.
  50. R7C5 = 9 · Naked SingleLooking at R7C5:- Row 7 already has 1, 2, 3, 4, 5, 7 and 8 → ruled out.- Column 5 already has 6 → ruled out.So this cell can only be 9.
  51. R7C6 = 6 · Naked SingleLooking at R7C6:- Row 7 already has 1, 2, 3, 4, 5, 7, 8 and 9 → ruled out.So this cell can only be 6.

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