Hard Star Battle answer — February 3, 2025

Full written solution

Every deduction from the walkthrough above, in order. Each technique is explained in the Star Battle strategy guide.

1. Starting position — the grid is split into regions (bold outlines). Each row, column, and region needs exactly two stars, and no two stars may touch.
2. Blocking rule: a star here would touch every other open cell in its region, leaving no room for the region's second star (row 3, column 8).
3. Blocking rule: a star here would touch every other open cell in its region, leaving no room for the region's second star (row 6, column 8).
4. Blocking rule: a star here would touch every other open cell in its region, leaving no room for the region's second star (row 6, column 9).
5. Three candidates with two adjacent: Isolated candidate must hold a star (row 7, column 9).
6. Mark 3 cells adjacent to stars as X (row 7, column 8).
7. Two-option rule: Cell adjacent to both candidates (row 4, column 8).
8. Two-option rule: Cell adjacent to both candidates (row 4, column 9).
9. Three candidates with two adjacent: Isolated candidate must hold a star (row 3, column 7).
10. Mark 6 cells adjacent to stars as X (row 2, column 6).
11. Blocking rule: a star here would touch every other open cell in its region, leaving no room for the region's second star (row 6, column 6).
12. Clump analysis (Row 4): candidate clumps can only just supply the remaining stars (row 3, column 2).
13. Clump analysis (Region 3): candidate clumps can only just supply the remaining stars (row 1, column 9).
14. Region completion: 1 star needed, 1 candidate (row 5, column 8).
15. Mark 2 cells adjacent to stars as X (row 5, column 7).
16. Three candidates with two adjacent: Isolated candidate must hold a star (row 1, column 8).
17. Mark 2 cells adjacent to stars as X (row 1, column 7).
18. Region completion: 1 star needed, 1 candidate (row 3, column 9).
19. Region completion: 1 star needed, 1 candidate (row 1, column 6).
20. Mark 2 cells adjacent to stars as X (row 1, column 5).
21. Row 1 complete: Mark 4 remaining cells as X (row 1, column 1).
22. Row 3 complete: Mark 3 remaining cells as X (row 3, column 1).
23. Column 8 complete: Mark 1 remaining cell as X (row 9, column 8).
24. Blocking rule: a star here would touch every other open cell in its region, leaving no room for the region's second star (row 8, column 6).
25. Blocking rule: a star here would touch every other open cell in its region, leaving no room for the region's second star (row 9, column 6).
26. Three candidates with two adjacent: Isolated candidate must hold a star (row 9, column 5).
27. Mark 3 cells adjacent to stars as X (row 8, column 4).
28. Two last candidates (column 6): Eliminate 1 cell adjacent to both (row 6, column 5).
29. Clump analysis (Row 2): candidate clumps can only just supply the remaining stars (row 4, column 1).
30. Clump analysis (Row 4): candidate clumps can only just supply the remaining stars (row 5, column 5).
31. Clump analysis (Row 4): each clump must supply its full share of stars (row 4, column 2).
32. Mark 2 cells adjacent to stars as X (row 5, column 1).
33. Row completion: 1 star needed, 1 candidate (row 5, column 6).
34. Mark 1 cell adjacent to stars as X (row 4, column 5).
35. Row completion: 1 star needed, 1 candidate (row 4, column 4).
36. Column completion: 1 star needed, 1 candidate (row 7, column 5).
37. Mark 3 cells adjacent to stars as X (row 6, column 4).
38. Region complete: Mark 1 remaining cell as X (row 7, column 7).
39. Region completion: 1 star needed, 1 candidate (row 6, column 3).
40. Mark 3 cells adjacent to stars as X (row 6, column 2).
41. Row completion: 1 star needed, 1 candidate (row 6, column 1).
42. Mark 1 cell adjacent to stars as X (row 7, column 1).
43. Region complete: Mark 2 remaining cells as X (row 8, column 1).
44. Row completion: 2 stars needed, 2 candidates (row 8, column 3).
45. Mark 2 cells adjacent to stars as X (row 9, column 2).
46. Region completion: 1 star needed, 1 candidate (row 9, column 1).
47. Row completion: 1 star needed, 1 candidate (row 8, column 7).
48. Mark 1 cell adjacent to stars as X (row 9, column 7).
49. Column 1 complete: Mark 1 remaining cell as X (row 2, column 1).
50. Column completion: 1 star needed, 1 candidate (row 2, column 2).
51. Mark 1 cell adjacent to stars as X (row 2, column 3).
52. Region completion: 1 star needed, 1 candidate (row 2, column 4).
53. Solved! Every row, column, and region has its two stars, none touching.